Simplexity of the n-cube ★★★


\begin{question} What is the minimum cardinality of a decomposition of the $n$-cube into $n$-simplices? \end{question}

Keywords: cube; decomposition; simplex

Cube-Simplex conjecture ★★★

Author(s): Kalai

\begin{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. \end{conjecture}

Keywords: cube; facet; polytope; simplex

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