M. Mixer

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20112026

most citedHighest rank of a polytope for

A_{n}

31 citations · 32 across the 8 of their papers we have counts for

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6 papers · 1 filter

math.GR2026

Representing alternating groups as self-dual string C-groups of high rank

Gabe Cunningham, Mark Mixer

The highest rank of a string C-group representation of the alternating group $A_{n}$ is known for each $n$ , but no self-dual representations attaining this highest rank are known whe…

math.GR2019

The ranks of alternating string C-groups

Mark Mixer

In this paper, string C-groups of all ranks $3 \leq r \leq \frac{n}{2}$ are provided for each alternating group $A_{n}$ , $n \geq 12$ . As the string C-group representations of $A_{n}$ h…

math.GR2018

Archimedean toroidal maps and their minimal almost regular covers

Kostiantyn Drach, Yurii Haidamaka, Mark Mixer +1

The automorphism group of a map acts naturally on its flags (triples of incident vertices, edges, and faces). An Archimedean map on the torus is called almost regular if it has as…

math.GR2016

Internal and external duality in abstract polytopes

Gabe Cunningham, Mark Mixer

We define an abstract regular polytope to be internally self-dual if its self-duality can be realized as one of its symmetries. This property has many interesting implications on t…

math.GR2016★ 31 cited

Highest rank of a polytope for $A_{n}$

Peter J. Cameron, Maria Elisa Fernandes, Dimitri Leemans +1

We prove that the highest rank of a string C-group constructed from an alternating group $A l t_{n}$ is 0 if $n = 3, 4, 6, 7, 8$ ; 3 if $n = 5$ ; 4 if $n = 9$ ; 5 if $n = 10$ ; 6 if $n = 11$ ; and $\…

math.GR2014★ 1 cited

String C-groups as transitive subgroups of Sym(n)