diff --git a/index.html b/index.html index 8a2f210..2629674 100644 --- a/index.html +++ b/index.html @@ -38,16 +38,18 @@

- Johnson Solids made with vZome -

-

- Select a row in the table to view that Johnson solid.
- Check the box in the viewer to show struts and balls for - Zometool constructible solids listed in italics. -

-

- Use your mouse to manipulate the 3D view: left button to rotate, right button to pan, and scroll gesture to zoom. -

+ Johnson Solids Explorer + +
+

+ Select a row in the table to view that Johnson solid.
+ For Zometool-constructible solids highlighted in blue, + check the box in the viewer to show struts and balls. +

+

+ Use your mouse to manipulate the 3D view: left button to rotate, right button to pan, and scroll gesture to zoom. +

+
@@ -66,26 +68,28 @@

+ -
Show Zometool
-
-
-

- References -

-

+

+

+ References +

+ -

+
diff --git a/johnson-solids-listing.js b/johnson-solids-listing.js index bd13124..6ed7e59 100644 --- a/johnson-solids-listing.js +++ b/johnson-solids-listing.js @@ -7,6 +7,7 @@ const viewer = document.getElementById( "viewer" ); const showEdges = document.getElementById( "showEdges" ); const zomeSwitch = document.getElementById( "zome-switch" ); const downloadLink = document.getElementById( "download" ); +const sigfig = 1000000000; // significant digits for rounding const shapeColors = new Map(); shapeColors.set( 3, "#F0A000"); // yellow strut @@ -16,11 +17,13 @@ shapeColors.set( 6, "#008D36"); // green strut shapeColors.set( 8, "#DC4C00"); // orange strut shapeColors.set(10, "#6C00C6"); // purple strut -// include a "download=true" query param in the URL to make the ID in the viewer become the recolor download link +// include a "download=true" query param in the URL to make the ID in the viewer become the .shapes.json download link if(new URL(document.location).searchParams.get("download") == "true") { document.getElementById( "index" ).addEventListener( "click", downloadShapesJson ); } +// https://medium.com/charisol-community/downloading-resources-in-html5-a-download-may-not-work-as-expected-bf63546e2baa +// This method works with local files as well as cross origin files. function downloadShapesJson() { const url = viewer.src.replace( ".vZome", ".shapes.json" ); const filename = url.substring(url.lastIndexOf( "/" ) + 1); @@ -36,7 +39,7 @@ function downloadShapesJson() { return response.json(); } ) .then(modelData => { - var stringifiedData = JSON.stringify( recolor(modelData), null, 2); + const stringifiedData = JSON.stringify(postProcess(modelData), null, 2); const blobUrl = URL.createObjectURL(new Blob([stringifiedData], { type: "application/json" })); downloadLink.href = blobUrl; downloadLink.click(); @@ -49,36 +52,191 @@ function downloadShapesJson() { }); } -function recolor(modelData) { - const faceMap = new Map(); +function postProcess(modelData) { + recolor(modelData); + rescale(modelData); + standardizeCameras(modelData); + return modelData; +} + +function standardizeCameras(modelData) { + // Adjust all camera vector settings to the same values + // and zoom levels so that any model that's the first one loaded will be zoomed to fit + // and others will use the same initial zoom level. + // Any model could be the one that sets the default camera if the "J=" queryparam is used. + const distance = getDistanceScaledToFitView(modelData); + standardizeCamera(modelData.camera, distance); + for(let scene of modelData.scenes) { + // scene views are not used by the Johnson solids app, but we'll standardize their cameras too since we're here + standardizeCamera(scene.view, distance); + } + return modelData; +} + +function cameraFieldOfViewY ( width, distance ) { + const halfX = width / 2; + const halfY = halfX; // assumes aspectWtoH = 1.0; + return 360 * Math.atan( halfY / distance ) / Math.PI; +} + +function getDistanceScaledToFitView(modelData) { + const snapshots = getFaceSceneSnapshots(modelData); + const shapeMap = new Map(); for(const shape of modelData.shapes) { - faceMap.set(shape.id, shape.vertices.length); + shapeMap.set(shape.id, shape); } - // Get a list of facescene(s) of all models that use the selected jsolid's URL. - // There may be only one facescene, but there may be more than one. e.g. J38 & J39 - const url = viewer.src; - const facescenes = []; - for(const model of models) { - if(model.url == url) { - facescenes.push(model.facescene); + const origin = {x:0, y:0, z:0}; + var maxRadius = 0; + for(const snapshot of snapshots) { + const ss = modelData.snapshots[snapshot]; + for(let i = 0; i < ss.length; i++) { + const item = ss[i]; + const shapeGuid = item.shape; + const vertices = shapeMap.get(shapeGuid).vertices; + for(const vertex of vertices) { + maxRadius = Math.max( maxRadius, edgeLength(origin, vertex) ); + } } } - const snapshots = []; - if(facescenes.includes("default scene")) { - snapshots.push(0); + // Originally, I planned to determine the distance based on the view frustum + // and a sphere with radius = maxRadius, but I determined that a simple scaling + // of maxRadius is adequate and much simpler. + // Emperically, distance ends up being + // about 12 for J1 which is the smallest solid + // and 48 for J71 which is the biggest solid. + return maxRadius * 8; // Scale factor of 8 was determined empirically as a reasonable best-fit. +} + +function standardizeCamera(camera, distance) { + // Much of this is copied from camera.jsx + const NEAR_FACTOR = 0.1; + const FAR_FACTOR = 2.0; + const WIDTH_FACTOR = 0.5; + camera.viewDistance = distance; + camera.farClipDistance = distance * FAR_FACTOR; + camera.nearClipDistance = distance * NEAR_FACTOR; + camera.width = distance * WIDTH_FACTOR; + camera.fieldOfView = cameraFieldOfViewY ( camera.width, camera.viewDistance ); + + camera.perspective = true; + camera.stereo = false; + + camera.position.x = 0; + camera.position.y = 0; + camera.position.z = camera.viewDistance; + + camera.lookAtPoint.x = 0; + camera.lookAtPoint.y = 0; + camera.lookAtPoint.z = 0; + + camera.upDirection.x = 0; + camera.upDirection.y = 1; + camera.upDirection.z = 0; + + camera.lookDirection.x = 0; + camera.lookDirection.y = 0; + camera.lookDirection.z = -1; + + // don't need to return the camera because it's passed by reference and updated in situ +} + +function rescale(modelData) { + const snapshots = getFaceSceneSnapshots(modelData); + const shapeMap = new Map(); + for(const shape of modelData.shapes) { + shapeMap.set(shape.id, shape); } - for(const scene of modelData.scenes) { - if(facescenes.includes(scene.title)) { - snapshots.push(scene.snapshot); + var nTriangleEdges = 0; + var sumOfLengths = 0; + for(const snapshot of snapshots) { + const ss = modelData.snapshots[snapshot]; + for(let i = 0; i < ss.length; i++) { + const item = ss[i]; + const shapeGuid = item.shape; + const vertices = shapeMap.get(shapeGuid).vertices; + if(vertices.length == 3) { + // All Johnson solids have at least one equilateral triangle face. + // All other polygons are chopped into triangles that are not necessarily equilateral. + // I'll use the average length of all the edges of all the triangular faces + // to calculate the rescaling factor. + // Note that the edges will be counted twice when two triangles share an edge, + // and other triangle edges will only be counted once when a triangle shares + // an edge with a larger polygon such as a square. + // It's not worth the effort to distinguish the two cases for this application. + // In fact, it would work well enough by just using the first equilateral triangle + // edge length that we encounter. + sumOfLengths += edgeLength(vertices[0], vertices[1]); nTriangleEdges++; + sumOfLengths += edgeLength(vertices[1], vertices[2]); nTriangleEdges++; + sumOfLengths += edgeLength(vertices[2], vertices[0]); nTriangleEdges++; + } } } - console.log(snapshots); + + const averageLength = sumOfLengths / nTriangleEdges; + console.log("averageLength = " + averageLength + " (Ideal length = 2.0.)"); + + // Many models