Edges and faces coincide by 3, each sissid cell coincides with a 2sissid cell, so in fact this looks like having 3 coincident cells each as well. Vertices however are unique.

Incidence matrix according to Dynkin symbol

β5o5/2o5o

both( . .   . . ) | 120 |   60 |  30   60 |  12  12
------------------+-----+------+----------+--------
sefa( β5o   . . ) |   2 | 3600 |   1    2 |   2   1
------------------+-----+------+----------+--------
      β5o   . .   ♦   5 |    5 | 720    * |   2   0 {5/2}
sefa( β5o5/2o . ) |   5 |    5 |   * 1440 |   1   1 {5/2}
------------------+-----+------+----------+--------
      β5o5/2o .   ♦  12 |   60 |  12   12 | 120   *
sefa( β5o5/2o5o ) ♦  12 |   30 |   0   12 |   * 120

starting figure: x5o5/2o5o