This is simply the prism on the Grünbaumian base 2thah.

Incidence matrix according to Dynkin symbol

x x3o3/2x

. . .   . | 24 |  1  2  2 |  2  2 1  2 1 | 1 2 1 1
----------+----+----------+--------------+--------
x . .   . |  2 | 12  *  * |  2  2 0  0 0 | 1 2 1 0
. x .   . |  2 |  * 24  * |  1  0 1  1 0 | 1 1 0 1
. . .   x |  2 |  *  * 24 |  0  1 0  1 1 | 0 1 1 1
----------+----+----------+--------------+--------
x x .   . |  4 |  2  2  0 | 12  * *  * * | 1 1 0 0
x . .   x |  4 |  2  0  2 |  * 12 *  * * | 0 1 1 0
. x3o   . |  3 |  0  3  0 |  *  * 8  * * | 1 0 0 1
. x .   x |  4 |  0  2  2 |  *  * * 12 * | 0 1 0 1
. . o3/2x |  3 |  0  0  3 |  *  * *  * 8 | 0 0 1 1
----------+----+----------+--------------+--------
x x3o   . ♦  6 |  3  6  0 |  3  0 2  0 0 | 4 * * *
x x .   x ♦  8 |  4  4  4 |  2  2 0  2 0 | * 6 * *
x . o3/2x ♦  6 |  3  0  6 |  0  3 0  0 2 | * * 4 *
. x3o3/2x ♦ 12 |  0 12 12 |  0  0 4  6 4 | * * * 2