have an averageLength of 8.472135952064994 = (2+4phi) corresponding to blue zometool lengths. + // The target edge length will be 2 because most of the coordinates on qfbox and wikipedia + // have edge length of 2, resulting in a half edge length of 1 on each side of the symmetry plane(s). + const scaleFactor = Math.round((2.0 / averageLength) * sigfig) / sigfig; + + console.log("scaleFactor = " + scaleFactor); + if(!!modelData.scaleFactor) { + console.log("Previously calculated scaleFactor of " + modelData.scaleFactor + " will not be modified."); + } else { + // persist scaleFactor in the json + modelData.scaleFactor = scaleFactor; + + const sigScaleFactor = scaleFactor * sigfig; // scaleVector() will divide by sigfig after rounding + // scale all shapes + for(let s = 0; s < modelData.shapes.length; s++) { + for(let v = 0; v < modelData.shapes[s].vertices.length; v++) { + scaleVector(sigScaleFactor, modelData.shapes[s].vertices[v]); + } + } + // scale all instances + //console.log(modelData.instances.length + " instances"); + for(let i = 0; i < modelData.instances.length; i++) { + scaleVector(sigScaleFactor, modelData.instances[i].position); + } + // scale all snapshots + //console.log(modelData.snapshots.length + " snapshots"); + for(let i = 0; i < modelData.snapshots.length; i++) { + //console.log(modelData.snapshots[i].length + " snapshot[" + i + "]"); + for(let j = 0; j < modelData.snapshots[i].length; j++) { + scaleVector(sigScaleFactor, modelData.snapshots[i][j].position); + } + } + } + return modelData; +} + +function edgeLength(v0, v1) { + const x = v0.x - v1.x; + const y = v0.y - v1.y; + const z = v0.z - v1.z; + return Math.sqrt((x*x)+(y*y)+(z*z)); +} + +function scaleVector(scalar, vector) { + vector.x = Math.round( vector.x * scalar ) / sigfig; + vector.y = Math.round( vector.y * scalar ) / sigfig; + vector.z = Math.round( vector.z * scalar ) / sigfig; + // don't need to return the vector because it's passed by reference and updated in situ +} + +function recolor(modelData) { + const snapshots = getFaceSceneSnapshots(modelData); + const shapeMap = new Map(); + for(const shape of modelData.shapes) { + shapeMap.set(shape.id, shape.vertices.length); + } for(const snapshot of snapshots) { const ss = modelData.snapshots[snapshot]; for(let i = 0; i < ss.length; i++) { const item = ss[i]; const shapeGuid = item.shape; - const nVertices = faceMap.get(shapeGuid); + const nVertices = shapeMap.get(shapeGuid); const newColor = shapeColors.get(nVertices); if(newColor) { modelData.snapshots[snapshot][i].color = newColor; @@ -88,6 +246,29 @@ function recolor(modelData) { return modelData; } +function getFaceSceneSnapshots(modelData) { + // Get a list of facescene(s) of all models that use the selected jsolid's URL. + // There may be only one facescene, but there may be more than one. e.g. J38 & J39 + const url = viewer.src; + const facescenes = []; + for(const model of models) { + if(model.url == url) { + facescenes.push(model.facescene); + } + } + const snapshots = []; + // if(facescenes.includes("default scene")) { + // snapshots.push(0); + // } + for(const scene of modelData.scenes) { + if(facescenes.includes(scene.title)) { + snapshots.push(scene.snapshot); + } + } + // console.dir(snapshots); + return snapshots; +} + viewer .addEventListener( "vzome-scenes-discovered", (e) => { // Just logging this to the console for now. Not actually using the scenes list. const scenes = e.detail; @@ -95,12 +276,37 @@ viewer .addEventListener( "vzome-scenes-discovered", (e) => { console.log( JSON.stringify( scenes, null, 2 ) ); } ); +// TODO: Remove this listener after the race condition is fixed +viewer .addEventListener( "vzome-scenes-discovered", (e) => { + console.log( "This event handler is only triggered the first time a vzome scene is discovered after the page is loaded.\n" + + "It is a work around for the intermittant race condition that results in the wrong camera zoom level.\n" + + "The same race condition may still result in showing the wrong background color, but at least the camera zoom is consistent.\n" + + "If the vzome-viewer revision is shown ABOVE this message, then the background color was read from .shapes.json.\n" + + "If the vzome-viewer revision is shown BELOW this message, then the default background color of the viewer is being used.\n" + ); + viewer.update({ camera: true }); // force a camera update, but background color may still be wrong. +}, +{once: true}); // automatically remove this listener after it is fired once + for (const jsolid of models) { const tr = tbody.insertRow(); fillRow(tr, jsolid); tr.addEventListener("click", () => selectJohnsonSolid( jsolid, tr ) ); } -selectJohnsonSolid( models[ 0 ], tbody .rows[ 0 ] ); + +var initialId = 1; +const searchParams = new URL(document.location).searchParams; +let jId = parseInt(searchParams.get("J")); // upper case +if(Number.isNaN(jId)) { + jId = parseInt(searchParams.get("j")); // lower case +} +if(jId >= 1 && jId <= 92) { + initialId = jId; +} +const initialRow = tbody.rows[ initialId - 1 ]; +selectJohnsonSolid( models[ initialId - 1 ], initialRow ); +initialRow.scrollIntoView({ behavior: "smooth", block: "center" }); + showEdges.addEventListener("change", // use "change" here, not "click" () => { setScene(selectedRow.dataset); @@ -116,14 +322,6 @@ function selectJohnsonSolid( jsolid, tr ) { selectedRow = tr; selectedRow.className = "selected"; document.getElementById( "index" ).textContent = "J" +id; - //const shapes = url.replace( ".vZome", ".shapes.json" ); - //downloadLink.href = shapes; - //const filename = shapes.substring(shapes.lastIndexOf('/')+1); - //downloadLink.download = filename; - /* - Downloads local files as expected, but it won't directly download cross origin files in-situ. - One possible react solution is https://medium.com/charisol-community/downloading-resources-in-html5-a-download-may-not-work-as-expected-bf63546e2baa - */ switchModel(jsolid); } else { alert("Johnson solid J" + id + " is not yet available.\n\nPlease help us collect the full set."); diff --git a/style.css b/style.css index 3fc8556..aabcbbe 100644 --- a/style.css +++ b/style.css @@ -26,6 +26,7 @@ html, body { height: 100%; width: 100%; margin: 0; /* This is essential to avoid a small white border around the whole main div. */ + user-select: none; } .main-grid { @@ -33,19 +34,23 @@ html, body { grid-template-columns: 29.2rem minmax( 0, 1fr ); grid-template-rows: min-content minmax( 0, 1fr ); grid-template-areas: - "intro intro" - "table viewer"; + "intro intro refs" + "table viewer viewer"; gap: 7px; height: 100vh; max-width: 1400px; margin: auto; } -.intro, -.references { +.intro { + margin-inline-start: 2rem; grid-area: intro; max-width: 800px; - margin: auto; +} + +.references { + grid-area: refs; + min-width: 320px; } .viewer { @@ -95,6 +100,7 @@ input[type=checkbox] } #showEdges { + margin-left: 0.5rem; margin-right: 0.5rem; } @@ -232,3 +238,35 @@ tfoot td { rgba(0, 0, 0, 0.2) ); } + +@media ( max-aspect-ratio: 12/10 ) { + + .main-grid { + display: grid; + grid-template-columns: 1fr; + grid-template-rows: min-content minmax( 0, 5fr ) minmax( 0, 3fr ); + grid-template-areas: + "intro" + "viewer" + "table"; + height: 100vh; + margin: auto; + } + + .intro h1 { + display: block; + font-size: 1.5em; + margin-block-start: 0.37em; + margin-block-end: 0.2em; + font-weight: bold; +} + .intro { + grid-area: intro; + } + + .intro-text, + .references { + display: none; + } + +} \ No newline at end of file diff --git a/uploads/ThynStyx/J11-Gyroelongated-pentagonal-pyramid-Golden.shapes.json b/uploads/ThynStyx/J11-Gyroelongated-pentagonal-pyramid-Golden.shapes.json index 4c3198a..88c5ee9 100644 --- a/uploads/ThynStyx/J11-Gyroelongated-pentagonal-pyramid-Golden.shapes.json +++ b/uploads/ThynStyx/J11-Gyroelongated-pentagonal-pyramid-Golden.shapes.json @@ -1117,19 +1117,19 @@ "position": { "x": 0, "y": 0, - "z": 83.83742 + "z": 15.88382424424847 }, - "width": 37.726833, - "nearClipDistance": 