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The rhombs {(r,R)²} have corner angles r = arccos[(3+3 sqrt(5))/20] = 60.960649° and R = arccos[-(3+3 sqrt(5))/20] = 119.039351°.

Incidence matrix

60  *  * |  2   2  1 |  1  2  2  [3,5,3,r2]
 * 30  * |  0   4  0 |  0  2  2  [(3,R)2]
 *  * 20 |  0   0  3 |  0  0  3  [R3]
---------+-----------+---------
 2  0  0 | 60   *  * |  1  1  0
 1  1  0 |  * 120  * |  0  1  1
 1  0  1 |  *   * 60 |  0  0  2
---------+-----------+---------
 5  0  0 |  5   0  0 | 12  *  *  {5}
 2  1  0 |  1   2  0 |  * 60  *  {3}
 2  1  1 |  0   2  2 |  *  * 60  {(r,R)2}