Looks like a compound of 6 tesseract (tes) with vertices identified, while edges and faces coincide by 6, and cells coincide by 3. Both, the vertex figure and the cells are Grünbaumian figures in turn.

Incidence matrix according to Dynkin symbol

x4o3o3o4*a4/3*c *b3/2*d

. . . .                 | 16 ♦  24 | 12 12 12 | 4 4 4
------------------------+----+-----+----------+------
x . . .                 |  2 | 192 |  1  1  1 | 1 1 1
------------------------+----+-----+----------+------
x4o . .                 |  4 |   4 | 48  *  * | 1 1 0
x . o . *a4/3*c         |  4 |   4 |  * 48  * | 1 0 1
x . . o4*a              |  4 |   4 |  *  * 48 | 0 1 1
------------------------+----+-----+----------+------
x4o3o . *a4/3*c         ♦  8 |  24 |  6  6  0 | 8 * *
x4o . o4*a      *b3/2*d ♦  8 |  24 |  6  0  6 | * 8 *
x . o3o4*a4/3*c         ♦  8 |  24 |  0  6  6 | * * 8

or
. . . .                    | 16 ♦  24 | 24 12 |  8 4
---------------------------+----+-----+-------+-----
x . . .                    |  2 | 192 |  2  1 |  2 1
---------------------------+----+-----+-------+-----
x4o . .                  & |  4 |   4 | 96  * |  1 1
x . o . *a4/3*c            |  4 |   4 |  * 48 |  2 0
---------------------------+----+-----+-------+-----
x4o3o . *a4/3*c          & ♦  8 |  24 |  6  6 | 16 *
x4o . o4*a      *b3/2*d    ♦  8 |  24 | 12  0 |  * 8

x4o3/2o3/2o4*a4*c *b3/2*d

. .   .   .               | 16 ♦  24 | 12 12 12 | 4 4 4
--------------------------+----+-----+----------+------
x .   .   .               |  2 | 192 |  1  1  1 | 1 1 1
--------------------------+----+-----+----------+------
x4o   .   .               |  4 |   4 | 48  *  * | 1 1 0
x .   o   . *a4*c         |  4 |   4 |  * 48  * | 1 0 1
x .   .   o4*a            |  4 |   4 |  *  * 48 | 0 1 1
--------------------------+----+-----+----------+------
x4o3/2o   . *a4*c         ♦  8 |  24 |  6  6  0 | 8 * *
x4o   .   o4*a    *b3/2*d ♦  8 |  24 |  6  0  6 | * 8 *
x .   o3/2o4*a4*c         ♦  8 |  24 |  0  6  6 | * * 8

or
. .   .   .                  | 16 ♦  24 |  36 | 12
-----------------------------+----+-----+-----+---
x .   .   .                  |  2 | 192 |   3 |  3
-----------------------------+----+-----+-----+---
x4o   .   .                & |  4 |   4 | 144 |  2
-----------------------------+----+-----+-----+---
x4o3/2o   . *a4*c          & ♦  8 |  24 |  12 | 24

x4/3o3o3o4/3*a4*c *b3/2*d

.   . . .                 | 16 ♦  24 | 12 12 12 | 4 4 4
--------------------------+----+-----+----------+------
x   . . .                 |  2 | 192 |  1  1  1 | 1 1 1
--------------------------+----+-----+----------+------
x4/3o . .                 |  4 |   4 | 48  *  * | 1 1 0
x   . o .   *a4*c         |  4 |   4 |  * 48  * | 1 0 1
x   . . o4/3*a            |  4 |   4 |  *  * 48 | 0 1 1
--------------------------+----+-----+----------+------
x4/3o3o .   *a4*c         ♦  8 |  24 |  6  6  0 | 8 * *
x4/3o . o4/3*a    *b3/2*d ♦  8 |  24 |  6  0  6 | * 8 *
x   . o3o4/3*a4*c         ♦  8 |  24 |  0  6  6 | * * 8

or
.   . . .                    | 16 ♦  24 | 24 12 |  8 4
-----------------------------+----+-----+-------+-----
x   . . .                    |  2 | 192 |  2  1 |  2 1
-----------------------------+----+-----+-------+-----
x4/3o . .                  & |  4 |   4 | 96  * |  1 1
x   . o .   *a4*c            |  4 |   4 |  * 48 |  2 0
-----------------------------+----+-----+-------+-----
x4/3o3o .   *a4*c          & ♦  8 |  24 |  6  6 | 16 *
x4/3o . o4/3*a    *b3/2*d    ♦  8 |  24 | 12  0 |  * 8

x4/3o3/2o3/2o4/3*a4/3*c *b3/2*d

.   .   .   .                   | 16 ♦  24 | 12 12 12 | 4 4 4
--------------------------------+----+-----+----------+------
x   .   .   .                   |  2 | 192 |  1  1  1 | 1 1 1
--------------------------------+----+-----+----------+------
x4/3o   .   .                   |  4 |   4 | 48  *  * | 1 1 0
x   .   o   .   *a4/3*c         |  4 |   4 |  * 48  * | 1 0 1
x   .   .   o4/3*a              |  4 |   4 |  *  * 48 | 0 1 1
--------------------------------+----+-----+----------+------
x4/3o3/2o   .   *a4/3*c         ♦  8 |  24 |  6  6  0 | 8 * *
x4/3o   .   o4/3*a      *b3/2*d ♦  8 |  24 |  6  0  6 | * 8 *
x   .   o3/2o4/3*a4/3*c         ♦  8 |  24 |  0  6  6 | * * 8

or
.   .   .   .                      | 16 ♦  24 |  36 | 12
-----------------------------------+----+-----+-----+---
x   .   .   .                      |  2 | 192 |   3 |  3
-----------------------------------+----+-----+-----+---
x4/3o   .   .                    & |  4 |   4 | 144 |  2
-----------------------------------+----+-----+-----+---
x4/3o3/2o   .   *a4/3*c          & ♦  8 |  24 |  12 | 24