0.20959353, + "width": 7.941912122124235, + "nearClipDistance": 1.588382424424847, "lookAtPoint": { "x": 0, "y": 0, "z": 0 }, - "farClipDistance": 167.67484, + "farClipDistance": 31.76764848849694, "perspective": true, - "fieldOfView": 0.44262883, - "viewDistance": 83.83742, + "fieldOfView": 28.072486935852954, + "viewDistance": 15.88382424424847, "upDirection": { "x": 0, "y": 1, @@ -1165,19 +1165,19 @@ "id": "a5f2ce2f-c109-4d53-bc69-c42eb4f7e852", "vertices": [ { - "x": -4.236068, - "y": -0.62310016, - "z": 6.469005 + "x": -0.999999999, + "y": -0.147093994, + "z": 1.527124917 }, { - "x": -6.854102, - "y": -4.859168, - "z": -0.3850971 + "x": -1.618033986, + "y": -1.147093955, + "z": -0.090909093 }, { "x": 0, - "y": -7.477202, - "z": 3.850971 + "y": -1.765127942, + "z": 0.90909093 } ], "faces": [ @@ -1201,19 +1201,19 @@ "id": "5d4f3d12-b7bc-4dbf-b73d-b4685fd0204a", "vertices": [ { - "x": -4.236068, - "y": -0.62310016, - "z": 6.469005 + "x": -0.999999999, + "y": -0.147093994, + "z": 1.527124917 }, { "x": 0, - "y": -7.477202, - "z": 3.850971 + "y": -1.765127942, + "z": 0.90909093 }, { - "x": 4.236068, - "y": -0.62310016, - "z": 6.469005 + "x": 0.999999999, + "y": -0.147093994, + "z": 1.527124917 } ], "faces": [ @@ -1238,28 +1238,28 @@ "vertices": [ { "x": 0, - "y": -7.477202, - "z": 3.850971 + "y": -1.765127942, + "z": 0.90909093 }, { - "x": -6.854102, - "y": -4.859168, - "z": -0.3850971 + "x": -1.618033986, + "y": -1.147093955, + "z": -0.090909093 }, { - "x": -4.236068, - "y": -0.62310016, - "z": -7.239199 + "x": -0.999999999, + "y": -0.147093994, + "z": -1.708943056 }, { - "x": 4.236068, - "y": -0.62310016, - "z": -7.239199 + "x": 0.999999999, + "y": -0.147093994, + "z": -1.708943056 }, { - "x": 6.854102, - "y": -4.859168, - "z": -0.3850971 + "x": 1.618033986, + "y": -1.147093955, + "z": -0.090909093 } ], "faces": [ @@ -1311,19 +1311,19 @@ "id": "7f234202-cf56-4308-9dbf-fc1c69b61900", "vertices": [ { - "x": 4.236068, - "y": -0.62310016, - "z": -7.239199 + "x": 0.999999999, + "y": -0.147093994, + "z": -1.708943056 }, { - "x": 6.854102, - "y": 3.6129677, - "z": -0.3850971 + "x": 1.618033986, + "y": 0.852905972, + "z": -0.090909093 }, { - "x": 6.854102, - "y": -4.859168, - "z": -0.3850971 + "x": 1.618033986, + "y": -1.147093955, + "z": -0.090909093 } ], "faces": [ @@ -1348,18 +1348,18 @@ "vertices": [ { "x": 0, - "y": 6.231002, - "z": 3.850971 + "y": 1.470940031, + "z": 0.90909093 }, { "x": 0, - "y": 6.231002, - "z": -4.6211653 + "y": 1.470940031, + "z": -1.090909139 }, { - "x": -6.854102, - "y": 3.6129677, - "z": -0.3850971 + "x": -1.618033986, + "y": 0.852905972, + "z": -0.090909093 } ], "faces": [ @@ -1383,19 +1383,19 @@ "id": "daea7c96-2974-4705-9227-eaa07e7b2274", "vertices": [ { - "x": 6.854102, - "y": -4.859168, - "z": -0.3850971 + "x": 1.618033986, + "y": -1.147093955, + "z": -0.090909093 }, { - "x": 6.854102, - "y": 3.6129677, - "z": -0.3850971 + "x": 1.618033986, + "y": 0.852905972, + "z": -0.090909093 }, { - "x": 4.236068, - "y": -0.62310016, - "z": 6.469005 + "x": 0.999999999, + "y": -0.147093994, + "z": 1.527124917 } ], "faces": [ @@ -1419,19 +1419,19 @@ "id": "c27701c2-5ff6-4e5a-a388-3b3c2a7c5a1e", "vertices": [ { - "x": 6.854102, - "y": -4.859168, - "z": -0.3850971 + "x": 1.618033986, + "y": -1.147093955, + "z": -0.090909093 }, { - "x": 4.236068, - "y": -0.62310016, - "z": 6.469005 + "x": 0.999999999, 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"faces": [ @@ -11055,24 +11055,24 @@ "id": "d09af906-504a-446d-8d46-f83c84f9276b", "vertices": [ { - "x": -10.300975, - "y": -7.484096, - "z": -3.9346223 + "x": -2.618034062, + "y": -1.90211298, + "z": -1.00000002 }, { - "x": -3.9346223, - "y": -12.109522, - "z": -3.9346223 + "x": -1.00000002, + "y": -3.077683527, + "z": -1.00000002 }, { - "x": -3.9346223, - "y": -12.109522, - "z": 3.9346223 + "x": -1.00000002, + "y": -3.077683527, + "z": 1.00000002 }, { - "x": -10.300975, - "y": -7.484096, - "z": 3.9346223 + "x": -2.618034062, + "y": -1.90211298, + "z": 1.00000002 } ], "faces": [ @@ -11402,31 +11402,31 @@ "title": "Step 1", "content": "In octahedral symmetry, drag a unit length blue strut to the Z axis, make a ball at the midpoint then delete the strut and both endpoints, leaving just a ball at (0,0,1/2). Call that ball A.", "view": { - "width": 48.92907, + "width": 13.548216814608011, "position": { - "x": 16.995777, - "y": 19.270166, - "z": 105.651855 + "x": 0, + "y": 0, + "z": 27.096433629216023 }, "perspective": true, - "farClipDistance": 217.46254, - "fieldOfView": 0.44262886, - "viewDistance": 108.73127, + "farClipDistance": 54.192867258432045, + "fieldOfView": 28.072486935852954, + "viewDistance": 27.096433629216023, "lookAtPoint": { "x": 0, "y": 0, "z": 0 }, - "nearClipDistance": 0.27182817, + "nearClipDistance": 2.7096433629216023, "lookDirection": { - "x": -0.15630993, - "y": -0.17722745, - "z": -0.9716787 + "x": 0, + "y": 0, + "z": -1 }, "upDirection": { - "x": -0.08450758, - "y": 0.9825665, - "z": -0.16561803 + "x": 0, + "y": 1, + "z": 0 }, "stereo": false }, @@ -11436,31 +11436,31 @@ "title": "Step 2", "content": "From ball A, drag a strut of custom length phi in the +X direction. Call the new ball B.", "view": { - "width": 48.92907, + "width": 13.548216814608011, "position": { - "x": 16.995777, - "y": 19.270166, - "z": 105.651855 + "x": 0, + "y": 0, + "z": 27.096433629216023 }, "perspective": true, - "farClipDistance": 217.46254, - "fieldOfView": 0.44262886, - "viewDistance": 108.73127, + "farClipDistance": 54.192867258432045, + "fieldOfView": 28.072486935852954, + "viewDistance": 27.096433629216023, "lookAtPoint": { "x": 0, "y": 0, "z": 0 }, - "nearClipDistance": 0.27182817, + "nearClipDistance": 2.7096433629216023, "lookDirection": { - "x": -0.15630993, - "y": -0.17722745, - "z": -0.9716787 + "x": 0, + "y": 0, + "z": -1 }, "upDirection": { - "x": -0.08450758, - "y": 0.9825665, - "z": -0.16561803 + "x": 0, + "y": 1, + "z": 0 }, "stereo": false }, @@ -11470,31 +11470,31 @@ "title": "Step 3", "content": "From ball A, drag a strut of custom length 1/(-a+c) in the +Z direction. Call the new ball C.", "view": { - "width": 48.92907, + "width": 13.548216814608011, "position": { - "x": 16.995777, - "y": 19.270166, - "z": 105.651855 + "x": 0, + "y": 0, + "z": 27.096433629216023 }, "perspective": true, - "farClipDistance": 217.46254, - "fieldOfView": 0.44262886, - "viewDistance": 108.73127, + "farClipDistance": 54.192867258432045, + "fieldOfView": 28.072486935852954, + "viewDistance": 27.096433629216023, "lookAtPoint": { "x": 0, "y": 0, "z": 0 }, - "nearClipDistance": 0.27182817, + "nearClipDistance": 2.7096433629216023, "lookDirection": { - "x": -0.15630993, - "y": -0.17722745, - "z": -0.9716787 + "x": 0, + "y": 0, + "z": -1 }, "upDirection": { - "x": -0.08450758, - "y": 0.9825665, - "z": -0.16561803 + "x": 0, + "y": 1, + "z": 0 }, "stereo": false }, @@ -11504,31 +11504,31 @@ "title": "Step 4", "content": "From ball A, drag a strut of custom length 1/(a+2c+e-2g) in the +Y direction. Call the new ball D.", "view": { - "width": 48.92907, + "width": 13.548216814608011, "position": { - "x": 16.995777, - "y": 19.270166, - "z": 105.651855 + "x": 0, + "y": 0, + "z": 27.096433629216023 }, "perspective": true, - "farClipDistance": 217.46254, - "fieldOfView": 0.44262886, - "viewDistance": 108.73127, + "farClipDistance": 54.192867258432045, + "fieldOfView": 28.072486935852954, + "viewDistance": 27.096433629216023, "lookAtPoint": { "x": 0, "y": 0, "z": 0 }, - "nearClipDistance": 0.27182817, + "nearClipDistance": 2.7096433629216023, "lookDirection": { - "x": -0.15630993, - "y": -0.17722745, - "z": -0.9716787 + "x": 0, + "y": 0, + "z": -1 }, "upDirection": { - "x": -0.08450758, - "y": 0.9825665, - "z": -0.16561803 + "x": 0, + "y": 1, + "z": 0 }, "stereo": false }, @@ -11538,31 +11538,31 @@ "title": "Step 5", "content": "Switch to antiprism symmetry then select balls B and D.", "view": { - "width": 48.92907, + "width": 13.548216814608011, "position": { - "x": 16.995777, - "y": 