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

        _o_        
    _3-  |  5/2    
 o<      3      >x 
    5/4  |  5/3    
        -x-        

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

        _o_        
    3/2  |  5/2    
 o<      3      >x 
    -5_  |  5/3    
        -x-        

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

        _o_        
    _3-  |  5/3    
 o<     3/2     >x 
    -5_  |  5/3    
        -x-        

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

        _o_        
    3/2  |  5/3    
 o<     3/2     >x 
    5/4  |  5/3    
        -x-        

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