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

Incidence matrix according to Dynkin symbol

ofx3xoo4xxx&#xt   → height(1,2) = sqrt[sqrt(5)-1]/2 = 0.555893
                    height(2,3) = sqrt[1+sqrt(5)]/2 = 0.899454
(tic || pseudo (f,x)-sirco || sirco)

o..3o..4o..     | 24  *  * |  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.4.o.     |  * 24  * |  0  0  2  2  1  0  0 | 0 0  2  1  2 1  2 0  0 0 | 0 1  2 1 1 0
..o3..o4..o     |  *  * 24 |  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 | 24  *  *  *  *  *  * | 1 1  0  1  0 0  0 0  0 0 | 1 1  0 1 0 0
... ... x..     |  2  0  0 |  * 12  *  *  *  *  * | 0 2  0  0  2 0  0 0  0 0 | 1 0  1 2 0 0
oo.3oo.4oo.&#x  |  1  1  0 |  *  * 48  *  *  *  * | 0 0  1  1  1 0  0 0  0 0 | 0 1  1 1 0 0
... ... .x.     |  0  2  0 |  *  *  * 24  *  *  * | 0 0  0  0  1 1  1 0  0 0 | 0 0  1 1 1 0
.oo3.oo4.oo&#x  |  0  1  1 |  *  *  *  * 24  *  * | 0 0  2  0  0 0  2 0  0 0 | 0 1  2 0 1 0
..x ... ...     |  0  0  2 |  *  *  *  *  * 24  * | 0 0  1  0  0 0  0 1  1 0 | 0 1  1 0 0 1
... ... ..x     |  0  0  2 |  *  *  *  *  *  * 24 | 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 | 8 *  *  *  * *  * *  * * | 1 1  0 0 0 0
... x..4x..     |  8  0  0 |  4  4  0  0  0  0  0 | * 6  *  *  * *  * *  * * | 1 0  0 1 0 0
ofx ... ...&#xt |  1  2  2 |  0  0  2  0  2  1  0 | * * 24  *  * *  * *  * * | 0 1  1 0 0 0
... xo. ...&#x  |  2  1  0 |  1  0  2  0  0  0  0 | * *  * 24  * *  * *  * * | 0 1  0 1 0 0
... ... xx.&#x  |  2  2  0 |  0  1  2  1  0  0  0 | * *  *  * 24 *  * *  * * | 0 0  1 1 0 0
... .o.4.x.     |  0  4  0 |  0  0  0  4  0  0  0 | * *  *  *  * 6  * *  * * | 0 0  0 1 1 0
... ... .xx&#x  |  0  2  2 |  0  0  0  1  2  0  1 | * *  *  *  * * 24 *  * * | 0 0  1 0 1 0
..x3..o ...     |  0  0  3 |  0  0  0  0  0  3  0 | * *  *  *  * *  * 8  * * | 0 1  0 0 0 1
..x ... ..x     |  0  0  4 |  0  0  0  0  0  2  2 | * *  *  *  * *  * * 12 * | 0 0  1 0 0 1
... ..o4..x     |  0  0  4 |  0  0  0  0  0  0  4 | * *  *  *  * *  * *  * 6 | 0 0  0 0 1 1
----------------+----------+----------------------+--------------------------+-------------
o..3x..4x..     ♦ 24  0  0 | 24 12  0  0  0  0  0 | 8 6  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 | * 8  * * * *
ofx ... xxx&#xt ♦  2  4  4 |  0  1  4  2  4  2  2 | 0 0  2  0  2 0  2 0  1 0 | * * 12 * * *
... xo.4xx.&#x  ♦  8  4  0 |  4  4  8  4  0  0  0 | 0 1  0  4  4 1  0 0  0 0 | * *  * 6 * *
... .oo4.xx&#x  ♦  0  4  4 |  0  0  0  4  4  0  4 | 0 0  0  0  0 1  4 0  0 1 | * *  * * 6 *
..x3..o4..x     ♦  0  0 24 |  0  0  0  0  0 24 24 | 0 0  0  0  0 0  0 8 12 6 | * *  * * * 1