On the realization space of the cube
Combinatorics
2019-12-23 v1
Abstract
We consider the realization space of the -dimensional cube, and show that any two realizations are connected by a finite sequence of projective transformations and normal transformations. We use this fact to define an analog of the connected sum construction for cubical -polytopes, and apply this construction to certain cubical -polytopes to conclude that the rays spanned by -vectors of cubical -polytopes are dense in Adin's cone. The connectivity result on cubes extends to any product of simplices, and further, it shows the respective realization spaces are contractible.
Cite
@article{arxiv.1912.09554,
title = {On the realization space of the cube},
author = {Karim Adiprasito and Daniel Kalmanovich and Eran Nevo},
journal= {arXiv preprint arXiv:1912.09554},
year = {2019}
}