This group of tetrahedrons includes all paths of four steps or less that start in three of the four directions and do not have equal length paths that step in the fourth direction for the first two steps. All five step paths of the same type are included that end with a smaller tetrahedron than the largest four step path (4321). The starting tetrahedron is not included in this shape. This produces 69 different tetrahedrons. The matrices in this shape are as follows.

(1) (2) (3) |
(21) (31) (12) (32) (13) (23) |
(121) (321) (421) (131) (231) (431) (312) (412) (132) (232) (432) (213) (413) (123) (423) |
(3121) (4121) (1321) (2321) (4321) (1421) (3421) (2131) (4131) (1231) (4231) (1431) (2431) (1312) (2312) (4312) (2412) (3412) (2132) (4132) (1232) (4232) (1432) (2432) (1213) (3213) (4213) (2413) (3413) (3123) (4123) (1423) (3423) |
(13121) (23121) (14121) (24121) (12131) (32131) (14131) (34131) (12132) (31232) (24232) (34232) |

The sum of all the matrices used to generate this shape is

21 33 33 33 0 |
33 21 33 33 0 |
33 33 21 33 0 |
153 153 153 135 0 |
-171 -171 -171 -171 69 |

The sum of columns is (120 120 120 594 -954)

The sum of products is 3*14400+3*71280 = 4257040

The volume ratio is sqrt(257040/6) = 206.978

The mass ratio of a mu lepton to an electron is 206.768

A projection of this shape onto a plane follows.

A projection of this shape from the other side follows.