Looks like a compound of a prismatointercepted prismatohexacontahecatonicosachoron (pinpixhi) plus 1800 additional squares. Indeed the diametral squares of the former octahedra (oct) here are coincident pairs.

Incidence matrix according to Dynkin symbol

o3β3o5x

both( . . . . ) | 3600 |    2    4    4 |   1    2    2    4    4    4 |   1    2   2   4
----------------+------+----------------+------------------------------+-----------------
both( . . . x ) |    2 | 3600    *    * |   1    0    0    0    2    2 |   0    1   2   2
sefa( o3β . . ) |    2 |    * 7200    * |   0    1    0    1    1    0 |   1    1   0   1
sefa( . β3o . ) |    2 |    *    * 7200 |   0    0    1    1    0    1 |   1    0   1   1
----------------+------+----------------+------------------------------+-----------------
both( . . o5x ) |    5 |    5    0    0 | 720    *    *    *    *    * |   0    0   2   0
      o3β . .   ♦    3 |    0    3    0 |   * 2400    *    *    *    * |   1    1   0   0
      . β3o .   ♦    3 |    0    0    3 |   *    * 2400    *    *    * |   1    0   1   0
sefa( o3β3o . ) |    4 |    0    2    2 |   *    *    * 3600    *    * |   1    0   0   1
sefa( o3β 2 x ) |    4 |    2    2    0 |   *    *    *    * 3600    * |   0    1   0   1
sefa( . β3o5x ) |   10 |    5    0    5 |   *    *    *    *    * 1440 |   0    0   1   1
----------------+------+----------------+------------------------------+-----------------
      o3β3o .   ♦    6 |    0   12   12 |   0    4    4    6    0    0 | 600    *   *   *
      o3β 2 x   ♦    6 |    3    6    0 |   0    2    0    0    3    0 |   * 1200   *   *
      . β3o5x   ♦   60 |   60    0   60 |  12    0   20    0    0   12 |   *    * 120   *
sefa( o3β3o5x ) ♦   20 |   10   10   10 |   0    0    0    5    5    2 |   *    *   * 720

starting figure: o3x3o5x