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The non-regular hexagons {(h,H)³} are shield hexagons. Their vertex angles are alternatingly h = arccos[(5-3 sqrt(5))/4] = 115.280553° resp. H = 240°-h = 124.719447°.

Incidence matrix

60  * |  2   2 |  1  1  2  [3,5,3,H]
 * 30 |  0   4 |  0  2  2  [3,h,3,h]
------+--------+---------
 2  0 | 60   * |  1  0  1
 1  1 |  * 120 |  0  1  1
------+--------+---------
 5  0 |  5   0 | 12  *  *
 3  3 |  0   6 |  * 20  *  {(h,H)3}
 2  1 |  1   2 |  *  * 60