An edge of a triangulated manifold is said to be contractible if it may be contracted to a vertex without modifying the topological type of the underlying manifold. Otherwise, the …

I hope this is not too trivial for this forum. I was wondering if someone has come across this polytope. You start with the rhombic dodecahedron, subdivide it into four parallelle …

Suppose $P$ is a convex lattice polytope in $Z^3$ without interior lattice points, and we require the interior lattice points of each facet(i.e. dimensional 2 faces) are neither to …

When considering classification problems about polytopes, I sometimes has the feeling that one need to talk about certain parametrized families, i.e. moduli space of such polytopes …

Is there a known algorithm which, given a finite multiset (unordered list) of integers $A$, returns a yes/no answer for "Is there a polyhedron such that the multiset of areas of a …

The following question might be elementary — it is too far from my area of expertise to tell. It has shown up in my research in an interesting way, which I will not go into here, …

Can someone help me solve the following question please? Let v be a vertex of a d-polytope P such that $ 0 \in intP $ . Prove that $ P^* \cap \{ y \in \mathbb{R}^d \mid\left &l …

I want to construct Birkohoff Polytopes for which the volume is known in Matlab. How can I construct so?

Here is a variation on the classical polygon illumination problem. For $c \geq 0$ we say that a mirror has reflection index $c$ if whenever a ray hits the mirror with angle of inci …

I have a binary space partitioning (BSP) tree which recursively partitions a hypercube using linear hyperplanes. That is, a hyperplane splits the hybercube in half, creating two co …

In the plane, the exterior angle of a vertex is $\pi -$ the standard ("interior") angle, which may be negative in some cases. The following is true for non-weird polygons: The …

Hamiltonian cycles (seen as spanning polygons) are interesting for several reasons (only a few of which I am aware of), but especially because not every connected graph has a Hamil …

Sometimes a point set in Euclidean space may have a shadow with an unexpected symmetry. The purpose here is to ask when this happens or when it doesn't happen (in some generality) …