Geodesic
Non-flat regular polytopes and restrictions on chiral polytopes
Gabe Cunningham1
1University of Massachusetts Boston
The electronic journal of combinatorics, Tome 24 (2017) no. 3
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An abstract polytope is flat if every facet is incident on every vertex. In this paper, we prove that no chiral polytope has flat finite regular facets and finite regular vertex-figures. We then determine the three smallest non-flat regular polytopes in each rank, and use this to show that for $n \geq 8$, a chiral $n$-polytope has at least $48(n-2)(n-2)!$ flags.
DOI : 10.37236/7070
Classification : 52B05, 51M20, 52B15
Mots-clés : abstract regular polytope, chiral polytope, flat polytope, tight polytope

Gabe Cunningham  1

1 University of Massachusetts Boston 
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     title = {Non-flat regular polytopes and restrictions on chiral polytopes},
     journal = {The electronic journal of combinatorics},
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     doi = {10.37236/7070},
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Gabe Cunningham. Non-flat regular polytopes and restrictions on chiral polytopes. The electronic journal of combinatorics, Tome 24 (2017) no. 3. doi: 10.37236/7070

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