# Combinatorics of Antiprism Triangulations

@article{Athanasiadis2022CombinatoricsOA, title={Combinatorics of Antiprism Triangulations}, author={Christos A. Athanasiadis and Jan-Marten Brunink and Martina Juhnke-Kubitzke}, journal={Discret. Comput. Geom.}, year={2022}, volume={68}, pages={72-106} }

The antiprism triangulation provides a natural way to subdivide a simplicial complex $\Delta$, similar to barycentric subdivision, which appeared independently in combinatorial algebraic topology and computer science. It can be defined as the simplicial complex of chains of multi-pointed faces of $\Delta$, from a combinatorial point of view, and by successively applying the antiprism construction, or balanced stellar subdivisions, on the faces of $\Delta$, from a geometric point of view.
This…

## 2 Citations

### Face Numbers of Uniform Triangulations of Simplicial Complexes

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A triangulation of a simplicial complex $\Delta $ is said to be uniform if the $f$-vector of its restriction to a face of $\Delta $ depends only on the dimension of that face. This paper proves…

### Triangulations of simplicial complexes and theta polynomials

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. The theta polynomial of a triangulation ∆ of a ball with boundary ∂ ∆ is deﬁned as the diﬀerence of the h -polynomial of ∂ ∆ from the h -polynomial of ∆. A basic theory for the face enumeration of…

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