Acronym gefirdit xethi Name great exofissary retroditetrahedronary hexacositrishecatonicosachoron Circumradius sqrt(2) = 1.414214 General of army hi Colonel of regiment dattady Confer grad tathi   teppix

As abstract polytope gefirdit xethi is isomorphic to gefridit xethi, thereby interchanging the roles of pentagrams and pentagons, resp. replacing gissid by doe and gidtid by sidtid.

Looks like the compound of grad tathi and teppix. Indeed, vertices coincide by 4, edges by 3, and triangles and hexagons each coincide by pairs.

Incidence matrix according to Dynkin symbol

```o3o3x3x5/2*a5/4*c

. . . .           | 2400 |    6    3 |    3    3    3    6 |   1   1   3   3
------------------+------+-----------+---------------------+----------------
. . x .           |    2 | 7200    * |    1    0    1    1 |   1   0   1   1
. . . x           |    2 |    * 3600 |    0    2    0    2 |   0   1   2   1
------------------+------+-----------+---------------------+----------------
o . x .   *a5/4*c |    5 |    5    0 | 1440    *    *    * |   1   0   1   0
o . . x5/2*a      |    5 |    0    5 |    * 1440    *    * |   0   1   1   0
. o3x .           |    3 |    3    0 |    *    * 2400    * |   1   0   0   1
. . x3x           |    6 |    3    3 |    *    *    * 2400 |   0   0   1   1
------------------+------+-----------+---------------------+----------------
o3o3x .   *a5/4*c ♦   20 |   60    0 |   12    0   20    0 | 120   *   *   *
o3o . x5/2*a      ♦   20 |    0   30 |    0   12    0    0 |   * 120   *   *
o . x3x5/2*a5/4*c ♦   60 |   60   60 |   12   12    0   20 |   *   * 120   *
. o3x3x           ♦   12 |   12    6 |    0    0    4    4 |   *   *   * 600
```

```o3o3/2x3x5/3*a5*c

. .   . .         | 2400 |    6    3 |    3    3    3    6 |   1   1   3   3
------------------+------+-----------+---------------------+----------------
. .   x .         |    2 | 7200    * |    1    0    1    1 |   1   0   1   1
. .   . x         |    2 |    * 3600 |    0    2    0    2 |   0   1   2   1
------------------+------+-----------+---------------------+----------------
o .   x .   *a5*c |    5 |    5    0 | 1440    *    *    * |   1   0   1   0
o .   . x5/3*a    |    5 |    0    5 |    * 1440    *    * |   0   1   1   0
. o3/2x .         |    3 |    3    0 |    *    * 2400    * |   1   0   0   1
. .   x3x         |    6 |    3    3 |    *    *    * 2400 |   0   0   1   1
------------------+------+-----------+---------------------+----------------
o3o3/2x .   *a5*c ♦   20 |   60    0 |   12    0   20    0 | 120   *   *   *
o3o   . x5/3*a    ♦   20 |    0   30 |    0   12    0    0 |   * 120   *   *
o .   x3x5/3*a5*c ♦   60 |   60   60 |   12   12    0   20 |   *   * 120   *
. o3/2x3x         ♦   12 |   12    6 |    0    0    4    4 |   *   *   * 600
```

```o3/2o3x3x5/3*a5*c

.   . . .         | 2400 |    6    3 |    3    3    3    6 |   1   1   3   3
------------------+------+-----------+---------------------+----------------
.   . x .         |    2 | 7200    * |    1    0    1    1 |   1   0   1   1
.   . . x         |    2 |    * 3600 |    0    2    0    2 |   0   1   2   1
------------------+------+-----------+---------------------+----------------
o   . x .   *a5*c |    5 |    5    0 | 1440    *    *    * |   1   0   1   0
o   . . x5/3*a    |    5 |    0    5 |    * 1440    *    * |   0   1   1   0
.   o3x .         |    3 |    3    0 |    *    * 2400    * |   1   0   0   1
.   . x3x         |    6 |    3    3 |    *    *    * 2400 |   0   0   1   1
------------------+------+-----------+---------------------+----------------
o3/2o3x .   *a5*c ♦   20 |   60    0 |   12    0   20    0 | 120   *   *   *
o3/2o . x5/3*a    ♦   20 |    0   30 |    0   12    0    0 |   * 120   *   *
o   . x3x5/3*a5*c ♦   60 |   60   60 |   12   12    0   20 |   *   * 120   *
.   o3x3x         ♦   12 |   12    6 |    0    0    4    4 |   *   *   * 600
```

```o3/2o3/2x3x5/2*a5/4*c

.   .   . .           | 2400 |    6    3 |    3    3    3    6 |   1   1   3   3
----------------------+------+-----------+---------------------+----------------
.   .   x .           |    2 | 7200    * |    1    0    1    1 |   1   0   1   1
.   .   . x           |    2 |    * 3600 |    0    2    0    2 |   0   1   2   1
----------------------+------+-----------+---------------------+----------------
o   .   x .   *a5/4*c |    5 |    5    0 | 1440    *    *    * |   1   0   1   0
o   .   . x5/2*a      |    5 |    0    5 |    * 1440    *    * |   0   1   1   0
.   o3/2x .           |    3 |    3    0 |    *    * 2400    * |   1   0   0   1
.   .   x3x           |    6 |    3    3 |    *    *    * 2400 |   0   0   1   1
----------------------+------+-----------+---------------------+----------------
o3/2o3/2x .   *a5/4*c ♦   20 |   60    0 |   12    0   20    0 | 120   *   *   *
o3/2o   . x5/2*a      ♦   20 |    0   30 |    0   12    0    0 |   * 120   *   *
o   .   x3x5/2*a5/4*c ♦   60 |   60   60 |   12   12    0   20 |   *   * 120   *
.   o3/2x3x           ♦   12 |   12    6 |    0    0    4    4 |   *   *   * 600
```