Looks like a compound of a cuboctahedra (co) plus 4 diametral hexagons.

Incidence matrix according to Dynkin symbol

o2-3-x2-4-o2

      .    .    .  | 12 |  4 | 2 2 2
-------------------+----+----+------
      .    x2   .  |  2 | 24 | 1 1 1
-------------------+----+----+------
      o2-3-x2   .  |  3 |  3 | 8 * *
sefa: x2-3-x2   .  |  6 |  6 | * 4 *
      .    x2-4-o2 |  4 |  4 | * * 6

x2-3-o2-3-x2
---------------------+----+-------+------
      .    .    .    | 12 |  2  2 | 1 2 2 1
---------------------+----+-------+------
      x2   .    .    |  2 | 12  * | 1 1 1 0
      .    .    x2   |  2 |  * 12 | 0 1 1 1
---------------------+----+-------+------
      x2-3-o2   .    |  3 |  3  0 | 4 * * *
sefa: x2-3-x2   .  & |  6 |  3  3 | * 4 * *
      x2   .    x2   |  4 |  2  2 | * * 6 *
      .    o2-3-x2   |  3 |  0  3 | * * * 4