Acronym ... Name icositetrachoron-derived Gévay polychoron,rectified o3m4o3o Circumradius ... Confer similar Gévay polytopes: oq3oo3qo3oc&#zx   rico   oq3oo3qo5oc&#zx   oa4oo3bo3oc&#zx   oa5oo3bo3oc&#zx   xuo3uoo3oou3oux&#z(q,q,h)   aco3boo4oob3oca&#z(x,x,d)   related Catalan polytope: o3m4o3o

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 ico by placing smaller rads into its octs in such a way, that one class of its vertices becomes coincident to their 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 a and b 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 icositetrachoron. In fact, when both the octs and the rads get augmented by corresponding pyramids of such an height that the obo3coc&#xt in turn get augmented into full (i.e. non-truncated) oxo3ooo&#yt bipyramids, then this polychoron would become o3m4o3o again. (See there also for the individual applicability of the rectification process wrt. a non-Wythoffian setup.)

Incidence matrix according to Dynkin symbol

```oa3oo4bo3oc&#zx   → height = 0
a = sqrt(8/3) = 1.632993
b = 2/sqrt(3) = 1.154701
c = 1/sqrt(3) = 0.577350
(tegum sum of b-rico and (a,c)-spic)

o.3o.4o.3o.     | 96   * |   6   0 |   6   3   0 |  2  3  0
.o3.o4.o3.o     |  * 144 |   4   4 |   4   4   4 |  1  4  1
----------------+--------+---------+-------------+---------
oo3oo4oo3oo&#x  |  1   1 | 576   * |   2   1   0 |  1  2  0
.. .. .. .c     |  0   2 |   * 288 |   0   1   2 |  0  2  1
----------------+--------+---------+-------------+---------
oa .. bo ..&#zx |  2   2 |   4   0 | 288   *   * |  1  1  0
.. .. .. oc&#x  |  1   2 |   2   1 |   * 288   * |  0  2  0
.. .. .o3.c     |  0   3 |   0   3 |   *   * 192 |  0  1  1
----------------+--------+---------+-------------+---------
oa3oo4bo ..&#zx ♦  8   6 |  24   0 |  12   0   0 | 24  *  *
oa .. bo3oc&#zx ♦  3   6 |  12   6 |   3   6   2 |  * 96  *
.. .o4.o3.c     ♦  0   6 |   0  12 |   0   0   8 |  *  * 24
```

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