The existance of a circumradius shows that this CRF polychoron even is orbiform.

Incidence matrix according to Dynkin symbol

ofx3xoo5xxx&#xt   → height(1,2) = 1/2
                    height(2,3) = (1+sqrt(5))/4 = 0.809017
(tid || pseudo (f,x)-srid || srid)

o..3o..5o..     | 60  *  * |  2  1   2  0  0  0  0 |  1  2  1  2  2  0  0  0  0  0 | 1  1  1  2  0 0
.o.3.o.5.o.     |  * 60  * |  0  0   2  2  1  0  0 |  0  0  2  1  2  1  2  0  0  0 | 0  1  2  1  1 0
..o3..o5..o     |  *  * 60 |  0  0   0  0  1  2  2 |  0  0  2  0  0  0  2  1  2  1 | 0  1  2  0  1 1
----------------+----------+-----------------------+-------------------------------+----------------
... x.. ...     |  2  0  0 | 60  *   *  *  *  *  * |  1  1  0  1  0  0  0  0  0  0 | 1  1  0  1  0 0
... ... x..     |  2  0  0 |  * 30   *  *  *  *  * |  0  2  0  0  2  0  0  0  0  0 | 1  0  1  2  0 0
oo.3oo.5oo.&#x  |  1  1  0 |  *  * 120  *  *  *  * |  0  0  1  1  1  0  0  0  0  0 | 0  1  1  1  0 0
... ... .x.     |  0  2  0 |  *  *   * 60  *  *  * |  0  0  0  0  1  1  1  0  0  0 | 0  0  1  1  1 0
.oo3.oo5.oo&#x  |  0  1  1 |  *  *   *  * 60  *  * |  0  0  2  0  0  0  2  0  0  0 | 0  1  2  0  1 0
..x ... ...     |  0  0  2 |  *  *   *  *  * 60  * |  0  0  1  0  0  0  0  1  1  0 | 0  1  1  0  0 1
... ... ..x     |  0  0  2 |  *  *   *  *  *  * 60 |  0  0  0  0  0  0  1  0  1  1 | 0  0  1  0  1 1
----------------+----------+-----------------------+-------------------------------+----------------
o..3x.. ...     |  3  0  0 |  3  0   0  0  0  0  0 | 20  *  *  *  *  *  *  *  *  * | 1  1  0  0  0 0
... x..5x..     | 10  0  0 |  5  5   0  0  0  0  0 |  * 12  *  *  *  *  *  *  *  * | 1  0  0  1  0 0
ofx ... ...&#xt |  1  2  2 |  0  0   2  0  2  1  0 |  *  * 60  *  *  *  *  *  *  * | 0  1  1  0  0 0
... xo. ...&#x  |  2  1  0 |  1  0   2  0  0  0  0 |  *  *  * 60  *  *  *  *  *  * | 0  1  0  1  0 0
... ... xx.&#x  |  2  2  0 |  0  1   2  1  0  0  0 |  *  *  *  * 60  *  *  *  *  * | 0  0  1  1  0 0
... .o.5.x.     |  0  5  0 |  0  0   0  5  0  0  0 |  *  *  *  *  * 12  *  *  *  * | 0  0  0  1  1 0
... ... .xx&#x  |  0  2  2 |  0  0   0  1  2  0  1 |  *  *  *  *  *  * 60  *  *  * | 0  0  1  0  1 0
..x3..o ...     |  0  0  3 |  0  0   0  0  0  3  0 |  *  *  *  *  *  *  * 20  *  * | 0  1  0  0  0 1
..x ... ..x     |  0  0  4 |  0  0   0  0  0  2  2 |  *  *  *  *  *  *  *  * 30  * | 0  0  1  0  0 1
... ..o5..x     |  0  0  5 |  0  0   0  0  0  0  5 |  *  *  *  *  *  *  *  *  * 12 | 0  0  0  0  1 1
----------------+----------+-----------------------+-------------------------------+----------------
o..3x..5x..     ♦ 60  0  0 | 60 30   0  0  0  0  0 | 20 12  0  0  0  0  0  0  0  0 | 1  *  *  *  * *
ofx3xoo ...&#xt ♦  3  3  3 |  3  0   6  0  3  3  0 |  1  0  3  3  0  0  0  1  0  0 | * 20  *  *  * *
ofx ... xxx&#xt ♦  2  4  4 |  0  1   4  2  4  2  2 |  0  0  2  0  2  0  2  0  1  0 | *  * 30  *  * *
... xo.5xx.&#x  ♦ 10  5  0 |  5  5  10  5  0  0  0 |  0  1  0  5  5  1  0  0  0  0 | *  *  * 12  * *
... .oo5.xx&#x  ♦  0  5  5 |  0  0   0  5  5  0  5 |  0  0  0  0  0  1  5  0  0  1 | *  *  *  * 12 *
..x3..o5..x     ♦  0  0 60 |  0  0   0  0  0 60 60 |  0  0  0  0  0  0  0 20 30 12 | *  *  *  *  * 1