Acronym gadixhix (old: gixhix) Name great dodecahedronary hexacosahemihexacosachoron,compound of 25 ihi (but not sadixhix) Circumradius 1 Coordinates (1, 0, 0, 0)                                         & all permutations, all changes of sign (vertex inscribed q-hex) (1/2, 1/2, 1/2, 1/2)                             & all permutations, all changes of sign (vertex inscribed tes) ((1+sqrt(5))/4, (sqrt(5)-1)/4, 1/4, 0)   & all even permutations, all changes of sign (vertex inscribed v-sadi) General of army ex Colonel of regiment sishi

Gadixhix and sadixhix both are built from the same components, but within different relative orientations.

Gadixhix occurs in 2 different forms depending on whether the vertices (coincident by 5) will be counted separately (type A), or will be identified (type B).

Incidence matrix

```(Type A)

600 |    8 |   12   12 |   6   6 ||  1
-----+------+-----------+---------++---
2 | 2400 |    3    3 |   3   3 ||  1
-----+------+-----------+---------++---
3 |    3 | 2400    * |   1   1 ||  1
4 |    4 |    * 1800 |   1   1 ||  1
-----+------+-----------+---------++---
♦  6 |   12 |    4    3 | 600   * ||  1
♦ 12 |   24 |    8    6 |   * 300 ||  1
-----+------+-----------+---------++---
♦ 24 |   96 |   96   72 |  24  12 || 25
```

```(Type B)

120 |   40 |   48   48 |  30  30 ||  5
-----+------+-----------+---------++---
2 | 2400 |    3    3 |   3   3 ||  1
-----+------+-----------+---------++---
3 |    3 | 2400    * |   1   1 ||  1
4 |    4 |    * 1800 |   1   1 ||  1
-----+------+-----------+---------++---
♦  6 |   12 |    4    3 | 600   * ||  1
♦ 12 |   24 |    8    6 |   * 300 ||  1
-----+------+-----------+---------++---
♦ 24 |   96 |   96   72 |  24  12 || 25
```