This group of tetrahedrons is generated as follows. Start with a single tetrahedron. Include three of the four nearest tetrahedrons. From these three tetrahedrons step in the fourth direction to produce three more tetrahedrons. Repeat this pattern until the original tetrahedron is generated. This takes six steps and produces 74 different tetrahedrons. The matrices in this shape are as follows.

I |
(1) (2) (3) |
(41) (42) (43) |
(141) (241) (341) (142) (242) (342) (143) (243) (343) |
(4141) (4241) (4341) (4142) (4242) (4342) (4143) (4243) (4343) |
(14141)* (24141) (34141) (14241) (24241) (34241) (14341) (24341) (34341) (14142) (24142) (34142) (14242) (24242)* (34242) (14342) (24342) (34342) (14143) (24143) (34143) (14243) (34243) (34243) (14343) (24343) (34343)* |
(414141)** (424141) (434141) (414241) (424241) (434241) (414341) (424341) (434341) (414142) (424142) (434142) (414242) (424242)** (434242) (414342) (424342) (434342) (414143) (424143) (434143) (414243) (434243) (434243) (414343) (424343) (434343)** |

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

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

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

64 68 68 100 0 |
68 64 68 100 0 |
68 68 64 100 0 |
44 44 44 66 0 |
-170 -170 -170 -292 74 |

The sum of columns is (300 300 300 198 –1098)

The sum of products is 3*90000+3*59400 = 448200

The volume ratio is sqrt(448200/6) = 273.313

The mass ratio of a charged pi meson to an electron is 273.132

A projection of this shape onto a plane follows.