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 pen by placing smaller cubes into its tets in such a way, that half of its vertices becomes coincident to their face centers, while the other half would be internal. The full polytope then is nothing but the convex hull of the so far obtained substructure.

All q = sqrt(2) edges, provided in the below description, only qualify as pseudo edges wrt. the full polychoron.

Alternatively this polychoron qualifies as rectification of the dual of the rectified pentachoron. In fact, when both the tets and the cubes get augmented by corresponding pyramids of such an height that the retrip in turn get augmented into full (i.e. non-truncated) oxo3ooo&#yt bipyramids, then this polychoron would become o3m3o3o again. (See there also for the individual applicability of the rectification process wrt. a non-Wythoffian setup.)

Incidence matrix according to Dynkin symbol

oq3oo3qo3oc&#zx   → height = 0 
                    c = q/2 = 1/sqrt(2) = 0.707107
(tegum sum of q-rap and (q,c)-spid)

o.3o.3o.3o.     | 10  * |  6  0 |  6  3  0 | 2  3 0
.o3.o3.o3.o     |  * 20 |  3  3 |  3  3  3 | 1  3 1
----------------+-------+-------+----------+-------
oo3oo3oo3oo&#x  |  1  1 | 60  * |  2  1  0 | 1  2 0
.. .. .. .c     |  0  2 |  * 30 |  0  1  2 | 0  2 1
----------------+-------+-------+----------+-------
oq .. qo ..&#zx |  2  2 |  4  0 | 30  *  * | 1  1 0
.. .. .. oc&#x  |  1  2 |  2  1 |  * 30  * | 0  2 0
.. .. .o3.c     |  0  3 |  0  3 |  *  * 20 | 0  1 1
----------------+-------+-------+----------+-------
oq3oo3qo ..&#zx ♦  4  4 | 12  0 |  6  0  0 | 5  * *
oq .. qo3oc&#zx ♦  3  6 | 12  6 |  3  6  2 | * 10 *
.. .o3.o3.c     ♦  0  4 |  0  6 |  0  0  4 | *  * 5