Vertices, edges and some triangles coincide by 3, the squares coincide by pairs, in fact this polychoron contains the Grünbaumian double cover 2thah as one type of cells. When omitting these (and reconnecting the still incident elements) one ends with pinnip.

Incidence matrix according to Dynkin symbol

x3o3/2x3o

. .   . . | 30 |  2  4 |  1  4  2  2 | 2  2 1
----------+----+-------+-------------+-------
x .   . . |  2 | 30  * |  1  2  0  0 | 2  1 0
. .   x . |  2 |  * 60 |  0  1  1  1 | 1  1 1
----------+----+-------+-------------+-------
x3o   . . |  3 |  3  0 | 10  *  *  * | 2  0 0
x .   x . |  4 |  2  2 |  * 30  *  * | 1  1 0
. o3/2x . |  3 |  0  3 |  *  * 20  * | 1  0 1
. .   x3o |  3 |  0  3 |  *  *  * 20 | 0  1 1
----------+----+-------+-------------+-------
x3o3/2x . ♦ 12 | 12 12 |  4  6  4  0 | 5  * *
x .   x3o ♦  6 |  3  6 |  0  3  0  2 | * 10 *
. o3/2x3o ♦  6 |  0 12 |  0  0  4  4 | *  * 5

x3o3/2x3/2o

. .   .   . | 30 |  2  4 |  1  4  2  2 | 2  2 1
------------+----+-------+-------------+-------
x .   .   . |  2 | 30  * |  1  2  0  0 | 2  1 0
. .   x   . |  2 |  * 60 |  0  1  1  1 | 1  1 1
------------+----+-------+-------------+-------
x3o   .   . |  3 |  3  0 | 10  *  *  * | 2  0 0
x .   x   . |  4 |  2  2 |  * 30  *  * | 1  1 0
. o3/2x   . |  3 |  0  3 |  *  * 20  * | 1  0 1
. .   x3/2o |  3 |  0  3 |  *  *  * 20 | 0  1 1
------------+----+-------+-------------+-------
x3o3/2x   . ♦ 12 | 12 12 |  4  6  4  0 | 5  * *
x .   x3/2o ♦  6 |  3  6 |  0  3  0  2 | * 10 *
. o3/2x3/2o ♦  6 |  0 12 |  0  0  4  4 | *  * 5

x3/2o3x3o

.   . . . | 30 |  2  4 |  1  4  2  2 | 2  2 1
----------+----+-------+-------------+-------
x   . . . |  2 | 30  * |  1  2  0  0 | 2  1 0
.   . x . |  2 |  * 60 |  0  1  1  1 | 1  1 1
----------+----+-------+-------------+-------
x3/2o . . |  3 |  3  0 | 10  *  *  * | 2  0 0
x   . x . |  4 |  2  2 |  * 30  *  * | 1  1 0
.   o3x . |  3 |  0  3 |  *  * 20  * | 1  0 1
.   . x3o |  3 |  0  3 |  *  *  * 20 | 0  1 1
----------+----+-------+-------------+-------
x3/2o3x . ♦ 12 | 12 12 |  4  6  4  0 | 5  * *
x   . x3o ♦  6 |  3  6 |  0  3  0  2 | * 10 *
.   o3x3o ♦  6 |  0 12 |  0  0  4  4 | *  * 5

x3/2o3x3/2o

.   . .   . | 30 |  2  4 |  1  4  2  2 | 2  2 1
------------+----+-------+-------------+-------
x   . .   . |  2 | 30  * |  1  2  0  0 | 2  1 0
.   . x   . |  2 |  * 60 |  0  1  1  1 | 1  1 1
------------+----+-------+-------------+-------
x3/2o .   . |  3 |  3  0 | 10  *  *  * | 2  0 0
x   . x   . |  4 |  2  2 |  * 30  *  * | 1  1 0
.   o3x   . |  3 |  0  3 |  *  * 20  * | 1  0 1
.   . x3/2o |  3 |  0  3 |  *  *  * 20 | 0  1 1
------------+----+-------+-------------+-------
x3/2o3x   . ♦ 12 | 12 12 |  4  6  4  0 | 5  * *
x   . x3/2o ♦  6 |  3  6 |  0  3  0  2 | * 10 *
.   o3x3/2o ♦  6 |  0 12 |  0  0  4  4 | *  * 5