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

Looks like a compound of sitphi and sand tathi.

Incidence matrix according to Dynkin symbol

x5x5o3o5/3*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
------------------+------+-----------+---------------------+----------------
x5x . .           |   10 |    5    5 | 1440    *    *    * |   1   1   0   0
x . o .   *a3/2*c |    3 |    3    0 |    * 2400    *    * |   1   0   1   0
x . . o5/3*a      |    5 |    5    0 |    *    * 1440    * |   0   1   1   0
. x5o .           |    5 |    0    5 |    *    *    * 1440 |   1   0   0   1
------------------+------+-----------+---------------------+----------------
x5x5o .   *a3/2*c ♦   60 |   60   60 |   12   20    0   12 | 120   *   *   *
x5x . o5/3*a      ♦   60 |   60   30 |   12    0   12    0 |   * 120   *   *
x . o3o5/3*a3/2*c ♦   20 |   60    0 |    0   20   12    0 |   *   * 120   *
. x5o3o           ♦   20 |    0   30 |    0    0    0   12 |   *   *   * 120

x5x5o3/2o5/2*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
--------------------+------+-----------+---------------------+----------------
x5x .   .           |   10 |    5    5 | 1440    *    *    * |   1   1   0   0
x . o   .   *a3/2*c |    3 |    3    0 |    * 2400    *    * |   1   0   1   0
x . .   o5/2*a      |    5 |    5    0 |    *    * 1440    * |   0   1   1   0
. x5o   .           |    5 |    0    5 |    *    *    * 1440 |   1   0   0   1
--------------------+------+-----------+---------------------+----------------
x5x5o   .   *a3/2*c ♦   60 |   60   60 |   12   20    0   12 | 120   *   *   *
x5x .   o5/2*a      ♦   60 |   60   30 |   12    0   12    0 |   * 120   *   *
x . o3/2o5/2*a3/2*c ♦   20 |   60    0 |    0   20   12    0 |   *   * 120   *
. x5o3/2o           ♦   20 |    0   30 |    0    0    0   12 |   *   *   * 120

x5x5/4o3o5/2*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
------------------+------+-----------+---------------------+----------------
x5x   . .         |   10 |    5    5 | 1440    *    *    * |   1   1   0   0
x .   o .   *a3*c |    3 |    3    0 |    * 2400    *    * |   1   0   1   0
x .   . o5/2*a    |    5 |    5    0 |    *    * 1440    * |   0   1   1   0
. x5/4o .         |    5 |    0    5 |    *    *    * 1440 |   1   0   0   1
------------------+------+-----------+---------------------+----------------
x5x5/4o .   *a3*c ♦   60 |   60   60 |   12   20    0   12 | 120   *   *   *
x5x   . o5/2*a    ♦   60 |   60   30 |   12    0   12    0 |   * 120   *   *
x .   o3o5/2*a3*c ♦   20 |   60    0 |    0   20   12    0 |   *   * 120   *
. x5/4o3o         ♦   20 |    0   30 |    0    0    0   12 |   *   *   * 120

x5x5/4o3/2o5/3*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
--------------------+------+-----------+---------------------+----------------
x5x   .   .         |   10 |    5    5 | 1440    *    *    * |   1   1   0   0
x .   o   .   *a3*c |    3 |    3    0 |    * 2400    *    * |   1   0   1   0
x .   .   o5/3*a    |    5 |    5    0 |    *    * 1440    * |   0   1   1   0
. x5/4o   .         |    5 |    0    5 |    *    *    * 1440 |   1   0   0   1
--------------------+------+-----------+---------------------+----------------
x5x5/4o   .   *a3*c ♦   60 |   60   60 |   12   20    0   12 | 120   *   *   *
x5x   .   o5/3*a    ♦   60 |   60   30 |   12    0   12    0 |   * 120   *   *
x .   o3/2o5/3*a3*c ♦   20 |   60    0 |    0   20   12    0 |   *   * 120   *
. x5/4o3/2o         ♦   20 |    0   30 |    0    0    0   12 |   *   *   * 120