19.270166, - "z": 105.651855 + "x": 0, + "y": 0, + "z": 27.096433629216023 }, "perspective": true, - "farClipDistance": 217.46254, - "fieldOfView": 0.44262886, - "viewDistance": 108.73127, + "farClipDistance": 54.192867258432045, + "fieldOfView": 28.072486935852954, + "viewDistance": 27.096433629216023, "lookAtPoint": { "x": 0, "y": 0, "z": 0 }, - "nearClipDistance": 0.27182817, + "nearClipDistance": 2.7096433629216023, "lookDirection": { - "x": -0.15630993, - "y": -0.17722745, - "z": -0.9716787 + "x": 0, + "y": 0, + "z": -1 }, "upDirection": { - "x": -0.08450758, - "y": 0.9825665, - "z": -0.16561803 + "x": 0, + "y": 1, + "z": 0 }, "stereo": false }, @@ -11572,22 +11572,22 @@ "title": "Step 6", "content": "Apply the built-in \"symmetry around red through origin\" tool, deselect all, then select every 3rd ball on the outer ring, starting at ball B and every 6th ball around the inner ring starting at ball D.", "view": { - "width": 55.167377, + "width": 13.548216814608011, "position": { "x": 0, "y": 0, - "z": 122.59417 + "z": 27.096433629216023 }, "perspective": true, - "farClipDistance": 245.18834, - "fieldOfView": 0.4426289, - "viewDistance": 122.59417, + "farClipDistance": 54.192867258432045, + "fieldOfView": 28.072486935852954, + "viewDistance": 27.096433629216023, "lookAtPoint": { "x": 0, "y": 0, "z": 0 }, - "nearClipDistance": 0.3064854, + "nearClipDistance": 2.7096433629216023, "lookDirection": { "x": 0, "y": 0, @@ -11606,22 +11606,22 @@ "title": "Step 7", "content": "Invert the selection, then delete, leaving 15 balls.\nAt this point, select all and save the file as the common starting point for J38 and J39.", "view": { - "width": 55.167377, + "width": 13.548216814608011, "position": { "x": 0, "y": 0, - "z": 122.59417 + "z": 27.096433629216023 }, "perspective": true, - "farClipDistance": 245.18834, - "fieldOfView": 0.4426289, - "viewDistance": 122.59417, + "farClipDistance": 54.192867258432045, + "fieldOfView": 28.072486935852954, + "viewDistance": 27.096433629216023, "lookAtPoint": { "x": 0, "y": 0, "z": 0 }, - "nearClipDistance": 0.3064854, + "nearClipDistance": 2.7096433629216023, "lookDirection": { "x": 0, "y": 0, @@ -11640,22 +11640,22 @@ "title": "Step 8 for J38", "content": "Either use \"Point Reflection\" from the \"Tools\" menu to make the vertices of J38...", "view": { - "width": 55.167377, + "width": 13.548216814608011, "position": { "x": 0, "y": 0, - "z": 122.59417 + "z": 27.096433629216023 }, "perspective": true, - "farClipDistance": 245.18834, - "fieldOfView": 0.4426289, - "viewDistance": 122.59417, + "farClipDistance": 54.192867258432045, + "fieldOfView": 28.072486935852954, + "viewDistance": 27.096433629216023, "lookAtPoint": { "x": 0, "y": 0, "z": 0 }, - "nearClipDistance": 0.3064854, + "nearClipDistance": 2.7096433629216023, "lookDirection": { "x": 0, "y": 0, @@ -11674,22 +11674,22 @@ "title": "Step 8 for J39", "content": "... or else use the built-in \"reflection through XY plane\" tool, then \"Select All\" to make the vertices of J39.", "view": { - "width": 55.167377, + "width": 13.548216814608011, "position": { "x": 0, "y": 0, - "z": 122.59417 + "z": 27.096433629216023 }, "perspective": true, - "farClipDistance": 245.18834, - "fieldOfView": 0.4426289, - "viewDistance": 122.59417, + "farClipDistance": 54.192867258432045, + "fieldOfView": 28.072486935852954, + "viewDistance": 27.096433629216023, "lookAtPoint": { "x": 0, "y": 0, "z": 0 }, - "nearClipDistance": 0.3064854, + "nearClipDistance": 2.7096433629216023, "lookDirection": { "x": 0, "y": 0, @@ -11708,31 +11708,31 @@ "title": "Step 9 for J38", "content": "In either case, use a 3D convex hull to generate the balls, struts and panels.", "view": { - "width": 55.167377, + "width": 13.548216814608011, "position": { "x": 0, - "y": -86.687164, - "z": 86.687164 + "y": 0, + "z": 27.096433629216023 }, "perspective": true, - "farClipDistance": 245.18834, - "fieldOfView": 0.4426289, - "viewDistance": 122.59417, + "farClipDistance": 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+ 0, + 4, + 1 + ] + }, + { + "vertices": [ + 2, + 4, + 5 + ] + }, + { + "vertices": [ + 2, + 5, + 3 + ] + }, + { + "vertices": [ + 0, + 6, + 3 + ] + }, + { + "vertices": [ + 0, + 3, + 5 + ] + }, + { + "vertices": [ + 0, + 1, + 7 + ] + }, + { + "vertices": [ + 0, + 7, + 6 + ] + }, + { + "vertices": [ + 1, + 4, + 2 + ] + }, + { + "vertices": [ + 1, + 2, + 7 + ] + } + ] + }, + { + "id": "ead1b20b-8910-4bf1-86f9-9b8009f0e3e6", + "vertices": [ + { + "x": 0.922028406, + "y": 1.060389918, + "z": -1.283873709 + }, + { + "x": 0.973921619, + "y": 1.047416624, + "z": -1.270900416 + }, + { + "x": 0.077971596, + "y": 0.061642753, + "z": -0.035612054 + }, + { + "x": 0.026078426, + "y": 0.074616047, + "z": -0.048585347 + }, + { + "x": 0.991219301, + "y": 1.086336505, + "z": -1.240629441 + }, + { + "x": 0.939326178, + "y": 1.099309928, + "z": -1.253602735 + }, + { + "x": 0.008780701, + "y": 0.035696164, + "z": -0.078856361 + }, + { + "x": 0.060673875, + "y": 0.022722871, + "z": -0.065883076 + } + ], + "faces": [ + { + "vertices": [ + 2, + 3, + 6 + ] + }, + { + "vertices": [ + 2, + 6, + 7 + ] + }, + { + "vertices": [ + 0, + 5, + 4 + ] + }, + { + "vertices": [ + 0, + 4, + 1 + ] + }, + { + "vertices": [ + 2, + 4, + 5 + ] + }, + { + "vertices": [ + 2, + 5, + 3 + ] + }, + { + "vertices": [ + 0, + 6, + 3 + ] + }, + { + "vertices": [ + 0, + 3, + 5 + ] + }, + { + "vertices": [ + 0, + 1, + 7 + ] + }, + { + "vertices": [ + 0, + 7, + 6 + ] + }, + { + "vertices": [ + 1, + 4, + 2 + ] + }, + { + "vertices": [ + 1, + 2, + 7 + ] + } + ] } - }, { - "shape" : "a49630f2-d746-4b20-bfe8-8345b20118ee", - "color" : "#F0A000", - "position" : { - "x" : 0.0, - "y" : 0.0, - "z" : 0.0 - } - }, { - "shape" : "bc7f680d-c398-4ccc-b5a0-3e4eefbe5c83", - "color" : "#F0A000", - "position" : { - "x" : 0.0, - "y" : 0.0, - "z" : 0.0 - } - }, { - "shape" : "9abbed24-597a-4d83-87fb-30347b080080", - "color" : "#AF0000", - "position" : { - "x" : 0.0, - "y" : 0.0, - "z" : 0.0 - } - }, { - "shape" : "04e5a2c9-fe0c-484c-8dfe-909afff30e37", - "color" : "#F0A000", - "position" : { - "x" : 0.0, - "y" : 0.0, - "z" : 0.0 - } - }, { - "shape" : "e568c4f7-3815-4594-a240-cfeea15f5c2d", - "color" : "#F0A000", - "position" : { - "x" : 0.0, - "y" : 0.0, - "z" : 0.0 - } - }, { - "shape" : "d619e4f5-2d0f-4b68-b8a4-0bf1c30e510d", - "color" : "#AF0000", - "position" : { - "x" : 0.0, - "y" : 0.0, - "z" : 0.0 - } - }, { - "shape" : "f3e266e0-d055-4a5c-af02-5a4338f838c1", - "color" : "#F0A000", - "position" : { - "x" : 0.0, - "y" : 0.0, - "z" : 0.0 - } - } ], - "scenes" : [ { - "title" : "First icosahedral vertex", - "content" : "Use octahedral symmetry system.\nDrag B1 toward +X.\nUse a custom blue length of phi.\nDrag that length from the prior ball in the +Z direction.", - "view" : { - "position" : { - "x" : 12.283063, - "y" : 45.64537, - "z" : 151.80693 - }, - "width" : 71.54824, - "perspective" : true, - "fieldOfView" : 0.44262895, - "viewDistance" : 158.99606, - "farClipDistance" : 317.99213, - "lookAtPoint" : { - "x" : 0.0, - "y" : 0.0, - "z" : 0.0 - }, - "nearClipDistance" : 0.3974902, - "lookDirection" : { - "x" : -0.07725388, - "y" : -0.2870849, - "z" : -0.9547842 - }, - "stereo" : false, - "upDirection" : { - "x" : 0.001990197, - "y" : 0.9576006, - "z" : -0.28809252 + ], + "instances": [ + { + "shape": "8a7ad7d5-05e3-449b-9365-759cd32a6334", + "color": "#F0A000", + "position": { + "x": 0, + "y": 0, + "z": 0 } }, - "snapshot" : 0 - }, { - "title" : "All icosahedral vertices", - "content" : "Apply the tetrahedral symmetry tool in the octahedral symmetry system to generate all 12 icosa vertices.", - "view" : { - "position" : { - "x" : 12.283063, - "y" : 45.64537, - "z" : 151.80693 - }, - "width" : 71.54824, - "perspective" : true, - "fieldOfView" : 0.44262895, - "viewDistance" : 158.99606, - "farClipDistance" : 317.99213, - "lookAtPoint" : { - "x" : 0.0, - "y" : 0.0, - "z" : 0.0 - }, - "nearClipDistance" : 0.3974902, - "lookDirection" : { - "x" : -0.07725388, - "y" : -0.2870849, - "z" : -0.9547842 - }, - "stereo" : false, - "upDirection" : { - "x" : 0.001990197, - "y" : 0.9576006, - "z" : -0.28809252 + { + "shape": "d6a7569a-10e6-458e-9c4b-9f9e12fc9f4a", + "color": "#F0A000", + "position": { + "x": 0, + "y": 0, + "z": 0 } }, - "snapshot" : 1 - }, { - "title" : "Remove icosa scafolding", - "content" : "Delete the two struts, the ball at their common vertex, and the origin, leaving just the icosahedron's 12 vertices.", - "view" : { - "position" : { - "x" : 12.283063, - "y" : 45.64537, - "z" : 151.80693 - }, - "width" : 71.54824, - "perspective" : true, - "fieldOfView" : 0.44262895, - "viewDistance" : 158.99606, - "farClipDistance" : 317.99213, - "lookAtPoint" : { - "x" : 0.0, - "y" : 0.0, - "z" : 0.0 - }, - "nearClipDistance" : 0.3974902, - "lookDirection" : { - "x" : -0.07725388, - "y" : -0.2870849, - "z" : -0.9547842 - }, - "stereo" : false, - "upDirection" : { - "x" : 0.001990197, - "y" : 0.9576006, - "z" : -0.28809252 + { + "shape": "4584da1c-d128-408f-b3be-28e68ca5c574", + "color": "#AF0000", + "position": { + "x": 0, + "y": 0, + "z": 0 } }, - "snapshot" : 2 - }, { - "title" : "Remove tridimished vertices", - "content" : "Remove the three vertices that are ot part of J63.", - "view" : { - "position" : { - "x" : 12.283063, - "y" : 45.64537, - "z" : 151.80693 - }, - "width" : 71.54824, - "perspective" : true, - "fieldOfView" : 0.44262895, - "viewDistance" : 158.99606, - "farClipDistance" : 317.99213, - "lookAtPoint" : { - "x" : 0.0, - "y" : 0.0, - "z" : 0.0 - }, - "nearClipDistance" : 0.3974902, - "lookDirection" : { - "x" : -0.07725388, - "y" : -0.2870849, - "z" : -0.9547842 - }, - "stereo" : false, - "upDirection" : { - "x" : 0.001990197, - "y" : 0.9576006, - "z" : -0.28809252 + { + "shape": "a49630f2-d746-4b20-bfe8-8345b20118ee", + "color": "#F0A000", + "position": { + "x": 0, + "y": 0, + "z": 0 } }, - "snapshot" : 3 - }, { - "title" : "J63 convex hull", - "content" : "Select all of the balls and make a convex hull having struts only (no panels yet).", - "view" : { - "position" : { - "x" : 12.283063, - "y" : 45.64537, - "z" : 151.80693 - }, - "width" : 71.54824, - "perspective" : true, - "fieldOfView" : 0.44262895, - "viewDistance" : 158.99606, - "farClipDistance" : 317.99213, - "lookAtPoint" : { - "x" : 0.0, - "y" : 0.0, - "z" : 0.0 - }, - "nearClipDistance" : 0.3974902, - "lookDirection" : { - "x" : -0.07725388, - "y" : -0.2870849, - "z" : -0.9547842 - }, - "stereo" : false, - "upDirection" : { - "x" : 0.001990197, - "y" : 0.9576006, - "z" : -0.28809252 + { + "shape": "bc7f680d-c398-4ccc-b5a0-3e4eefbe5c83", + "color": "#F0A000", + "position": { + "x": 0, + "y": 0, + "z": 0 } }, - "snapshot" : 4 - }, { - "title" : "Midpoint of near blue strut", - "content" : "Make a ball at the midpoint of the near blue strut.\nUse a custom blue length of sqrt(2).\nDrag that length from the midpoint ball in the +Z direction.", - "view" : { - "position" : { - "x" : 12.283063, - "y" : 45.64537, - "z" : 151.80693 - }, - "width" : 71.54824, - "perspective" : true, - "fieldOfView" : 0.44262895, - "viewDistance" : 158.99606, - "farClipDistance" : 317.99213, - "lookAtPoint" : { - "x" : 0.0, - "y" : 0.0, - "z" : 0.0 - }, - "nearClipDistance" : 0.3974902, - "lookDirection" : { - "x" : -0.07725388, - "y" : -0.2870849, - "z" : -0.9547842 - }, - "stereo" : false, - "upDirection" : { - "x" : 0.001990197, - "y" : 0.9576006, - "z" : -0.28809252 + { + "shape": "9abbed24-597a-4d83-87fb-30347b080080", + "color": "#AF0000", + "position": { + "x": 0, + "y": 0, + "z": 0 } }, - "snapshot" : 5 - }, { - "title" : "Vertical edge of tetrahedron", - "content" : "Use \"build with this\" to set the blue length to the edge of the icosahedron.\nDrag a blue strut in the +Y direction from the most recently added ball, having that length.\nGenerate a ball at the midpoint of that strut.\nUse the midpoint and the ball at the bottom of that strut to make a translation tool to move in the -Y direction by half the length of that strut.", - "view" : { - "position" : { - "x" : 12.283063, - "y" : 45.64537, - "z" : 151.80693 - }, - "width" : 71.54824, - "perspective" : true, - "fieldOfView" : 0.44262895, - "viewDistance" : 158.99606, - "farClipDistance" : 317.99213, - "lookAtPoint" : { - "x" : 0.0, - "y" : 0.0, - "z" : 0.0 - }, - "nearClipDistance" : 0.3974902, - "lookDirection" : { - "x" : -0.07725388, - "y" : -0.2870849, - "z" : -0.9547842 - }, - "stereo" : false, - "upDirection" : { - "x" : 0.001990197, - "y" : 0.9576006, - "z" : -0.28809252 + { + "shape": "04e5a2c9-fe0c-484c-8dfe-909afff30e37", + "color": "#F0A000", + "position": { + "x": 0, + "y": 0, + "z": 0 } }, - "snapshot" : 6 - }, { - "title" : "Translate tetrahedron edge", - "content" : "Use \"select collinear\" on the most recently built strut to select it, its two end points and its midpoint.\nApply the translation tool created in the previous step to move it in the -Y direction.", - "view" : { - "position" : { - "x" : 12.283063, - "y" : 45.64537, - "z" : 151.80693 - }, - "width" : 71.54824, - "perspective" : true, - "fieldOfView" : 0.44262895, - "viewDistance" : 158.99606, - "farClipDistance" : 317.99213, - "lookAtPoint" : { - "x" : 0.0, - "y" : 0.0, - "z" : 0.0 - }, - "nearClipDistance" : 0.3974902, - "lookDirection" : { - "x" : -0.07725388, - "y" : -0.2870849, - "z" : -0.9547842 - }, - "stereo" : false, - "upDirection" : { - "x" : 0.001990197, - "y" : 0.9576006, - "z" : -0.28809252 + { + "shape": "e568c4f7-3815-4594-a240-cfeea15f5c2d", + "color": "#F0A000", + "position": { + "x": 0, + "y": 0, + "z": 0 } }, - "snapshot" : 7 - }, { - "title" : "Generate tetrahedron", - "content" : "Select the most recently moved strut and the nearest (blue) edge of the icosahedren.\nMake a convex hull having struts only (no panels yet).", - "view" : { - "position" : { - "x" : 12.283063, - "y" : 45.64537, - "z" : 151.80693 - }, - "width" : 71.54824, - "perspective" : true, - "fieldOfView" : 0.44262895, - "viewDistance" : 158.99606, - "farClipDistance" : 317.99213, - "lookAtPoint" : { - "x" : 0.0, - "y" : 0.0, - "z" : 0.0 - }, - "nearClipDistance" : 0.3974902, - "lookDirection" : { - "x" : -0.07725388, - "y" : -0.2870849, - "z" : -0.9547842 - }, - "stereo" : false, - "upDirection" : { - "x" : 0.001990197, - "y" : 0.9576006, - "z" : -0.28809252 + { + "shape": "d619e4f5-2d0f-4b68-b8a4-0bf1c30e510d", + "color": "#AF0000", + "position": { + "x": 0, + "y": 0, + "z": 0 } }, - "snapshot" : 8 - }, { - "title" : "Remove tetrahedron scafolding", - "content" : "Delete the strut between the midpoints of the tetrahedron's edges and the two balls at its ends.", - "view" : { - "position" : { - "x" : 12.283063, - "y" : 45.64537, - "z" : 151.80693 - }, - "width" : 71.54824, - "perspective" : true, - "fieldOfView" : 0.44262895, - "viewDistance" : 158.99606, - "farClipDistance" : 317.99213, - "lookAtPoint" : { - "x" : 0.0, - "y" : 0.0, - "z" : 0.0 - }, - "nearClipDistance" : 0.3974902, - "lookDirection" : { - "x" : -0.07725388, - "y" : -0.2870849, - "z" : -0.9547842 - }, - "stereo" : false, - "upDirection" : { - "x" : 0.001990197, - "y" : 0.9576006, - "z" : -0.28809252 + { + "shape": "f3e266e0-d055-4a5c-af02-5a4338f838c1", + "color": "#F0A000", + "position": { + "x": 0, + "y": 0, + "z": 0 } - }, - "snapshot" : 9 - }, { - "title" : "Cross product of icosahedron face", - "content" : "Select the three vertices of the icosahedron face where the tetrahedron will eventually attach to it. Select the one that's at the bottom (on the X=0 plane) first, then move counterclockwise around the triangle.\nApply the cross product tool.", - "view" : { - "position" : { - "x" : 12.283063, - "y" : 45.64537, - "z" : 151.80693 - }, - "width" : 71.54824, - "perspective" : true, - "fieldOfView" : 0.44262895, - "viewDistance" : 158.99606, - "farClipDistance" : 317.99213, - "lookAtPoint" : { - "x" : 0.0, - "y" : 0.0, - "z" : 0.0 - }, - "nearClipDistance" : 0.3974902, - "lookDirection" : { - "x" : -0.07725388, - "y" : -0.2870849, - "z" : -0.9547842 - }, - "stereo" : false, - "upDirection" : { - "x" : 0.001990197, - "y" : 0.9576006, - "z" : -0.28809252 + } + ], + "scenes": [ + { + "title": "First icosahedral vertex", + "content": "Use octahedral symmetry system.