2 problems

A $d$-dimensional simplex is the convex hull of $d+1$ affinely independent points. A simplex is a $k$-reptile if it can be dissected into $k$ smaller simplices, each similar to the…

Let $d\geq 3$, let $k$ be a positive integer, and let a $d$-dimensional $k$-reptile simplex be a $d$-dimensional simplex that can be dissected into $k$ smaller simplices similar to…