Looks like a compound of 2 tesseract (tes) with vertices and edges identified, while faces and cells coincide by pairs.

Incidence matrix according to Dynkin symbol

x4o3o3o3/2*b

. . . .      | 16 ♦  4 | 12 | 4 4
-------------+----+----+----+----
x . . .      |  2 | 32 |  6 | 3 3
-------------+----+----+----+----
x4o . .      |  4 |  4 | 48 | 1 1
-------------+----+----+----+----
x4o3o .      ♦  8 | 12 |  6 | 8 *
x4o . o3/2*b ♦  8 | 12 |  6 | * 8

x4o3o3/2o3*b

. . .   .    | 16 ♦  4 | 12 | 4 4
-------------+----+----+----+----
x . .   .    |  2 | 32 |  6 | 3 3
-------------+----+----+----+----
x4o .   .    |  4 |  4 | 48 | 1 1
-------------+----+----+----+----
x4o3o   .    ♦  8 | 12 |  6 | 8 *
x4o .   o3*b ♦  8 | 12 |  6 | * 8

or
. . .   .      | 16 ♦  4 | 12 |  8
---------------+----+----+----+---
x . .   .      |  2 | 32 |  6 |  6
---------------+----+----+----+---
x4o .   .      |  4 |  4 | 48 |  2
---------------+----+----+----+---
x4o3o   .    & ♦  8 | 12 |  6 | 16

x4o3/2o3/2o3/2*b

. .   .   .      | 16 ♦  4 | 12 | 4 4
-----------------+----+----+----+----
x .   .   .      |  2 | 32 |  6 | 3 3
-----------------+----+----+----+----
x4o   .   .      |  4 |  4 | 48 | 1 1
-----------------+----+----+----+----
x4o3/2o   .      ♦  8 | 12 |  6 | 8 *
x4o   .   o3/2*b ♦  8 | 12 |  6 | * 8

or
. .   .   .        | 16 ♦  4 | 12 |  8
-------------------+----+----+----+---
x .   .   .        |  2 | 32 |  6 |  6
-------------------+----+----+----+---
x4o   .   .        |  4 |  4 | 48 |  2
-------------------+----+----+----+---
x4o3/2o   .      & ♦  8 | 12 |  6 | 16

x4/3o3o3o3/2*b

.   . . .      | 16 ♦  4 | 12 | 4 4
---------------+----+----+----+----
x   . . .      |  2 | 32 |  6 | 3 3
---------------+----+----+----+----
x4/3o . .      |  4 |  4 | 48 | 1 1
---------------+----+----+----+----
x4/3o3o .      ♦  8 | 12 |  6 | 8 *
x4/3o . o3/2*b ♦  8 | 12 |  6 | * 8

x4/3o3o3/2o3*b

.   . .   .    | 16 ♦  4 | 12 | 4 4
---------------+----+----+----+----
x   . .   .    |  2 | 32 |  6 | 3 3
---------------+----+----+----+----
x4/3o .   .    |  4 |  4 | 48 | 1 1
---------------+----+----+----+----
x4/3o3o   .    ♦  8 | 12 |  6 | 8 *
x4/3o .   o3*b ♦  8 | 12 |  6 | * 8

or
.   . .   .      | 16 ♦  4 | 12 |  8
-----------------+----+----+----+---
x   . .   .      |  2 | 32 |  6 |  6
-----------------+----+----+----+---
x4/3o .   .      |  4 |  4 | 48 |  2
-----------------+----+----+----+---
x4/3o3o   .    & ♦  8 | 12 |  6 | 16

x4/3o3/2o3/2o3/2*b

.   .   .   .      | 16 ♦  4 | 12 | 4 4
-------------------+----+----+----+----
x   .   .   .      |  2 | 32 |  6 | 3 3
-------------------+----+----+----+----
x4/3o   .   .      |  4 |  4 | 48 | 1 1
-------------------+----+----+----+----
x4/3o3/2o   .      ♦  8 | 12 |  6 | 8 *
x4/3o   .   o3/2*b ♦  8 | 12 |  6 | * 8

or
.   .   .   .        | 16 ♦  4 | 12 |  8
---------------------+----+----+----+---
x   .   .   .        |  2 | 32 |  6 |  6
---------------------+----+----+----+---
x4/3o   .   .        |  4 |  4 | 48 |  2
---------------------+----+----+----+---
x4/3o3/2o   .      & ♦  8 | 12 |  6 | 16