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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

120  *  * |  1  1   1   1  0 |  1  1  1  1  0  [3,10,4,r]
  * 30  * |  0  0   4   0  0 |  0  2  2  0  0  [(3,R)2]
  *  * 60 |  0  0   0   2  2 |  0  0  1  2  1  [3,4,R,4]
----------+------------------+---------------
  2  0  0 | 60  *   *   *  * |  1  1  0  0  0
  2  0  0 |  * 60   *   *  * |  1  0  0  1  0
  1  1  0 |  *  * 120   *  * |  0  1  1  0  0
  1  0  1 |  *  *   * 120  * |  0  0  1  1  0
  0  0  2 |  *  *   *   * 60 |  0  0  0  1  1
----------+------------------+---------------
 10  0  0 |  3  3   0   0  0 | 12  *  *  *  *  {10}
  2  1  0 |  1  0   2   0  0 |  * 60  *  *  *  {3}
  2  1  1 |  0  0   2   2  0 |  *  * 60  *  *  {(r,R)2}
  2  0  2 |  0  1   0   2  1 |  *  *  * 60  *  {4}
  0  0  3 |  0  0   0   0  3 |  *  *  *  * 20  {3}