Splitting a cube in tetrahedras


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)