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Results tagged with convex-polytopes
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user 5010
Convex polytopes are the convex hulls of a finite set of points in Euclidean spaces. They have rich combinatorial, arithmetic, and metrical theory, and are related to toric varieties and to linear programming
54
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5
answers
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Unusual symmetries of the Cayley-Menger determinant for the volume of tetrahedra
Suppose you have a tetrahedron $T$ in Euclidean space with edge lengths $\ell_{01}$, $\ell_{02}$, $\ell_{03}$, $\ell_{12}$, $\ell_{13}$, and $\ell_{23}$. Now consider the tetrahedron $T'$ with edge le …
- 12.9k
5
votes
1
answer
271
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Is every triangulation of a Euclidean ball by convex tetrahedra shellable?
Suppose you are given a 3-ball $B$ in $\mathbb{R}^3$ that is bounded by a PL sphere, a triangulation $T$ of $B$ by Euclidean tetrahedra. Is that triangulation necessarily shellable?
I know that if $ …
- 15.5k
7
votes
4-polytope with vertices at the binary octahedral group
I just came across this old question, which I happened to think about earlier. Let me give a more explicit description. As you noted, the binary tetrahedral group forms the vertices of a 24-cell. The …
- 10.1k