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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

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