Looks like a sid pippady, but with all its pseudo sissids filled in by according Grünbaumian double covers, 2sissid.

Incidence matrix according to Dynkin symbol

x5o5/2x5/2o5/2*b

. .   .   .      | 1440 |    5   10 |    5   10    5    5 |   5   1   5   1
-----------------+------+-----------+---------------------+----------------
x .   .   .      |    2 | 3600    * |    2    2    0    0 |   2   1   1   0
. .   x   .      |    2 |    * 7200 |    0    1    1    1 |   1   0   1   1
-----------------+------+-----------+---------------------+----------------
x5o   .   .      |    5 |    5    0 | 1440    *    *    * |   1   1   0   0
x .   x   .      |    4 |    2    2 |    * 3600    *    * |   1   0   1   0
. o5/2x   .      |    5 |    0    5 |    *    * 1440    * |   1   0   0   1
. .   x5/2o      |    5 |    0    5 |    *    *    * 1440 |   0   0   1   1
-----------------+------+-----------+---------------------+----------------
x5o5/2x   .      ♦   60 |   60   60 |   12   30   12    0 | 120   *   *   *
x5o   .   o5/2*b ♦   12 |   30    0 |   12    0    0    0 |   * 120   *   *
x .   x5/2o      ♦   10 |    5   10 |    0    5    0    2 |   *   * 720   *
. o5/2x5/2o5/2*b ♦   12 |    0   60 |    0    0   12   12 |   *   *   * 120

β5o5/2o5x
both( . .   . . ) | 1440 |    5   10 |    5    5    5   10 |   1   1   5   5
------------------+------+-----------+---------------------+----------------
both( . .   . x ) |    2 | 3600    * |    2    0    0    2 |   1   0   1   2
sefa( β5o   . . ) |    2 |    * 7200 |    0    1    1    1 |   0   1   1   1
------------------+------+-----------+---------------------+----------------
both( . .   o5x ) |    5 |    5    0 | 1440    *    *    * |   1   0   0   1  {5}
      β5o   . .   |    5 |    0    5 |    * 1440    *    * |   0   1   1   0  {5/2}
sefa( β5o5/2o . ) |    5 |    0    5 |    *    * 1440    * |   0   1   0   1  {5/2}
sefa( β5o   2 x ) |    4 |    2    2 |    *    *    * 3600 |   0   0   1   1
------------------+------+-----------+---------------------+----------------
both( . o5/2o5x ) ♦   12 |   30    0 |   12    0    0    0 | 120   *   *   *
      β5o5/2o .   ♦   12 |    0   60 |    0   12   12    0 |   * 120   *   *
      β5o   2 x   ♦   10 |    5   10 |    0    2    0    5 |   *   * 720   *
sefa( β5o5/2o5x ) ♦   60 |   60   60 |   12    0   12   30 |   *   *   * 120

starting figure: x5o5/2o5x