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

Voir la notice de l'article provenant de la source The Electronic Journal of Combinatorics website

Zbl arXiv
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 
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
@article{10_37236_7070,
     author = {Gabe Cunningham},
     title = {Non-flat regular polytopes and restrictions on chiral polytopes},
     journal = {The electronic journal of combinatorics},
     year = {2017},
     volume = {24},
     number = {3},
     doi = {10.37236/7070},
     zbl = {1372.52013},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/7070/}
}
TY  - JOUR
AU  - Gabe Cunningham
TI  - Non-flat regular polytopes and restrictions on chiral polytopes
JO  - The electronic journal of combinatorics
PY  - 2017
VL  - 24
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.37236/7070/
DO  - 10.37236/7070
ID  - 10_37236_7070
ER  - 
%0 Journal Article
%A Gabe Cunningham
%T Non-flat regular polytopes and restrictions on chiral polytopes
%J The electronic journal of combinatorics
%D 2017
%V 24
%N 3
%U http://geodesic.mathdoc.fr/articles/10.37236/7070/
%R 10.37236/7070
%F 10_37236_7070

Cité par Sources :