This group consists of the following 15 tetrahedrons.

(1) (2) |
(41) (42) |
(4141) (4242) |
(14141)* (24141) (24241) (14142) (14242) (24242)* |
(414141)** (424141) (424241) (414142) (414242) (424242)** |

* all these matrices are the same as (4) so only one is counted

** all these matrices are the identity matrix so none are counted

A projection of this shape onto a plane follows.