lattice_sphere_cmp

$hull(p\in\mathbb{Z}^3, norml2(p)==n)$ for $n\neq 4^a(8b+7)$ is a lattice polyhedron. By Legendre's three-square theorem, such $n$ have representation(s) as the sum of $3$ squares.

After updating lattice_sphere_cmp.js, run make and then open index.html in browser.

You can use last pushed version on github.io:
https://Hermann-sw.github.io/lattice_sphere_cmp

Related question:
https://math.stackexchange.com/questions/4917740/which-faces-does-sphere-lattice-polyhedron-operatornamehullp-in-mathbbz

Analysis output added (#faces/#edges/#vertices) in 3rd last logged line.
In case of cmp="= pq" output of r3(pq) as well (should be same as #vertices).

Dual of lattice sphere (dual vertices determined with small system of 3 linear equations solver for each face):

Experimental:
https://hermann-sw.github.io/lattice_sphere_cmp/tangential_faces.html