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<h4>Warm Up Activity</h4>
<p>In an earlier lesson, you saw the equation \( V + F - 2 = E \), which relates the number of vertices, faces, and edges in a Platonic solid.<br></p>
<p>In questions 1 - 2, write an equation that makes it easier to find the number of vertices in each of the Platonic solids described:</p>
<!--Q1-->
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="e7c21dc8-bcc0-4c6e-ad01-3e6201f40203" data-fire-event="eventShow" data-schema-version="1.0">
<div class="os-raise-ib-input-content">
<ol class="os-raise-noindent">
<li>An octahedron (shown here), which has 8 faces</li>
</ol>
<img alt="Three dimensonal octahedron. Two triangular pyramids joined at rectangular bases. " class="h-max-height--6-lines" height="156" src="https://k12.openstax.org/contents/raise/resources/f423d901280c52353b8777700a16bde267ef4ffa" width="156">
<br>
<br>
</div>
<div class="os-raise-ib-input-prompt">
Enter your answer here:
</div>
<div class="os-raise-ib-input-ack">
<p>Compare your answer: \(V=E-6\)</p>
<p>
\(V+8−2=E\)<br>
\(V+6=E\)<br>
\(V=E-6\)</p>
</div>
</div>
<!--Interaction End -->
<br>
<!--Q2-->
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="e5dd4a7d-ae92-42b7-b0a6-7c2a79491575" data-fire-event="eventShow" data-schema-version="1.0">
<div class="os-raise-ib-input-content">
<ol class="os-raise-noindent" start="2">
<li>An icosahedron, which has 30 edges</li>
</ol>
</div>
<div class="os-raise-ib-input-prompt">
Enter your answer here:
</div>
<div class="os-raise-ib-input-ack">
<p>Compare your answer: \(V=32-F\)</p>
<p>
\(V+F−2=30\)<br>
\(V+F−2+2=30+2\)<br>
\(V+F=32\)<br>
\(F=32-F\)
</p>
</div>
</div>
<!--Interaction End -->
<br>
<!--Q3-->
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="0f5f9404-82a4-4040-8d28-1ab541b24a84" data-fire-event="eventShow" data-schema-version="1.0">
<div class="os-raise-ib-input-content">
<ol class="os-raise-noindent" start="3">
<li>A Buckminsterfullerene (also called a “Buckyball”) is a polyhedron with 60 vertices. It is not a
Platonic solid, but the numbers of faces, edges, and vertices are related the same way as those in a Platonic
solid.<br><br>
Write an equation that makes it easier to find the number of faces a Buckyball has if we know how many edges it
has.</li>
</ol>
</div>
<div class="os-raise-ib-input-prompt">
Enter your answer:
</div>
<div class="os-raise-ib-input-ack">
<p>Compare your answer: \(F=E−58\)</p>
<p>
\(V+F−2=E\)<br>
\(60+F−2=E\)<br>
\(58+F=E\)<br>
\(58-58+F=E-58\)<br>
\(F=E-58\)<br>
</p>
</div>
</div>
<!--Interaction End -->
<br>
<div class="os-raise-student-reflection">
<p class="os-raise-student-reflection-title">Why Should I Care?</p>
<img src="https://k12.openstax.org/contents/raise/resources/8ee23d673070e7f50b696be19d4071f9b88d8119" width="300px"/>
<p>Alex's brother can use algebra to budget his paycheck from his job at a pizza place. He uses some money for food, some for going out with his friends, and some, he saves for college.</p>
<p>If he uses variables to represent the different ways he uses his money, he can put those variables into an equation to make sure he has enough money to last until his next paycheck.</p>
</div>