Simplexity of the n-cube ★★★


Question   What is the minimum cardinality of a decomposition of the $ n $-cube into $ n $-simplices?

Keywords: cube; decomposition; simplex

Cube-Simplex conjecture ★★★

Author(s): Kalai

Conjecture   For every positive integer $ k $, there exists an integer $ d $ so that every polytope of dimension $ \ge d $ has a $ k $-dimensional face which is either a simplex or is combinatorially isomorphic to a $ k $-dimensional cube.

Keywords: cube; facet; polytope; simplex

Syndicate content