©

This non-convex deltahedron happens to be isohedral and acoptic (non-selfintersecting), but only is triform (has 3 different vertex types).
© Idea and animation are courteous to T. Dorozinski.

Incidence matrix

30  *  * |  2  2  0 |   4	[34]
 * 20  * |  3  0  3 |   6	[36]
 *  * 12 |  0  5  5 |  10	[310]
---------+----------+----
 1  1  0 | 60  *  * |   2
 1  0  1 |  * 60  * |   2
 0  1  1 |  *  * 60 |   2
---------+----------+----
 1  1  1 |  1  1  1 | 120	{3}