\nDrag B1 toward +X.\nUse a custom blue length of phi.\nDrag that length from the prior ball in the +Z direction.", + "view": { + "position": { + "x": 0, + "y": 0, + "z": 25.15612635481111 + }, + "width": 12.578063177405555, + "perspective": true, + "fieldOfView": 28.072486935852954, + "viewDistance": 25.15612635481111, + "farClipDistance": 50.31225270962222, + "lookAtPoint": { + "x": 0, + "y": 0, + "z": 0 + }, + "nearClipDistance": 2.5156126354811112, + "lookDirection": { + "x": 0, + "y": 0, + "z": -1 + }, + "stereo": false, + "upDirection": { + "x": 0, + "y": 1, + "z": 0 + } + }, + "snapshot": 0 + }, + { + "title": "All icosahedral vertices", + "content": "Apply the tetrahedral symmetry tool in the octahedral symmetry system to generate all 12 icosa vertices.", + "view": { + "position": { + "x": 0, + "y": 0, + "z": 25.15612635481111 + }, + "width": 12.578063177405555, + "perspective": true, + "fieldOfView": 28.072486935852954, + "viewDistance": 25.15612635481111, + "farClipDistance": 50.31225270962222, + "lookAtPoint": { + "x": 0, + "y": 0, + "z": 0 + }, + "nearClipDistance": 2.5156126354811112, + "lookDirection": { + "x": 0, + "y": 0, + "z": -1 + }, + "stereo": false, + "upDirection": { + "x": 0, + "y": 1, + "z": 0 + } + }, + "snapshot": 1 + }, + { + "title": "Remove icosa scafolding", + "content": "Delete the two struts, the ball at their common vertex, and the origin, leaving just the icosahedron's 12 vertices.", + "view": { + "position": { + "x": 0, + "y": 0, + "z": 25.15612635481111 + }, + "width": 12.578063177405555, + "perspective": true, + "fieldOfView": 28.072486935852954, + "viewDistance": 25.15612635481111, + "farClipDistance": 50.31225270962222, + "lookAtPoint": { + "x": 0, + "y": 0, + "z": 0 + }, + "nearClipDistance": 2.5156126354811112, + "lookDirection": { + "x": 0, + "y": 0, + "z": -1 + }, + "stereo": false, + "upDirection": { + "x": 0, + "y": 1, + "z": 0 + } + }, + "snapshot": 2 + }, + { + "title": "Remove tridimished vertices", + "content": "Remove the three vertices that are ot part of J63.", + "view": { + "position": { + "x": 0, + "y": 0, + "z": 25.15612635481111 + }, + "width": 12.578063177405555, + "perspective": true, + "fieldOfView": 28.072486935852954, + "viewDistance": 25.15612635481111, + "farClipDistance": 50.31225270962222, + "lookAtPoint": { + "x": 0, + "y": 0, + "z": 0 + }, + "nearClipDistance": 2.5156126354811112, + "lookDirection": { + "x": 0, + "y": 0, + "z": -1 + }, + "stereo": false, + "upDirection": { + "x": 0, + "y": 1, + "z": 0 + } + }, + "snapshot": 3 + }, + { + "title": "J63 convex hull", + "content": "Select all of the balls and make a convex hull having struts only (no panels yet).", + "view": { + "position": { + "x": 0, + "y": 0, + "z": 25.15612635481111 + }, + "width": 12.578063177405555, + "perspective": true, + "fieldOfView": 28.072486935852954, + "viewDistance": 25.15612635481111, + "farClipDistance": 50.31225270962222, + "lookAtPoint": { + "x": 0, + "y": 0, + "z": 0 + }, + "nearClipDistance": 2.5156126354811112, + "lookDirection": { + "x": 0, + "y": 0, + "z": -1 + }, + "stereo": false, + "upDirection": { + "x": 0, + "y": 1, + "z": 0 + } + }, + "snapshot": 4 + }, + { + "title": "Midpoint of near blue strut", + "content": "Make a ball at the midpoint of the near blue strut.\nUse a custom blue length of sqrt(2).\nDrag that length from the midpoint ball in the +Z direction.", + "view": { + "position": { + "x": 0, + "y": 0, + "z": 25.15612635481111 + }, + "width": 12.578063177405555, + "perspective": true, + "fieldOfView": 28.072486935852954, + "viewDistance": 25.15612635481111, + "farClipDistance": 50.31225270962222, + "lookAtPoint": { + "x": 0, + "y": 0, + "z": 0 + }, + "nearClipDistance": 2.5156126354811112, + "lookDirection": { + "x": 0, + "y": 0, + "z": -1 + }, + "stereo": false, + "upDirection": { + "x": 0, + "y": 1, + "z": 0 + } + }, + "snapshot": 5 + }, + { + "title": "Vertical edge of tetrahedron", + "content": "Use \"build with this\" to set the blue length to the edge of the icosahedron.\nDrag a blue strut in the +Y direction from the most recently added ball, having that length.\nGenerate a ball at the midpoint of that strut.\nUse the midpoint and the ball at the bottom of that strut to make a translation tool to move in the -Y direction by half the length of that strut.", + "view": { + "position": { + "x": 0, + "y": 0, + "z": 25.15612635481111 + }, + "width": 12.578063177405555, + "perspective": true, + "fieldOfView": 28.072486935852954, + "viewDistance": 25.15612635481111, + "farClipDistance": 50.31225270962222, + "lookAtPoint": { + "x": 0, + "y": 0, + "z": 0 + }, + "nearClipDistance": 2.5156126354811112, + "lookDirection": { + "x": 0, + "y": 0, + "z": -1 + }, + "stereo": false, + "upDirection": { + "x": 0, + "y": 1, + "z": 0 + } + }, + "snapshot": 6 + }, + { + "title": "Translate tetrahedron edge", + "content": "Use \"select collinear\" on the most recently built strut to select it, its two end points and its midpoint.\nApply the translation tool created in the previous step to move it in the -Y direction.", + "view": { + "position": { + "x": 0, + "y": 0, + "z": 25.15612635481111 + }, + "width": 12.578063177405555, + "perspective": true, + "fieldOfView": 28.072486935852954, + "viewDistance": 25.15612635481111, + "farClipDistance": 50.31225270962222, + "lookAtPoint": { + "x": 0, + "y": 0, + "z": 0 + }, + "nearClipDistance": 2.5156126354811112, + "lookDirection": { + "x": 0, + "y": 0, + "z": -1 + }, + "stereo": false, + "upDirection": { + "x": 0, + "y": 1, + "z": 0 + } + }, + "snapshot": 7 + }, + { + "title": "Generate tetrahedron", + "content": "Select the most recently moved strut and the nearest (blue) edge of the icosahedren.\nMake a convex hull having struts only (no panels yet).", + "view": { + "position": { + "x": 0, + "y": 0, + "z": 25.15612635481111 + }, + "width": 12.578063177405555, + "perspective": true, + "fieldOfView": 28.072486935852954, + "viewDistance": 25.15612635481111, + "farClipDistance": 50.31225270962222, + "lookAtPoint": { + "x": 0, + "y": 0, + "z": 0 + }, + "nearClipDistance": 2.5156126354811112, + "lookDirection": { + "x": 0, + "y": 0, + "z": -1 + }, + "stereo": false, + "upDirection": { + "x": 0, + "y": 1, + "z": 0 + } + }, + "snapshot": 8 + }, + { + "title": "Remove tetrahedron scafolding", + "content": "Delete the strut between the midpoints of the tetrahedron's edges and the two balls at its ends.", + "view": { + "position": { + "x": 0, + "y": 0, + "z": 25.15612635481111 + }, + "width": 12.578063177405555, + "perspective": true, + "fieldOfView": 28.072486935852954, + "viewDistance": 25.15612635481111, + "farClipDistance": 50.31225270962222, + "lookAtPoint": { + "x": 0, + "y": 0, + "z": 0 + }, + "nearClipDistance": 2.5156126354811112, + "lookDirection": { + "x": 0, + "y": 0, + "z": -1 + }, + "stereo": false, + "upDirection": { + "x": 0, + "y": 1, + "z": 0 + } + }, + "snapshot": 9 + }, + { + "title": "Cross product of icosahedron face", + "content": "Select the three vertices of the icosahedron face where the tetrahedron will eventually attach to it. Select the one that's at the bottom (on the X=0 plane) first, then move counterclockwise around the triangle.\nApply the cross product tool.", + "view": { + "position": { + "x": 0, + "y": 0, + "z": 25.15612635481111 + }, + "width": 12.578063177405555, + "perspective": true, + "fieldOfView": 28.072486935852954, + "viewDistance": 25.15612635481111, + "farClipDistance": 50.31225270962222, + "lookAtPoint": { + "x": 0, + "y": 0, + "z": 0 + }, + "nearClipDistance": 2.5156126354811112, + "lookDirection": { + "x": 0, + "y": 0, + "z": -1 + }, + "stereo": false, + "upDirection": { + "x": 0, + "y": 1, + "z": 0 + } + }, + "snapshot": 10 + }, + { + "title": "Cross product of tetrahedron face", + "content": "Select the three vertices of the tetrahedron face where the icosahedron will eventually attach to it. As before, select the one that's at the bottom (on the X=0 plane) first, then move counterclockwise around the triangle.