On the realization space of the cube
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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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Journal | Journal of the European Mathematical Society |
Volume | 26 |
Issue number | 1 |
Pages (from-to) | 261-273 |
ISSN | 1435-9855 |
DOIs | |
Publication status | Published - 2024 |
Bibliographical note
Publisher Copyright:
© 2023 European Mathematical Society.
- connected sum, Cubical polytopes, face numbers, realization space
Research areas
ID: 390929681