This is an example for a reducible complex polyhedron. Its incidence matrix readily derives from those of its factors. In fact it just happens to be the "usual" prism of the complex polygon of its second factor, all lacing edges are just 2-fold ones.

Incidence matrix according to Dynkin symbol

x2   x2-4-or

.    .    .  | 4r |  1  2  | r  1
------------+----+--------+-----
x2   .    .  |  2 | 2r  *  | r  0
.    x2   .  |  2 |  * 2r2 | 1  1
------------+----+--------+-----
x2   x2   .  |  4 |  2  2  | r2 *
.    x2-4-or ♦ 2r |  0  r2 | *  2