Q:

dissecting a hypercube to simplexes

I read that an n-cube (hypercube) can be dissected into $n!$ n-simplexes.  In case of 2D, I can see that a square can be dissected into two 2-simplexes (traingles).  Incase of cube, how we can fit six, tetrahedron inside it ?

A:

Please see also this YouTube video: https://www.youtube.com/watch?v=ffnVCEAcOns

