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This chiral polyhedron is obtained as a relaxed (to unit edges only) variant of a hexa-stellated snub cube. In fact, it can be considered as an external blend of some snic variant (with larger squares) and 6 quite low squippy variants. The short diagonal RR of the rhombs here is determined by the coplanarity of these blending triangle pairs.

Incidence matrix

24 * |  2  1  1 | 1  3  [3,r,R,R]
 * 6 |  0  0  4 | 0  4  [r4]
-----+----------+-----
 2 0 | 24  *  * | 1  1  {3} edges
 2 0 |  * 12  * | 0  2
 1 1 |  *  * 24 | 0  2
-----+----------+-----
 3 0 |  3  0  0 | 8  *  {3}
 3 1 |  1  1  2 | * 24  ((r,R)2)