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The rhombs {(r,R)²} have corner angles r = arccos[(2 sqrt(2)-1)/4] = 62.799430° and R = arccos[-(2 sqrt(2)-1)/4] = 117.200570°.

Incidence matrix

24  * * |  2  2  1 | 1  2  2  [3,4,3,r2]
 * 12 * |  0  4  0 | 0  2  2  [(3,R)2]
 *  * 8 |  0  0  3 | 0  0  3  [R3]
--------+----------+--------
 2  0 0 | 24  *  * | 1  1  0
 1  1 0 |  * 48  * | 0  1  1
 1  0 1 |  *  * 24 | 0  0  2
--------+----------+--------
 4  0 0 |  4  0  0 | 6  *  *  {4}
 2  1 0 |  1  2  0 | * 24  *  {3}
 2  1 1 |  0  2  2 | *  * 24  {(r,R)2}