This polychoron is a mere bistratic stack of segmentochora.

Incidence matrix according to Dynkin symbol

oxo3oox5xxo&#xt   → height(1,2) = (sqrt(5)-1)/4 = 0.309017
                    height(2,3) = 1/2
(doe || pseudo srid || id)

o..3o..5o..    | 20  *  * |  3  3  0  0   0  0 |  3  3  6  0  0  0  0  0  0  0  0 | 1  1  3  3  0  0  0 0
.o.3.o.5.o.    |  * 60  * |  0  1  2  2   2  0 |  0  2  2  1  2  1  2  1  2  0  0 | 0  1  2  1  1  2  1 0
..o3..o5..o    |  *  * 30 |  0  0  0  0   4  4 |  0  0  0  0  0  0  2  4  2  2  2 | 0  0  0  0  2  1  2 1
---------------+----------+--------------------+----------------------------------+----------------------
... ... x..    |  2  0  0 | 30  *  *  *   *  * |  2  0  2  0  0  0  0  0  0  0  0 | 1  0  1  2  0  0  0 0
oo.3oo.5oo.&#x |  1  1  0 |  * 60  *  *   *  * |  0  2  2  0  0  0  0  0  0  0  0 | 0  1  2  1  0  0  0 0
.x. ... ...    |  0  2  0 |  *  * 60  *   *  * |  0  1  0  1  1  0  1  0  0  0  0 | 0  1  1  0  1  1  0 0
... ... .x.    |  0  2  0 |  *  *  * 60   *  * |  0  0  1  0  1  1  0  0  1  0  0 | 0  0  1  1  0  1  1 0
.oo3.oo5.oo&#x |  0  1  1 |  *  *  *  * 120  * |  0  0  0  0  0  0  1  1  1  0  0 | 0  0  0  0  1  1  1 0
... ..x ...    |  0  0  2 |  *  *  *  *   * 60 |  0  0  0  0  0  0  0  1  0  1  1 | 0  0  0  0  1  0  1 1
---------------+----------+--------------------+----------------------------------+----------------------
... o..5x..    |  5  0  0 |  5  0  0  0   0  0 | 12  *  *  *  *  *  *  *  *  *  * | 1  0  0  1  0  0  0 0
ox. ... ...&#x |  1  2  0 |  0  2  1  0   0  0 |  * 60  *  *  *  *  *  *  *  *  * | 0  1  1  0  0  0  0 0
... ... xx.&#x |  2  2  0 |  1  2  0  1   0  0 |  *  * 60  *  *  *  *  *  *  *  * | 0  0  1  1  0  0  0 0
.x.3.o. ...    |  0  3  0 |  0  0  3  0   0  0 |  *  *  * 20  *  *  *  *  *  *  * | 0  1  0  0  1  0  0 0
.x. ... .x.    |  0  4  0 |  0  0  2  2   0  0 |  *  *  *  * 30  *  *  *  *  *  * | 0  0  1  0  0  1  0 0
... .o.5.x.    |  0  5  0 |  0  0  0  5   0  0 |  *  *  *  *  * 12  *  *  *  *  * | 0  0  0  1  0  0  1 0
.xo ... ...&#x |  0  2  1 |  0  0  1  0   2  0 |  *  *  *  *  *  * 60  *  *  *  * | 0  0  0  0  1  1  0 0
... .ox ...&#x |  0  1  2 |  0  0  0  0   2  1 |  *  *  *  *  *  *  * 60  *  *  * | 0  0  0  0  1  0  1 0
... ... .xo&#x |  0  2  1 |  0  0  0  1   2  0 |  *  *  *  *  *  *  *  * 60  *  * | 0  0  0  0  0  1  1 0
..o3..x ...    |  0  0  3 |  0  0  0  0   0  3 |  *  *  *  *  *  *  *  *  * 20  * | 0  0  0  0  1  0  0 1
... ..x5..o    |  0  0  5 |  0  0  0  0   0  5 |  *  *  *  *  *  *  *  *  *  * 12 | 0  0  0  0  0  0  1 1
---------------+----------+--------------------+----------------------------------+----------------------
o..3o..5x..    ♦ 20  0  0 | 30  0  0  0   0  0 | 12  0  0  0  0  0  0  0  0  0  0 | 1  *  *  *  *  *  * *
ox.3oo. ...&#x ♦  1  3  0 |  0  3  3  0   0  0 |  0  3  0  1  0  0  0  0  0  0  0 | * 20  *  *  *  *  * *
ox. ... xx.&#x ♦  2  4  0 |  1  4  2  2   0  0 |  0  2  2  0  1  0  0  0  0  0  0 | *  * 30  *  *  *  * *
... oo.5xx.&#x ♦  5  5  0 |  5  5  0  5   0  0 |  1  0  5  0  0  1  0  0  0  0  0 | *  *  * 12  *  *  * *
.xo3.ox ...&#x ♦  0  3  3 |  0  0  3  0   6  3 |  0  0  0  1  0  0  3  3  0  1  0 | *  *  *  * 20  *  * *
.xo ... .xo&#x ♦  0  4  1 |  0  0  2  2   4  0 |  0  0  0  0  1  0  2  0  2  0  0 | *  *  *  *  * 30  * *
... .ox5.xo&#x ♦  0  5  5 |  0  0  0  5  10  5 |  0  0  0  0  0  1  0  5  5  0  1 | *  *  *  *  *  * 12 *
..o3..x5..o    ♦  0  0 30 |  0  0  0  0   0 60 |  0  0  0  0  0  0  0  0  0 20 12 | *  *  *  *  *  *  * 1