As abstract polytope gefdit dixdy is isomorphic to sefdit dixdy, thereby replacing pentagons by pentagrams, resp. id by gid and giid by siid.

This polychoron is exotic, as 2 classes of triangles coincide pairwise. Also the edges coincide pairwise. It also is fissary, as its vertices coincide by 3. In fact, each vertex figure is kind a x2x || x2f, linked diametrically by edges of length u.

This polychoron can be obtained as blend of gaddit thix with todtixhi, blending out their ri. Alternatively it can be obtained as blend of giddit thix with stodatixhi, blending out their siddy.

Incidence matrix according to Dynkin symbol

x3o3/2x3o5/4*a3*c

. .   . .         | 3600 |    4    4 |    2    4    2    2    2 |   2   1   2   1
------------------+------+-----------+--------------------------+----------------
x .   . .         |    2 | 7200    * |    1    1    1    0    0 |   1   1   1   0
. .   x .         |    2 |    * 7200 |    0    1    0    1    1 |   1   0   1   1
------------------+------+-----------+--------------------------+----------------
x3o   . .         |    3 |    3    0 | 2400    *    *    *    * |   1   1   0   0
x .   x .   *a3*c |    6 |    3    3 |    * 2400    *    *    * |   1   0   1   0
x .   . o5/4*a    |    5 |    5    0 |    *    * 1440    *    * |   0   1   1   0
. o3/2x .         |    3 |    0    3 |    *    *    * 2400    * |   1   0   0   1
. .   x3o         |    3 |    0    3 |    *    *    *    * 2400 |   0   0   1   1
------------------+------+-----------+--------------------------+----------------
x3o3/2x .   *a3*c ♦   12 |   12   12 |    4    4    0    4    0 | 600   *   *   *
x3o   . o5/4*a    ♦   30 |   60    0 |   20    0   12    0    0 |   * 120   *   *
x .   x3o5/4*a3*c ♦   60 |   60   60 |    0   20   12    0   20 |   *   * 120   *
. o3/2x3o         ♦    6 |    0   12 |    0    0    0    4    4 |   *   *   * 600

x3o3/2x3/2o5*a3*c

. .   .   .       | 3600 |    4    4 |    2    4    2    2    2 |   2   1   2   1
------------------+------+-----------+--------------------------+----------------
x .   .   .       |    2 | 7200    * |    1    1    1    0    0 |   1   1   1   0
. .   x   .       |    2 |    * 7200 |    0    1    0    1    1 |   1   0   1   1
------------------+------+-----------+--------------------------+----------------
x3o   .   .       |    3 |    3    0 | 2400    *    *    *    * |   1   1   0   0
x .   x   . *a3*c |    6 |    3    3 |    * 2400    *    *    * |   1   0   1   0
x .   .   o5*a    |    5 |    5    0 |    *    * 1440    *    * |   0   1   1   0
. o3/2x   .       |    3 |    0    3 |    *    *    * 2400    * |   1   0   0   1
. .   x3/2o       |    3 |    0    3 |    *    *    *    * 2400 |   0   0   1   1
------------------+------+-----------+--------------------------+----------------
x3o3/2x   . *a3*c ♦   12 |   12   12 |    4    4    0    4    0 | 600   *   *   *
x3o   .   o5*a    ♦   30 |   60    0 |   20    0   12    0    0 |   * 120   *   *
x .   x3/2o5*a3*c ♦   60 |   60   60 |    0   20   12    0   20 |   *   * 120   *
. o3/2x3/2o       ♦    6 |    0   12 |    0    0    0    4    4 |   *   *   * 600

x3/2o3x3o5/4*a3*c

.   . . .         | 3600 |    4    4 |    2    4    2    2    2 |   2   1   2   1
------------------+------+-----------+--------------------------+----------------
x   . . .         |    2 | 7200    * |    1    1    1    0    0 |   1   1   1   0
.   . x .         |    2 |    * 7200 |    0    1    0    1    1 |   1   0   1   1
------------------+------+-----------+--------------------------+----------------
x3/2o . .         |    3 |    3    0 | 2400    *    *    *    * |   1   1   0   0
x   . x .   *a3*c |    6 |    3    3 |    * 2400    *    *    * |   1   0   1   0
x   . . o5/4*a    |    5 |    5    0 |    *    * 1440    *    * |   0   1   1   0
.   o3x .         |    3 |    0    3 |    *    *    * 2400    * |   1   0   0   1
.   . x3o         |    3 |    0    3 |    *    *    *    * 2400 |   0   0   1   1
------------------+------+-----------+--------------------------+----------------
x3/2o3x .   *a3*c ♦   12 |   12   12 |    4    4    0    4    0 | 600   *   *   *
x3/2o . o5/4*a    ♦   30 |   60    0 |   20    0   12    0    0 |   * 120   *   *
x   . x3o5/4*a3*c ♦   60 |   60   60 |    0   20   12    0   20 |   *   * 120   *
.   o3x3o         ♦    6 |    0   12 |    0    0    0    4    4 |   *   *   * 600

x3/2o3x3/2o5*a3*c

.   . .   .       | 3600 |    4    4 |    2    4    2    2    2 |   2   1   2   1
------------------+------+-----------+--------------------------+----------------
x   . .   .       |    2 | 7200    * |    1    1    1    0    0 |   1   1   1   0
.   . x   .       |    2 |    * 7200 |    0    1    0    1    1 |   1   0   1   1
------------------+------+-----------+--------------------------+----------------
x3/2o .   .       |    3 |    3    0 | 2400    *    *    *    * |   1   1   0   0
x   . x   . *a3*c |    6 |    3    3 |    * 2400    *    *    * |   1   0   1   0
x   . .   o5*a    |    5 |    5    0 |    *    * 1440    *    * |   0   1   1   0
.   o3x   .       |    3 |    0    3 |    *    *    * 2400    * |   1   0   0   1
.   . x3/2o       |    3 |    0    3 |    *    *    *    * 2400 |   0   0   1   1
------------------+------+-----------+--------------------------+----------------
x3/2o3x   . *a3*c ♦   12 |   12   12 |    4    4    0    4    0 | 600   *   *   *
x3/2o .   o5*a    ♦   30 |   60    0 |   20    0   12    0    0 |   * 120   *   *
x   . x3/2o5*a3*c ♦   60 |   60   60 |    0   20   12    0   20 |   *   * 120   *
.   o3x3/2o       ♦    6 |    0   12 |    0    0    0    4    4 |   *   *   * 600