2 papers
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.CO2016
Open problems on k-orbit polytopes
Gabe Cunningham, Daniel Pellicer
We present 35 open problems on combinatorial, geometric and algebraic aspects of k-orbit abstract polytopes. We also present a theory of rooted polytopes that has appeared implicit…