Abstract
We prove that the realization space of the d-dimensional cube is contractible. For this we first show that any two realizations are connected by a finite sequence of projective transformations and normal transformations. As an application we use this fact to define an analog of the connected sum construction for cubical d-polytopes, and apply this construction to certain cubical d-polytopes to conclude that the rays spanned by f -vectors of cubical d-polytopes are dense in Adin's cone. The connectivity result on cubes extends to any product of simplices, and further it shows that the respective realization spaces are contractible.
Original language | English |
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Pages (from-to) | 261-273 |
Number of pages | 13 |
Journal | Journal of the European Mathematical Society |
Volume | 26 |
Issue number | 1 |
DOIs | |
State | Published - 1 Jan 2024 |
Externally published | Yes |
Keywords
- Cubical polytopes
- connected sum
- face numbers
- realization space
ASJC Scopus subject areas
- General Mathematics
- Applied Mathematics