As abstract polytope 2dittafady is automorph, thereby interchanging the roles of pentagrams and pentagons.

Looks like a completely coincident compound of 2 dittafady. In fact, vertices coincide by 6, edges by 4, and all other elements by pairs.

Incidence matrix according to Dynkin symbol

x5o5/3x5o5/3*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
------------------+------+-----------+--------------------------+----------------
x5o   . .         |    5 |    5    0 | 1440    *    *    *    * |   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
. o5/3x .         |    5 |    0    5 |    *    *    * 1440    * |   1   0   0   1
. .   x5o         |    5 |    0    5 |    *    *    *    * 1440 |   0   0   1   1
------------------+------+-----------+--------------------------+----------------
x5o5/3x .   *a3*c ♦   60 |   60   60 |   12   20    0   12    0 | 120   *   *   *
x5o   . o5/3*a    ♦   30 |   60    0 |   12    0   12    0    0 |   * 120   *   *
x .   x5o5/3*a3*c ♦   60 |   60   60 |    0   20   12    0   12 |   *   * 120   *
. o5/3x5o         ♦   30 |    0   60 |    0    0    0   12   12 |   *   *   * 120

or
. .   . .          & | 3600 |     8 |    4    4    4 |   4   2
---------------------+------+-------+----------------+--------
x .   . .          & |    2 | 14400 |    1    1    1 |   2   1
---------------------+------+-------+----------------+--------
x5o   . .          & |    5 |     5 | 2880    *    * |   1   1
x .   x .   *a3*c    |    6 |     6 |    * 2400    * |   2   0
x .   . o5/3*a     & |    5 |     5 |    *    * 2880 |   1   1
---------------------+------+-------+----------------+--------
x5o5/3x .   *a3*c  & ♦   60 |   120 |   12   20   12 | 240   *
x5o   . o5/3*a     & ♦   30 |    60 |   12    0   12 |   * 240

x5o5/3x5/4o5/2*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
--------------------+------+-----------+--------------------------+----------------
x5o   .   .         |    5 |    5    0 | 1440    *    *    *    * |   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
. o5/3x   .         |    5 |    0    5 |    *    *    * 1440    * |   1   0   0   1
. .   x5/4o         |    5 |    0    5 |    *    *    *    * 1440 |   0   0   1   1
--------------------+------+-----------+--------------------------+----------------
x5o5/3x   .   *a3*c ♦   60 |   60   60 |   12   20    0   12    0 | 120   *   *   *
x5o   .   o5/2*a    ♦   30 |   60    0 |   12    0   12    0    0 |   * 120   *   *
x .   x5/4o5/2*a3*c ♦   60 |   60   60 |    0   20   12    0   12 |   *   * 120   *
. o5/3x5/4o         ♦   30 |    0   60 |    0    0    0   12   12 |   *   *   * 120

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

or
.   .   .   .          & | 3600 |     8 |    4    4    4 |   4   2
-------------------------+------+-------+----------------+--------
x   .   .   .          & |    2 | 14400 |    1    1    1 |   2   1
-------------------------+------+-------+----------------+--------
x5/4o   .   .          & |    5 |     5 | 2880    *    * |   1   1
x   .   x   .   *a3*c    |    6 |     6 |    * 2400    * |   2   0
x   .   .   o5/2*a     & |    5 |     5 |    *    * 2880 |   1   1
-------------------------+------+-------+----------------+--------
x5/4o5/2x   .   *a3*c  & ♦   60 |   120 |   12   20   12 | 240   *
x5/4o   .   o5/2*a     & ♦   30 |    60 |   12    0   12 |   * 240