Acronym ... Name decachoron-derived Gévay polychoron Circumradius ... Confer similar Gévay polytopes: oq3oo3qo3oc&#zx   rico   oq3oo3qo5oc&#zx   oa3oo4bo3oc&#zx   oa4oo3bo3oc&#zx   oa5oo3bo3oc&#zx   aco3boo4oob3oca&#z(x,x,d)

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.

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 a 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"
```