On the realization space of the cube

Karim Adiprasito, Daniel Kalmanovich, Eran Nevo

Research output: Contribution to journalArticlepeer-review


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 the respective realization spaces are contractible.

Original languageAmerican English
Article number80
JournalSeminaire Lotharingien de Combinatoire
Issue number84
StatePublished - 2020

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  • connected sum
  • cube
  • f-vector
  • polytope
  • realization space


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