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It can be thought of as a degenerate 4D segmentotope with zero height.

Note that it not truely is a decomposition, because opposite "lacing" squacues do overlap and would connect to the respectively other cubical squares of the "inner" gocco. In fact quite generally, the "lacing" facets of a non-convex "outer base" always are forced to overlap accordingly.

Incidence matrix according to Dynkin symbol

xx4/3ox3xo4*a&#x   → height = 0
(socco || gocco)

o.4/3o.3o.4*a    | 24  * |  2  2  2  0  0 | 1 2 1  2  1  2 0 0 0 | 1 1 2 1 0
.o4/3.o3.o4*a    |  * 24 |  0  0  2  2  2 | 0 0 0  2  2  1 2 1 1 | 0 2 1 1 1
-----------------+-------+----------------+----------------------+----------
x.   .. ..       |  2  0 | 24  *  *  *  * | 1 1 0  1  0  0 0 0 0 | 1 1 1 0 0
..   .. x.       |  2  0 |  * 24  *  *  * | 0 1 1  0  0  1 0 0 0 | 1 0 1 1 0
oo4/3oo3oo4*a&#x |  1  1 |  *  * 48  *  * | 0 0 0  1  1  1 0 0 0 | 0 1 1 1 0
.x   .. ..       |  0  2 |  *  *  * 24  * | 0 0 0  1  0  0 1 1 0 | 0 1 1 0 1
..   .x ..       |  0  2 |  *  *  *  * 24 | 0 0 0  0  1  0 1 0 1 | 0 1 0 1 1
-----------------+-------+----------------+----------------------+----------
x.4/3o. ..       |  4  0 |  4  0  0  0  0 | 6 * *  *  *  * * * * | 1 1 0 0 0
x.   .. x.4*a    |  8  0 |  4  4  0  0  0 | * 6 *  *  *  * * * * | 1 0 1 0 0  {8}
..   o.3x.       |  3  0 |  0  3  0  0  0 | * * 8  *  *  * * * * | 1 0 0 1 0
xx   .. ..   &#x |  2  2 |  1  0  2  1  0 | * * * 24  *  * * * * | 0 1 1 0 0
..   ox ..   &#x |  1  2 |  0  0  2  0  1 | * * *  * 24  * * * * | 0 1 0 1 0
..   .. xo   &#x |  2  1 |  0  1  2  0  0 | * * *  *  * 24 * * * | 0 0 1 1 0
.x4/3.x ..       |  0  8 |  0  0  0  4  4 | * * *  *  *  * 6 * * | 0 1 0 0 1  {8/3}
.x   .. .o4*a    |  0  4 |  0  0  0  4  0 | * * *  *  *  * * 6 * | 0 0 1 0 1
..   .x3.o       |  0  3 |  0  0  0  0  3 | * * *  *  *  * * * 8 | 0 0 0 1 1
-----------------+-------+----------------+----------------------+----------
x.4/3o.3x.4*a    ♦ 24  0 | 24 24  0  0  0 | 6 6 8  0  0  0 0 0 0 | 1 * * * *
xx4/3ox ..   &#x ♦  4  8 |  4  0  8  4  4 | 1 0 0  4  4  0 1 0 0 | * 6 * * *
xx   .. xo4*a&#x ♦  8  4 |  4  4  8  4  0 | 0 1 0  4  0  4 0 1 0 | * * 6 * *
..   ox3xo   &#x ♦  3  3 |  0  3  6  0  3 | 0 0 1  0  3  3 0 0 1 | * * * 8 *
.x4/3.x3.o4*a    ♦  0 24 |  0  0  0 24 24 | 0 0 0  0  0  0 6 6 8 | * * * * 1