Can we count number of Regular tetrahedrons formed out of Unit cube?
If vertices of Unit cube are taken as $(0,0,0,)$, $(0,0,1)$, $(0,1,1)$, $(0,1,0)$, $(1,0,0)$, $(1,0,1)$, $(1,1,1)$ and $(1,1,0)$
I have seen a post where any four vertices satisfying $x \le y \le z$ forms a Regular Tetrahedron.
But if i choose vertices as $(0,0,0)$, $(1,1,1)$,$(0,0,1)$,$(0, 1,1)$
will it form Regular tet?
Can i know any logical way to choose vertices of cube to form Tet?