Looks like a compound of 3 coincident octahedra (oct) plus 3 diametral pairs of squares, and indeed edges coincides by 5, squares by 2, and each octahedral triangle coincides with 2 further sefa triangles, while vertices coincide by 4.

Incidence matrix according to Dynkin symbol

s3s4/3s

demi( . .   . ) | 24 |  1  2  2 | 1 1  3
----------------+----+----------+-------
      s 2   s   ♦  2 | 12  *  * | 0 0  2
sefa( s3s   . ) |  2 |  * 24  * | 1 0  1
sefa( . s4/3s ) |  2 |  *  * 24 | 0 1  1
----------------+----+----------+-------
      s3s   .   ♦  3 |  0  3  0 | 8 *  *
      . s4/3s   ♦  4 |  0  0  4 | * 6  *
sefa( s3s4/3s ) |  3 |  1  1  1 | * * 24

starting figure: x3x4/3x