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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 is known for each , but no self-dual representations attaining this highest rank are known whe…
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…