As abstract polytope xhidy is automorphic, interchanging decagrams and decagons, respectively tid and quit gissid.

Incidence matrix according to Dynkin symbol

x5x5/3x3o3/2*a3*c

. .   . .         | 7200 |    2    1    2 |    2    2    1    2    1 |   2   1   1   1
------------------+------+----------------+--------------------------+----------------
x .   . .         |    2 | 7200    *    * |    1    1    1    0    0 |   1   1   1   0
. x   . .         |    2 |    * 3600    * |    2    0    0    2    0 |   2   1   0   1
. .   x .         |    2 |    *    * 7200 |    0    1    0    1    1 |   1   0   1   1
------------------+------+----------------+--------------------------+----------------
x5x   . .         |   10 |    5    5    0 | 1440    *    *    *    * |   1   1   0   0
x .   x .   *a3*c |    6 |    3    0    3 |    * 2400    *    *    * |   1   0   1   0
x .   . o3/2*a    |    3 |    3    0    0 |    *    * 2400    *    * |   0   1   1   0
. x5/3x .         |   10 |    0    5    5 |    *    *    * 1440    * |   1   0   0   1
. .   x3o         |    3 |    0    0    3 |    *    *    *    * 2400 |   0   0   1   1
------------------+------+----------------+--------------------------+----------------
x5x5/3x .   *a3*c   120 |   60   60   60 |   12   20    0   12    0 | 120   *   *   *
x5x   . o3/2*a       60 |   60   30    0 |   12    0   20    0    0 |   * 120   *   *
x .   x3o3/2*a3*c    12 |   12    0   12 |    0    4    4    0    4 |   *   * 600   *
. x5/3x3o            60 |    0   30   60 |    0    0    0   12   20 |   *   *   * 120

x5x5/3x3/2o3*a3*c

. .   .   .       | 7200 |    2    1    2 |    2    2    1    2    1 |   2   1   1   1
------------------+------+----------------+--------------------------+----------------
x .   .   .       |    2 | 7200    *    * |    1    1    1    0    0 |   1   1   1   0
. x   .   .       |    2 |    * 3600    * |    2    0    0    2    0 |   2   1   0   1
. .   x   .       |    2 |    *    * 7200 |    0    1    0    1    1 |   1   0   1   1
------------------+------+----------------+--------------------------+----------------
x5x   .   .       |   10 |    5    5    0 | 1440    *    *    *    * |   1   1   0   0
x .   x   . *a3*c |    6 |    3    0    3 |    * 2400    *    *    * |   1   0   1   0
x .   .   o3*a    |    3 |    3    0    0 |    *    * 2400    *    * |   0   1   1   0
. x5/3x   .       |   10 |    0    5    5 |    *    *    * 1440    * |   1   0   0   1
. .   x3/2o       |    3 |    0    0    3 |    *    *    *    * 2400 |   0   0   1   1
------------------+------+----------------+--------------------------+----------------
x5x5/3x   . *a3*c   120 |   60   60   60 |   12   20    0   12    0 | 120   *   *   *
x5x   .   o3*a       60 |   60   30    0 |   12    0   20    0    0 |   * 120   *   *
x .   x3/2o3*a3*c    12 |   12    0   12 |    0    4    4    0    4 |   *   * 600   *
. x5/3x3/2o          60 |    0   30   60 |    0    0    0   12   20 |   *   *   * 120