Looks like a compound of mesdi, rappisdi and 288 further squares. And indeed {4} come in coincident pairs.

Incidence matrix

both( rappisdi-vertices )   | 96 |   6   6  12   6  12  12 |  3   9   9   6  12  12  15  15 |  6  3  3 15
----------------------------+----+-------------------------+--------------------------------+------------
verf( rappisdi-triangle_1 ) |  2 | 288   *   *   *   *   * |  1   0   0   0   1   1   0   0 |  2  0  0  1
verf( rappisdi-triangle_2 ) |  2 |   * 288   *   *   *   * |  0   1   0   0   0   1   1   0 |  1  1  0  1
verf( rappisdi-triangle_2 ) |  2 |   *   * 576   *   *   * |  0   1   0   0   1   0   1   0 |  1  1  0  1
verf( rappisdi-triangle_3 ) |  2 |   *   *   * 288   *   * |  0   0   1   0   1   0   0   1 |  1  0  1  1
verf( rappisdi-triangle_3 ) |  2 |   *   *   *   * 576   * |  0   0   1   0   0   1   0   1 |  1  0  1  1
verf( rappisdi-triangle_4 ) |  2 |   *   *   *   *   * 576 |  0   0   0   1   0   0   1   1 |  0  1  1  1
----------------------------+----+-------------------------+--------------------------------+------------
      rappisdi-triangle_1   |  3 |   3   0   0   0   0   0 | 96   *   *   *   *   *   *   * |  2  0  0  0
      rappisdi-triangle_2   |  3 |   0   1   2   0   0   0 |  * 288   *   *   *   *   *   * |  1  1  0  0
      rappisdi-triangle_3   |  3 |   0   0   0   1   2   0 |  *   * 288   *   *   *   *   * |  1  0  1  0
      rappisdi-triangle_4   |  3 |   0   0   0   0   0   3 |  *   *   * 192   *   *   *   * |  0  1  1  0
verf( rappisdi-oct )        |  4 |   1   0   2   1   0   0 |  *   *   *   * 288   *   *   * |  1  0  0  1
verf( rappisdi-oct )        |  4 |   1   1   0   0   2   0 |  *   *   *   *   * 288   *   * |  1  0  0  1
verf( rappisdi-ike )        |  5 |   0   1   2   0   0   2 |  *   *   *   *   *   * 288   * |  0  1  0  1	{5}
verf( rappisdi-gike )       |  5 |   0   0   0   1   2   2 |  *   *   *   *   *   *   * 288 |  0  0  1  1	{5/2}
----------------------------+----+-------------------------+--------------------------------+------------
holosnub( rappisdi-oct )    |  6 |   6   3   6   3   6   0 |  2   3   3   0   3   3   0   0 | 96  *  *  *	(oct+6{4})
holosnub( rappisdi-ike )    | 12 |   0  12  24   0   0  24 |  0  12   0   8   0   0  12   0 |  * 24  *  *	(cid)
holosnub( rappisdi-gike )   | 12 |   0   0   0  12  24  24 |  0   0  12   8   0   0   0  12 |  *  * 24  *	(gacid)
both( rappisdi-verf )       | 15 |   3   3   6   3   6   6 |  0   0   0   0   3   3   3   3 |  *  *  * 96	(dritit)

starting figure: rappisdi