\nApply the cross product tool.", + "view": { + "position": { + "x": 0, + "y": 0, + "z": 25.15612635481111 + }, + "width": 12.578063177405555, + "perspective": true, + "fieldOfView": 28.072486935852954, + "viewDistance": 25.15612635481111, + "farClipDistance": 50.31225270962222, + "lookAtPoint": { + "x": 0, + "y": 0, + "z": 0 + }, + "nearClipDistance": 2.5156126354811112, + "lookDirection": { + "x": 0, + "y": 0, + "z": -1 + }, + "stereo": false, + "upDirection": { + "x": 0, + "y": 1, + "z": 0 + } + }, + "snapshot": 11 + }, + { + "title": "Hinge panels", + "content": "Two panels are added, not as part of the construction process, but rather to clarify the purpose of the next step. The next objective is to rotate the tetrahedron around the blue strut so the two panels coincide. A linear map tool wil be used to accomplish that rotation.", + "view": { + "position": { + "x": 0, + "y": 0, + "z": 25.15612635481111 + }, + "width": 12.578063177405555, + "perspective": true, + "fieldOfView": 28.072486935852954, + "viewDistance": 25.15612635481111, + "farClipDistance": 50.31225270962222, + "lookAtPoint": { + "x": 0, + "y": 0, + "z": 0 + }, + "nearClipDistance": 2.5156126354811112, + "lookDirection": { + "x": 0, + "y": 0, + "z": -1 + }, + "stereo": false, + "upDirection": { + "x": 0, + "y": 1, + "z": 0 + } + }, + "snapshot": 12 + }, + { + "title": "Build linear map tool", + "content": "The linear map tool requires 3 struts with a common endpoint as its input or \"from\" vectors. It requires three more struts as it's output or \"to\" vectors, and it requires a ball to represent the origin of the linear map.\n\nIn this case, one of the input vectors is the same as the corresponding output vector, so we need two parallel struts of the same lengths to represent them both. One for the input vector and one for the output. \nThe input and output struts are colored red, green and blue where the input struts and their corresponding output struts are the same color. The origin of the linear mapping is the black ball originally shared by the two cross product struts.\n\nThe red and green input struts are translated to the far side of the icosahedron so they will share a vertex with the parallel blue input strut.\n\nThe three input \"from\" vectors (in order) are the red, green and blue struts having a white ball at their common vertex. The green and blue are parallel to the edges of the tetrahedron's face that we want to rotate, and the red is the \"cross product\" strut that is normal to that same tetrahedron's face.\n\nThe three output \"to\" vectors are selected in the same order. They are the red, green and blue struts with a black ball at their common vertex. The green and blue output struts are on the icosahedron's face onto which we want to rotate. The red output strut is the \"cross product\" strut that is normal to that same icosahedron's face.", + "view": { + "position": { + "x": 0, + "y": 0, + "z": 25.15612635481111 + }, + "width": 12.578063177405555, + "perspective": true, + "fieldOfView": 28.072486935852954, + "viewDistance": 25.15612635481111, + "farClipDistance": 50.31225270962222, + "lookAtPoint": { + "x": 0, + "y": 0, + "z": 0 + }, + "nearClipDistance": 2.5156126354811112, + "lookDirection": { + "x": 0, + "y": 0, + "z": -1 + }, + "stereo": false, + "upDirection": { + "x": 0, + "y": 1, + "z": 0 + } + }, + "snapshot": 13 + }, + { + "title": "Rotate tetrahedron into place", + "content": "Select the edges, vertices abd face of the tetrahedron and apply the linear map tool to rotate it into place.", + "view": { + "position": { + "x": 0, + "y": 0, + "z": 25.15612635481111 + }, + "width": 12.578063177405555, + "perspective": true, + "fieldOfView": 28.072486935852954, + "viewDistance": 25.15612635481111, + "farClipDistance": 50.31225270962222, + "lookAtPoint": { + "x": 0, + "y": 0, + "z": 0 + }, + "nearClipDistance": 2.5156126354811112, + "lookDirection": { + "x": 0, + "y": 0, + "z": -1 + }, + "stereo": false, + "upDirection": { + "x": 0, + "y": 1, + "z": 0 + } + }, + "snapshot": 14 + }, + { + "title": "Remove linear map scaffolding", + "content": "Remove the extra struts that weer used to generate the linear map.", + "view": { + "position": { + "x": 0, + "y": 0, + "z": 25.15612635481111 + }, + "width": 12.578063177405555, + "perspective": true, + "fieldOfView": 28.072486935852954, + "viewDistance": 25.15612635481111, + "farClipDistance": 50.31225270962222, + "lookAtPoint": { + "x": 0, + "y": 0, + "z": 0 + }, + "nearClipDistance": 2.5156126354811112, + "lookDirection": { + "x": 0, + "y": 0, + "z": -1 + }, + "stereo": false, + "upDirection": { + "x": 0, + "y": 1, + "z": 0 + } + }, + "snapshot": 15 + }, + { + "title": "Edges", + "content": "Remove the internal triangular panel and reset the strut colors.", + "view": { + "position": { + "x": 0, + "y": 0, + "z": 25.15612635481111 + }, + "width": 12.578063177405555, + "perspective": true, + "fieldOfView": 28.072486935852954, + "viewDistance": 25.15612635481111, + "farClipDistance": 50.31225270962222, + "lookAtPoint": { + "x": 0, + "y": 0, + "z": 0 + }, + "nearClipDistance": 2.5156126354811112, + "lookDirection": { + "x": 0, + "y": 0, + "z": -1 + }, + "stereo": false, + "upDirection": { + "x": 0, + "y": 1, + "z": 0 + } + }, + "snapshot": 16 + }, + { + "title": "Faces", + "content": "Select all, apply a 3D convex hull, delete all balls and struts. Color the panels to match the Johnson solids web site.", + "view": { + "position": { + "x": 0, + "y": 0, + "z": 25.15612635481111 + }, + "width": 12.578063177405555, + "perspective": true, + "fieldOfView": 28.072486935852954, + "viewDistance": 25.15612635481111, + "farClipDistance": 50.31225270962222, + "lookAtPoint": { + "x": 0, + "y": 0, + "z": 0 + }, + "nearClipDistance": 2.5156126354811112, + "lookDirection": { + "x": 0, + "y": 0, + "z": -1 + }, + "stereo": false, + "upDirection": { + "x": 0, + "y": 1, + "z": 0 + } + }, + "snapshot": 17 + } + ], + "snapshots": [ + [ + { + "shape": "4f7c0515-590f-451c-aadc-e2d05e44a744", + "color": "#FFFFFF", + "position": { + "x": 0, + "y": 0, + "z": 0 + }, + "orientation": 0 + }, + { + "shape": "d90e2b1b-f44d-49ca-9d96-b43bda8a5352", + "color": "#007695", + "position": { + "x": 1.000000015, + "y": 0, + "z": 0 + }, + "orientation": 4 + }, + { + "shape": "367eff9c-ca60-4074-b492-cd274a58b22d", + "color": "#007695", + "position": { + "x": 0, + "y": 0, + "z": 0 + }, + "orientation": 0 + }, + { + "shape": "4f7c0515-590f-451c-aadc-e2d05e44a744", + "color": "#FFFFFF", + "position": { + "x": 1.000000015, + "y": 0, + "z": 1.618033965 + }, + "orientation": 0 + }, + { + "shape": "4f7c0515-590f-451c-aadc-e2d05e44a744", + "color": "#FFFFFF", + "position": { + "x": 1.000000015, + "y": 0, + "z": 0 + }, + "orientation": 0 } - }, - "snapshot" : 10 - }, { - "title" : "Cross product of tetrahedron face", - "content" : "Select the three vertices of the tetrahedron face where the icosahedron will eventually attach to it. As before, select the one that's at the bottom (on the X=0 plane) first, then move counterclockwise around the triangle.