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For HH : hH on gets here s.th. like 1.59904 in the shield hexagons, and for the pentagons one measures approximate corner angles 110.29° at P and 101.846° at p.

Incidence matrix

4  *  * |  3  0 0 |  3 0  [P03]
* 12  * |  1  2 0 |  2 1  [p,p,H]
*  * 12 |  0  2 1 |  2 1  [P,P,h]
--------+---------+-----
1  1  0 | 12  * * |  2 0
0  1  1 |  * 24 * |  1 1
0  0  2 |  *  * 6 |  2 0
--------+---------+-----
1  2  2 |  2  2 1 | 12 *  {(P,p,P0,p,P)}
0  3  3 |  0  6 0 |  * 4  {(h,H)3}