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6 votes
Accepted

Regularity of Delaunay triangulation of a hypercube

"Finally my question is: how to triangulate a hypercube resembling (B)?" This is easy to do, and is normally called the "standard triangulation" of the $n$-cube. Consider all the monotone edge paths …
Francisco Santos's user avatar
3 votes
Accepted

Dehn-Sommerville relations for $\Delta$-complexes

I think the answer is yes and the following is a sketch of proof: The second barycentric subdivision of a $\Delta$-complex is a triangulation. The f-vector of a $\Delta$-complex and of its barycentr …
Francisco Santos's user avatar
5 votes

Which (semi)regular polyhedra are combinations of two others?

I think the whole list of Gjiergji (and lightly more, see below) follows from Wythoffian operations. For the cube-octahedron family, for example, consider the following diagram: The polyhedron along a …
Francisco Santos's user avatar