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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 …
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 …
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 …