Acronym ... Name hexacosachoron-derived Gévay polychoron,rectified o3m3o5o Circumradius sqrt(21+9 sqrt(5)) = 6.412847 Confer similar Gévay polytopes: oq3oo3qo3oc&#zx   rico   oa3oo4bo3oc&#zx   oa4oo3bo3oc&#zx   oa5oo3bo3oc&#zx   xuo3uoo3oou3oux&#z(q,q,h)   aco3boo4oob3oca&#z(x,x,d)   related Catalan polytope: o3m3o5o

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 ex 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 hexacosachoron. In fact, when both the does and the cubes get augmented by corresponding pyramids of such an height that the oqo5coc&#xt in turn get augmented into full (i.e. non-truncated) oxo5ooo&#yt bipyramids, then this polychoron would become o3m3o5o again. (See there also for the individual applicability of the rectification process wrt. a non-Wythoffian setup.)

Incidence matrix according to Dynkin symbol

```oq3oo3qo5oc&#zx   → height = 0
c = (1+sqrt(5))/sqrt(8) = 1.144123
(tegum sum of q-rahi and (q,c)-sidpixhi)

o.3o.3o.5o.     | 1200    * |    6    0 |    6    3    0 |   2   3   0
.o3.o3.o5.o     |    * 2400 |    3    3 |    3    3    3 |   1   3   1
----------------+-----------+-----------+----------------+------------
oo3oo3oo5oo&#x  |    1    1 | 7200    * |    2    1    0 |   1   2   0
.. .. .. .c     |    0    2 |    * 3600 |    0    1    2 |   0   2   1
----------------+-----------+-----------+----------------+------------
oq .. qo ..&#zx |    2    2 |    4    0 | 3600    *    * |   1   1   0
.. .. .. oc&#x  |    1    2 |    2    1 |    * 3600    * |   0   2   0
.. .. .o5.c     |    0    5 |    0    5 |    *    * 1440 |   0   1   1
----------------+-----------+-----------+----------------+------------
oq3oo3qo ..&#zx ♦    4    4 |   12    0 |    6    0    0 | 600   *   *
oq .. qo5oc&#zx ♦    5   10 |   20   10 |    5   10    2 |   * 720   *
.. .o3.o5.c     ♦    0   20 |    0   30 |    0    0   12 |   *   * 120
```