Wythoff polytopes
The Wythoff construction takes a non-necessarily convex n-dimensional polytope P, a non-empty subset S of {0,...,n} and returns another n-dimensional polytope W(P,S). Particular cases are duality, medial polytope, clique clomplex, ... We determined a conjecturally complete list of polytopes W(P,S) that are L1-embeddable for P a regular polytope. The Wythoff construction was also used to compute the third homology group of the Mathieu group M24.