\nApply the cross product tool.", - "view" : { - "position" : { - "x" : 12.283063, - "y" : 45.64537, - "z" : 151.80693 - }, - "width" : 71.54824, - "perspective" : true, - "fieldOfView" : 0.44262895, - "viewDistance" : 158.99606, - "farClipDistance" : 317.99213, - "lookAtPoint" : { - "x" : 0.0, - "y" : 0.0, - "z" : 0.0 - }, - "nearClipDistance" : 0.3974902, - "lookDirection" : { - "x" : -0.07725388, - "y" : -0.2870849, - "z" : -0.9547842 - }, - "stereo" : false, - "upDirection" : { - "x" : 0.001990197, - "y" : 0.9576006, - "z" : -0.28809252 + ], + [ + { + "shape": "4f7c0515-590f-451c-aadc-e2d05e44a744", + "color": "#FFFFFF", + "position": { + "x": 1.000000015, + "y": 0, + "z": 0 + }, + "orientation": 0 + }, + { + "shape": "4f7c0515-590f-451c-aadc-e2d05e44a744", + "color": "#FFFFFF", + "position": { + "x": 0, + "y": 1.618033965, + "z": 1.000000015 + }, + "orientation": 0 + }, + { + "shape": "4f7c0515-590f-451c-aadc-e2d05e44a744", + "color": "#FFFFFF", + "position": { + "x": 0, + "y": 0, + "z": 0 + }, + "orientation": 0 + }, + { + "shape": "4f7c0515-590f-451c-aadc-e2d05e44a744", + "color": "#FFFFFF", + "position": { + "x": 1.000000015, + "y": 0, + "z": 1.618033965 + }, + "orientation": 0 + }, + { + "shape": "4f7c0515-590f-451c-aadc-e2d05e44a744", + "color": "#FFFFFF", + "position": { + "x": 1.000000015, + "y": 0, + "z": -1.618033965 + }, + "orientation": 0 + }, + { + "shape": "4f7c0515-590f-451c-aadc-e2d05e44a744", + "color": "#FFFFFF", + "position": { + "x": 0, + "y": -1.618033965, + "z": 1.000000015 + }, + "orientation": 0 + }, + { + "shape": "4f7c0515-590f-451c-aadc-e2d05e44a744", + "color": "#FFFFFF", + "position": { + "x": -1.618033965, + "y": 1.000000015, + "z": 0 + }, + "orientation": 0 + }, + { + "shape": "4f7c0515-590f-451c-aadc-e2d05e44a744", + "color": "#FFFFFF", + "position": { + "x": -1.000000015, + "y": 0, + "z": 1.618033965 + }, + "orientation": 0 + }, + { + "shape": "4f7c0515-590f-451c-aadc-e2d05e44a744", + "color": "#FFFFFF", + "position": { + "x": -1.618033965, + "y": -1.000000015, + "z": 0 + }, + "orientation": 0 + }, + { + "shape": "4f7c0515-590f-451c-aadc-e2d05e44a744", + "color": "#FFFFFF", + "position": { + "x": 0, + "y": 1.618033965, + "z": -1.000000015 + }, + "orientation": 0 + }, + { + "shape": "4f7c0515-590f-451c-aadc-e2d05e44a744", + "color": "#FFFFFF", + "position": { + "x": 1.618033965, + "y": 1.000000015, + "z": 0 + }, + "orientation": 0 + }, + { + "shape": "4f7c0515-590f-451c-aadc-e2d05e44a744", + "color": "#FFFFFF", + "position": { + "x": 0, + "y": -1.618033965, + "z": -1.000000015 + }, + "orientation": 0 + }, + { + "shape": "367eff9c-ca60-4074-b492-cd274a58b22d", + "color": "#007695", + "position": { + "x": 0, + "y": 0, + "z": 0 + }, + "orientation": 0 + }, + { + "shape": "4f7c0515-590f-451c-aadc-e2d05e44a744", + "color": "#FFFFFF", + "position": { + "x": 1.618033965, + "y": -1.000000015, + "z": 0 + }, + "orientation": 0 + }, + { + "shape": "4f7c0515-590f-451c-aadc-e2d05e44a744", + "color": "#FFFFFF", + "position": { + "x": -1.000000015, + "y": 0, + "z": -1.618033965 + }, + "orientation": 0 + }, + { + "shape": "d90e2b1b-f44d-49ca-9d96-b43bda8a5352", + "color": "#007695", + "position": { + "x": 1.000000015, + "y": 0, + "z": 0 + }, + "orientation": 4 } - }, - "snapshot" : 11 - }, { - "title" : "Hinge panels", - "content" : "Two panels are added, not as part of the construction process, but rather to clarify the purpose of the next step. The next objective is to rotate the tetrahedron around the blue strut so the two panels coincide. A linear map tool wil be used to accomplish that rotation.", - "view" : { - "position" : { - "x" : 12.283063, - "y" : 45.64537, - "z" : 151.80693 - }, - "width" : 71.54824, - "perspective" : true, - "fieldOfView" : 0.44262895, - "viewDistance" : 158.99606, - "farClipDistance" : 317.99213, - "lookAtPoint" : { - "x" : 0.0, - "y" : 0.0, - "z" : 0.0 - }, - "nearClipDistance" : 0.3974902, - "lookDirection" : { - "x" : -0.07725388, - "y" : -0.2870849, - "z" : -0.9547842 - }, - "stereo" : false, - "upDirection" : { - "x" : 0.001990197, - "y" : 0.9576006, - "z" : -0.28809252 + ], + [ + { + "shape": "4f7c0515-590f-451c-aadc-e2d05e44a744", + "color": "#FFFFFF", + "position": { + "x": -1.000000015, + "y": 0, + "z": 1.618033965 + }, + "orientation": 0 + }, + { + "shape": "4f7c0515-590f-451c-aadc-e2d05e44a744", + "color": "#FFFFFF", + "position": { + "x": 1.618033965, + "y": 1.000000015, + "z": 0 + }, + "orientation": 0 + }, + { + "shape": "4f7c0515-590f-451c-aadc-e2d05e44a744", + "color": "#FFFFFF", + "position": { + "x": 0, + "y": 1.618033965, + "z": -1.000000015 + }, + "orientation": 0 + }, + { + "shape": "4f7c0515-590f-451c-aadc-e2d05e44a744", + "color": "#FFFFFF", + "position": { + "x": 0, + "y": -1.618033965, + "z": 1.000000015 + }, + "orientation": 0 + }, + { + "shape": "4f7c0515-590f-451c-aadc-e2d05e44a744", + "color": "#FFFFFF", + "position": { + "x": -1.618033965, + "y": 1.000000015, + "z": 0 + }, + "orientation": 0 + }, + { + "shape": "4f7c0515-590f-451c-aadc-e2d05e44a744", + "color": "#FFFFFF", + "position": { + "x": -1.618033965, + "y": -1.000000015, + "z": 0 + }, + "orientation": 0 + }, + { + "shape": "4f7c0515-590f-451c-aadc-e2d05e44a744", + "color": "#FFFFFF", + "position": { + "x": 0, + "y": -1.618033965, + "z": -1.000000015 + }, + "orientation": 0 + }, + { + "shape": "4f7c0515-590f-451c-aadc-e2d05e44a744", + "color": "#FFFFFF", + "position": { + "x": 1.000000015, + "y": 0, + "z": 1.618033965 + }, + "orientation": 0 + }, + { + "shape": "4f7c0515-590f-451c-aadc-e2d05e44a744", + "color": "#FFFFFF", + "position": { + "x": 1.618033965, + "y": -1.000000015, + "z": 0 + }, + "orientation": 0 + }, + { + "shape": "4f7c0515-590f-451c-aadc-e2d05e44a744", + "color": "#FFFFFF", + "position": { + "x": 0, + "y": 1.618033965, + "z": 1.000000015 + }, + "orientation": 0 + }, + { + "shape": "4f7c0515-590f-451c-aadc-e2d05e44a744", + "color": "#FFFFFF", + "position": { + "x": -1.000000015, + "y": 0, + "z": -1.618033965 + }, + "orientation": 0 + }, + { + "shape": "4f7c0515-590f-451c-aadc-e2d05e44a744", + "color": "#FFFFFF", + "position": { + "x": 1.000000015, + "y": 0, + "z": -1.618033965 + }, + "orientation": 0 } - }, - "snapshot" : 12 - }, { - "title" : "Build linear map tool", - "content" : "The linear map tool requires 3 struts with a common endpoint as its input or \"from\" vectors. It requires three more struts as it's output or \"to\" vectors, and it requires a ball to represent the origin of the linear map.\n\nIn this case, one of the input vectors is the same as the corresponding output vector, so we need two parallel struts of the same lengths to represent them both. One for the input vector and one for the output. \nThe input and output struts are colored red, green and blue where the input struts and their corresponding output struts are the same color. The origin of the linear mapping is the black ball originally shared by the two cross product struts.\n\nThe red and green input struts are translated to the far side of the icosahedron so they will share a vertex with the parallel blue input strut.\n\nThe three input \"from\" vectors (in order) are the red, green and blue struts having a white ball at their common vertex. The green and blue are parallel to the edges of the tetrahedron's face that we want to rotate, and the red is the \"cross product\" strut that is normal to that same tetrahedron's face.\n\nThe three output \"to\" vectors are selected in the same order. They are the red, green and blue struts with a black ball at their common vertex. The green and blue output struts are on the icosahedron's face onto which we want to rotate. The red output strut is the \"cross product\" strut that is normal to that same icosahedron's face.", - "view" : { - "position" : { - "x" : 12.283063, - "y" : 45.64537, - "z" : 151.80693 - }, - "width" : 71.54824, - "perspective" : true, - "fieldOfView" : 0.44262895, - "viewDistance" : 158.99606, - "farClipDistance" : 317.99213, - "lookAtPoint" : { - "x" : 0.0, - "y" : 0.0, - "z" : 0.0 - }, - "nearClipDistance" : 0.3974902, - "lookDirection" : { - "x" : -0.07725388, - "y" : -0.2870849, - "z" : -0.9547842 - }, - "stereo" : false, - "upDirection" : { - "x" : 0.001990197, - "y" : 0.9576006, - "z" : -0.28809252 + ], + [ + { + "shape": "4f7c0515-590f-451c-aadc-e2d05e44a744", + "color": "#FFFFFF", + "position": { + "x": -1.618033965, + "y": 1.000000015, + "z": 0 + }, + "orientation": 0 + }, + { + "shape": "4f7c0515-590f-451c-aadc-e2d05e44a744", + "color": "#FFFFFF", + "position": { + "x": 0, + "y": 1.618033965, + "z": -1.000000015 + }, + "orientation": 0 + }, + { + "shape": 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