There exist
only 13 manners to split a cube in tetrahedras built exclusively with the 8
corners of the cube without counting simple rotations und reflections of the
splittings.

Using the
following notation

the splitting can be described
by a list of 4 corner numbers for each tetrahedra.

There are
12 splittings in 6 tetrahedra and one in 5 tetrahedra.

The number
13 is

and number
1 is

The
following is a stereoscopic view of an exploded splitting (No 3)