As abstract polytope efdit xithi is automorph, thereby interchanging the roles of pentagrams and pentagons, resp. interchanging the gid and id.

This polychoron is fissary as its vertices coincide by 3; further edges coincide by pairs, and it is also exotic as its triangles coincide by pairs.

It can be seen as blend of gidthidy hi with gotdatixhi, blending out the giddy. Alternatively as blend of sidthidy hi with stodatixhi, blending out the siddy.

Incidence matrix according to Dynkin symbol

        _x_        
    _3-  |  5/3    
 o<      3      >o 
    3/2  |  _5-    
        -x-        

x3o3/2x5o5/3*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 .   . o5/3*a    |    5 |    5    0 |    *    * 1440    *    * |   0   1   1   0
. o3/2x .         |    3 |    0    3 |    *    *    * 2400    * |   1   0   0   1
. .   x5o         |    5 |    0    5 |    *    *    *    * 1440 |   0   0   1   1
------------------+------+-----------+--------------------------+----------------
x3o3/2x .   *a3*c ♦   12 |   12   12 |    4    4    0    4    0 | 600   *   *   *
x3o   . o5/3*a    ♦   30 |   60    0 |   20    0   12    0    0 |   * 120   *   *
x .   x5o5/3*a3*c ♦   60 |   60   60 |    0   20   12    0   12 |   *   * 120   *
. o3/2x5o         ♦   30 |    0   60 |    0    0    0   20   12 |   *   *   * 120

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

x3o3/2x5/4o5/2*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 .   .   o5/2*a    |    5 |    5    0 |    *    * 1440    *    * |   0   1   1   0
. o3/2x   .         |    3 |    0    3 |    *    *    * 2400    * |   1   0   0   1
. .   x5/4o         |    5 |    0    5 |    *    *    *    * 1440 |   0   0   1   1
--------------------+------+-----------+--------------------------+----------------
x3o3/2x   .   *a3*c ♦   12 |   12   12 |    4    4    0    4    0 | 600   *   *   *
x3o   .   o5/2*a    ♦   30 |   60    0 |   20    0   12    0    0 |   * 120   *   *
x .   x5/4o5/2*a3*c ♦   60 |   60   60 |    0   20   12    0   12 |   *   * 120   *
. o3/2x5/4o         ♦   30 |    0   60 |    0    0    0   20   12 |   *   *   * 120

        _x_        
    3/2  |  5/3    
 o<      3      >o 
    -3_  |  _5-    
        -x-        

x3/2o3x5o5/3*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   . . o5/3*a    |    5 |    5    0 |    *    * 1440    *    * |   0   1   1   0
.   o3x .         |    3 |    0    3 |    *    *    * 2400    * |   1   0   0   1
.   . x5o         |    5 |    0    5 |    *    *    *    * 1440 |   0   0   1   1
------------------+------+-----------+--------------------------+----------------
x3/2o3x .   *a3*c ♦   12 |   12   12 |    4    4    0    4    0 | 600   *   *   *
x3/2o . o5/3*a    ♦   30 |   60    0 |   20    0   12    0    0 |   * 120   *   *
x   . x5o5/3*a3*c ♦   60 |   60   60 |    0   20   12    0   12 |   *   * 120   *
.   o3x5o         ♦   30 |    0   60 |    0    0    0   20   12 |   *   *   * 120

        _x_        
    3/2  |  5/2    
 o<      3      >o 
    -3_  |  5/4    
        -x-        

x3/2o3x5/4o5/2*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   . .   o5/2*a    |    5 |    5    0 |    *    * 1440    *    * |   0   1   1   0
.   o3x   .         |    3 |    0    3 |    *    *    * 2400    * |   1   0   0   1
.   . x5/4o         |    5 |    0    5 |    *    *    *    * 1440 |   0   0   1   1
--------------------+------+-----------+--------------------------+----------------
x3/2o3x   .   *a3*c ♦   12 |   12   12 |    4    4    0    4    0 | 600   *   *   *
x3/2o .   o5/2*a    ♦   30 |   60    0 |   20    0   12    0    0 |   * 120   *   *
x   . x5/4o5/2*a3*c ♦   60 |   60   60 |    0   20   12    0   12 |   *   * 120   *
.   o3x5/4o         ♦   30 |    0   60 |    0    0    0   20   12 |   *   *   * 120