Abstract Regular Polytopes of Finite Irreducible Coxeter Groups
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866914351082897408 |
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| author | Chen, Malcolm Hoong Wai Rowley, Peter |
| author_facet | Chen, Malcolm Hoong Wai Rowley, Peter |
| contents | Here, for $W$ the Coxeter group $\mathrm{D}_n$ where $n > 4$, it is proved that the maximal rank of an abstract regular polytope for $W$ is $n - 1$ if $n$ is even and $n$ if $n$ is odd. Further it is shown that $W$ has abstract regular polytopes of rank $r$ for all $r$ such that $3 \leq r \leq n - 1$, if $n$ is even, and $3 \leq r \leq n$, if $n$ is odd. The possible ranks of abstract regular polytopes for the exceptional finite irreducible Coxeter groups are also determined. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_01288 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Abstract Regular Polytopes of Finite Irreducible Coxeter Groups Chen, Malcolm Hoong Wai Rowley, Peter Group Theory Combinatorics 52B11, 20B25, 20F55 Here, for $W$ the Coxeter group $\mathrm{D}_n$ where $n > 4$, it is proved that the maximal rank of an abstract regular polytope for $W$ is $n - 1$ if $n$ is even and $n$ if $n$ is odd. Further it is shown that $W$ has abstract regular polytopes of rank $r$ for all $r$ such that $3 \leq r \leq n - 1$, if $n$ is even, and $3 \leq r \leq n$, if $n$ is odd. The possible ranks of abstract regular polytopes for the exceptional finite irreducible Coxeter groups are also determined. |
| title | Abstract Regular Polytopes of Finite Irreducible Coxeter Groups |
| topic | Group Theory Combinatorics 52B11, 20B25, 20F55 |
| url | https://arxiv.org/abs/2501.01288 |