This polychoron was designed to be a non-Wythoffian example within the class of perfect polytopes. Perfect polytopes by definition do not allow for variations without changing the action of its symmetry group on its face-lattice.

This specific case was derived from deca by placing smaller cubes into its tuts in such a way, that one class of its vertices becomes coincident to their hexagon face centers, while the other class would be internal. The full polytope then is nothing but the convex hull of the so far obtained substructure.

All u edges, provided in the below description, only qualify as pseudo edges wrt. the full polychoron.

By the very definition of Waterman polytopes, not necessarily all vertices are on the same sphere. However in here both layers of mutually inverted (x,u)-tips as well as that of the u-spid do belong to the same radius.

Omitting the u-spid layer would result in the then isogonal polychoron xo3uo3ou3ox&#zh.

Incidence matrix according to Dynkin symbol

xuo3uoo3oou3oux&#z(q,q,h)   → heights = 0
                              lacing(1,2) = lacing(2,3) = q
                              lacing(1,3) = h
(tegum sum of 2 mutually inverted (x,u)-tips and an u-spid)

o..3o..3o..3o..           | 20  *  * |  1  3   6  0  0 |  3  6  3   6  0 | 1  3  3  3 0
.o.3.o.3.o.3.o.           |  * 20  * |  0  3   0  3  0 |  3  0  0   6  3 | 1  0  3  3 1
..o3..o3..o3..o           |  *  * 20 |  0  0   6  3  1 |  0  3  6   6  3 | 0  3  3  3 1
--------------------------+----------+-----------------+-----------------+-------------
x.. ... ... ...           |  2  0  0 | 10  *   *  *  * |  0  6  0   0  0 | 0  3  3  0 0  x
oo.3oo.3oo.3oo.&#q        |  1  1  0 |  * 60   *  *  * |  2  0  0   2  0 | 1  0  1  2 0  q
o.o3o.o3o.o3o.o&#h        |  1  0  1 |  *  * 120  *  * |  0  1  1   1  0 | 0  1  1  1 0  h
.oo3.oo3.oo3.oo&#q        |  0  1  1 |  *  *   * 60  * |  0  0  0   2  2 | 0  0  2  1 1  q
... ... ... ..x           |  0  0  2 |  *  *   *  * 10 |  0  0  6   0  0 | 0  3  0  3 0  x
--------------------------+----------+-----------------+-----------------+-------------
... uo. ... ou.&#zq       |  2  2  0 |  0  4   0  0  0 | 30  *  *   *  * | 1  0  0  1 0  q-{4}
x.o ... ... ...&#h        |  2  0  1 |  1  0   2  0  0 |  * 60  *   *  * | 0  1  1  0 0  xhh
... ... ... o.x&#h        |  1  0  2 |  0  0   2  0  1 |  *  * 60   *  * | 0  1  0  1 0  xhh
ooo3ooo3ooo3ooo&#r(q,q,h) |  1  1  1 |  0  1   1  1  0 |  *  *  * 120  * | 0  0  1  1 0  qqh
.uo ... .ou ...&#zq       |  0  2  2 |  0  0   0  4  0 |  *  *  *   * 30 | 0  0  1  0 1  q-{4}
--------------------------+----------+-----------------+-----------------+-------------
... uo.3oo.3ou.&#zq       |  4  4  0 |  0 12   0  0  0 |  6  0  0   0  0 | 5  *  *  * *  q-cube
x.o ... ... o.x&#h        |  2  0  2 |  1  0   4  0  1 |  0  2  2   0  0 | * 30  *  * *  (x,h)-2ap
xuo ... oou ...&#(q,zq,h) |  2  2  2 |  1  2   4  4  0 |  0  2  0   4  1 | *  * 30  * *  diagonal square wedge
... uoo ... oux&#(zq,q,h) |  2  2  2 |  0  4   4  2  1 |  1  0  2   4  0 | *  *  * 30 *  diagonal square wedge
.uo3.oo3.ou ...&#zq       |  0  4  4 |  0  0   0 12  0 |  0  0  0   0  6 | *  *  *  * 5  q-cube

or
o..3o..3o..3o..           & | 40  * |  1   3   6 |  3   9   6 |  1  3  6
.o.3.o.3.o.3.o.             |  * 20 |  0   6   0 |  6   0   6 |  2  0  6
----------------------------+-------+------------+------------+---------
x.. ... ... ...           & |  2  0 | 20   *   * |  0   6   0 |  0  3  3  x
oo.3oo.3oo.3oo.&#q        & |  1  1 |  * 120   * |  2   0   2 |  1  0  3  q
o.o3o.o3o.o3o.o&#h          |  2  0 |  *   * 120 |  0   2   1 |  0  1  2  h
----------------------------+-------+------------+------------+---------
... uo. ... ou.&#zq       & |  2  2 |  0   4   0 | 60   *   * |  1  0  1  q-{4}
x.o ... ... ...&#h        & |  3  0 |  1   0   2 |  * 120   * |  0  1  1  xhh
ooo3ooo3ooo3ooo&#r(q,q,h)   |  2  1 |  0   2   1 |  *   * 120 |  0  0  2  qqh
----------------------------+-------+------------+------------+---------
... uo.3oo.3ou.&#zq       & |  4  4 |  0  12   0 |  6   0   0 | 10  *  *  q-cube
x.o ... ... o.x&#h          |  4  0 |  2   0   4 |  0   4   0 |  * 30  *  (x,h)-2ap
xuo ... oou ...&#(q,zq,h) & |  4  2 |  1   6   4 |  1   2   4 |  *  * 60  diagonal square wedge