As abstract polytope sidtaxady is isomorphic to gardtaxady, thereby replacing pentagons by pentagrams, resp. doe by gissid and gidtid by sidtid.

Incidence matrix according to Dynkin symbol

o3o3o3x5*a3/2*c

. . . .         | 600 |   12 |   12   12 |   4   4   4
----------------+-----+------+-----------+------------
. . . x         |   2 | 3600 |    2    2 |   1   2   1
----------------+-----+------+-----------+------------
o . . x5*a      |   5 |    5 | 1440    * |   1   1   0
. . o3x         |   3 |    3 |    * 2400 |   0   1   1
----------------+-----+------+-----------+------------
o3o . x5*a        20 |   30 |   12    0 | 120   *   *
o . o3x5*a3/2*c   20 |   60 |   12   20 |   * 120   *
. o3o3x            4 |    6 |    0    4 |   *   * 600

o3o3o3/2x5/4*a3/2*c

. . .   .           | 600 |   12 |   12   12 |   4   4   4
--------------------+-----+------+-----------+------------
. . .   x           |   2 | 3600 |    2    2 |   1   2   1
--------------------+-----+------+-----------+------------
o . .   x5/4*a      |   5 |    5 | 1440    * |   1   1   0
. . o3/2x           |   3 |    3 |    * 2400 |   0   1   1
--------------------+-----+------+-----------+------------
o3o .   x5/4*a        20 |   30 |   12    0 | 120   *   *
o . o3/2x5/4*a3/2*c   20 |   60 |   12   20 |   * 120   *
. o3o3/2x              4 |    6 |    0    4 |   *   * 600

o3o3/2o3x5/4*a3*c

. .   . .         | 600 |   12 |   12   12 |   4   4   4
------------------+-----+------+-----------+------------
. .   . x         |   2 | 3600 |    2    2 |   1   2   1
------------------+-----+------+-----------+------------
o .   . x5/4*a    |   5 |    5 | 1440    * |   1   1   0
. .   o3x         |   3 |    3 |    * 2400 |   0   1   1
------------------+-----+------+-----------+------------
o3o   . x5/4*a      20 |   30 |   12    0 | 120   *   *
o .   o3x5/4*a3*c   20 |   60 |   12   20 |   * 120   *
. o3/2o3x            4 |    6 |    0    4 |   *   * 600

o3o3/2o3/2x5*a3*c

. .   .   .       | 600 |   12 |   12   12 |   4   4   4
------------------+-----+------+-----------+------------
. .   .   x       |   2 | 3600 |    2    2 |   1   2   1
------------------+-----+------+-----------+------------
o .   .   x5*a    |   5 |    5 | 1440    * |   1   1   0
. .   o3/2x       |   3 |    3 |    * 2400 |   0   1   1
------------------+-----+------+-----------+------------
o3o   .   x5*a      20 |   30 |   12    0 | 120   *   *
o .   o3/2x5*a3*c   20 |   60 |   12   20 |   * 120   *
. o3/2o3/2x          4 |    6 |    0    4 |   *   * 600

o3/2o3o3x5/4*a3*c

.   . . .         | 600 |   12 |   12   12 |   4   4   4
------------------+-----+------+-----------+------------
.   . . x         |   2 | 3600 |    2    2 |   1   2   1
------------------+-----+------+-----------+------------
o   . . x5/4*a    |   5 |    5 | 1440    * |   1   1   0
.   . o3x         |   3 |    3 |    * 2400 |   0   1   1
------------------+-----+------+-----------+------------
o3/2o . x5/4*a      20 |   30 |   12    0 | 120   *   *
o   . o3x5/4*a3*c   20 |   60 |   12   20 |   * 120   *
.   o3o3x            4 |    6 |    0    4 |   *   * 600

o3/2o3o3/2x5*a3*c

.   . .   .       | 600 |   12 |   12   12 |   4   4   4
------------------+-----+------+-----------+------------
.   . .   x       |   2 | 3600 |    2    2 |   1   2   1
------------------+-----+------+-----------+------------
o   . .   x5*a    |   5 |    5 | 1440    * |   1   1   0
.   . o3/2x       |   3 |    3 |    * 2400 |   0   1   1
------------------+-----+------+-----------+------------
o3/2o .   x5*a      20 |   30 |   12    0 | 120   *   *
o   . o3/2x5*a3*c   20 |   60 |   12   20 |   * 120   *
.   o3o3/2x          4 |    6 |    0    4 |   *   * 600

o3/2o3/2o3x5*a3/2*c

.   .   . .         | 600 |   12 |   12   12 |   4   4   4
--------------------+-----+------+-----------+------------
.   .   . x         |   2 | 3600 |    2    2 |   1   2   1
--------------------+-----+------+-----------+------------
o   .   . x5*a      |   5 |    5 | 1440    * |   1   1   0
.   .   o3x         |   3 |    3 |    * 2400 |   0   1   1
--------------------+-----+------+-----------+------------
o3/2o   . x5*a        20 |   30 |   12    0 | 120   *   *
o   .   o3x5*a3/2*c   20 |   60 |   12   20 |   * 120   *
.   o3/2o3x            4 |    6 |    0    4 |   *   * 600

o3/2o3/2o3/2x5/4*a3/2*c

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