Acronym gefidtethi Name great exofissary ditetrahedronary tetrakishecatonicosachoron Circumradius sqrt[3-sqrt(5)] = 0.874032 General of army hi Colonel of regiment gadtaxady Confer gardatathi   gitphi

As abstract polytope gefidtethi is isomorphic to sefidtethi, thereby interchanging the roles of pentagrams and pentagons, and replacing the decagrams by decagons, resp. replacing gissid by doe, quit sissid by tigid, gaddid by saddid, and gidtid by sidtid.

Looks like a compound of gitphi and gardatathi.

Incidence matrix according to Dynkin symbol

```x5/3x5/2o3o5/4*a3*c

.   .   . .         | 2400 |    6    3 |    6    3    3    3 |   3   3   1   1
--------------------+------+-----------+---------------------+----------------
x   .   . .         |    2 | 7200    * |    1    1    1    0 |   1   1   1   0
.   x   . .         |    2 |    * 3600 |    2    0    0    2 |   2   1   0   1
--------------------+------+-----------+---------------------+----------------
x5/3x   . .         |   10 |    5    5 | 1440    *    *    * |   1   1   0   0
x   .   o .   *a3*c |    3 |    3    0 |    * 2400    *    * |   1   0   1   0
x   .   . o5/4*a    |    5 |    5    0 |    *    * 1440    * |   0   1   1   0
.   x5/2o .         |    5 |    0    5 |    *    *    * 1440 |   1   0   0   1
--------------------+------+-----------+---------------------+----------------
x5/3x5/2o .   *a3*c ♦   60 |   60   60 |   12   20    0   12 | 120   *   *   *
x5/3x   . o5/4*a    ♦   60 |   60   30 |   12    0   12    0 |   * 120   *   *
x   .   o3o5/4*a3*c ♦   20 |   60    0 |    0   20   12    0 |   *   * 120   *
.   x5/2o3o         ♦   20 |    0   30 |    0    0    0   12 |   *   *   * 120
```

```x5/3x5/2o3/2o5*a3*c

.   .   .   .       | 2400 |    6    3 |    6    3    3    3 |   3   3   1   1
--------------------+------+-----------+---------------------+----------------
x   .   .   .       |    2 | 7200    * |    1    1    1    0 |   1   1   1   0
.   x   .   .       |    2 |    * 3600 |    2    0    0    2 |   2   1   0   1
--------------------+------+-----------+---------------------+----------------
x5/3x   .   .       |   10 |    5    5 | 1440    *    *    * |   1   1   0   0
x   .   o   . *a3*c |    3 |    3    0 |    * 2400    *    * |   1   0   1   0
x   .   .   o5*a    |    5 |    5    0 |    *    * 1440    * |   0   1   1   0
.   x5/2o   .       |    5 |    0    5 |    *    *    * 1440 |   1   0   0   1
--------------------+------+-----------+---------------------+----------------
x5/3x5/2o   . *a3*c ♦   60 |   60   60 |   12   20    0   12 | 120   *   *   *
x5/3x   .   o5*a    ♦   60 |   60   30 |   12    0   12    0 |   * 120   *   *
x   .   o3/2o5*a3*c ♦   20 |   60    0 |    0   20   12    0 |   *   * 120   *
.   x5/2o3/2o       ♦   20 |    0   30 |    0    0    0   12 |   *   *   * 120
```

```x5/3x5/3o3o5*a3/2*c

.   .   . .         | 2400 |    6    3 |    6    3    3    3 |   3   3   1   1
--------------------+------+-----------+---------------------+----------------
x   .   . .         |    2 | 7200    * |    1    1    1    0 |   1   1   1   0
.   x   . .         |    2 |    * 3600 |    2    0    0    2 |   2   1   0   1
--------------------+------+-----------+---------------------+----------------
x5/3x   . .         |   10 |    5    5 | 1440    *    *    * |   1   1   0   0
x   .   o . *a3/2*c |    3 |    3    0 |    * 2400    *    * |   1   0   1   0
x   .   . o5*a      |    5 |    5    0 |    *    * 1440    * |   0   1   1   0
.   x5/3o .         |    5 |    0    5 |    *    *    * 1440 |   1   0   0   1
--------------------+------+-----------+---------------------+----------------
x5/3x5/3o . *a3/2*c ♦   60 |   60   60 |   12   20    0   12 | 120   *   *   *
x5/3x   . o5*a      ♦   60 |   60   30 |   12    0   12    0 |   * 120   *   *
x   .   o3o5*a3/2*c ♦   20 |   60    0 |    0   20   12    0 |   *   * 120   *
.   x5/3o3o         ♦   20 |    0   30 |    0    0    0   12 |   *   *   * 120
```

```x5/3x5/3o3/2o5/4*a3/2*c

.   .   .   .           | 2400 |    6    3 |    6    3    3    3 |   3   3   1   1
------------------------+------+-----------+---------------------+----------------
x   .   .   .           |    2 | 7200    * |    1    1    1    0 |   1   1   1   0
.   x   .   .           |    2 |    * 3600 |    2    0    0    2 |   2   1   0   1
------------------------+------+-----------+---------------------+----------------
x5/3x   .   .           |   10 |    5    5 | 1440    *    *    * |   1   1   0   0
x   .   o   .   *a3/2*c |    3 |    3    0 |    * 2400    *    * |   1   0   1   0
x   .   .   o5/4*a      |    5 |    5    0 |    *    * 1440    * |   0   1   1   0
.   x5/3o   .           |    5 |    0    5 |    *    *    * 1440 |   1   0   0   1
------------------------+------+-----------+---------------------+----------------
x5/3x5/3o   .   *a3/2*c ♦   60 |   60   60 |   12   20    0   12 | 120   *   *   *
x5/3x   .   o5/4*a      ♦   60 |   60   30 |   12    0   12    0 |   * 120   *   *
x   .   o3/2o5/4*a3/2*c ♦   20 |   60    0 |    0   20   12    0 |   *   * 120   *
.   x5/3o3/2o           ♦   20 |    0   30 |    0    0    0   12 |   *   *   * 120
```