Acronym rapu
Name rectified-pentachoron-based ursateron,
rap-based ursulate
Circumradius sqrt[(79+27 sqrt(5))/88] = 1.258489
Face vector 50, 190, 230, 110, 22
Confer
general polytopal classes:
ursatopes  

Incidence matrix according to Dynkin symbol

xoo3ofx3xoo3ooo&#xt   → height(1,2) = sqrt[(2 sqrt(5)-3)/5] = 0.542611
                        height(2,3) = sqrt[(1+3 sqrt(5))/10] = 0.877964
(srip || pseudo f-rap || rap)

o..3o..3o..3o..     | 30  *  * |  2  4  2  0  0 |  1  4  2  2  2  1  4  0  0 | 2  2 1  1  4  2  2 0 0 | 1 2  2 1 0
.o.3.o.3.o.3.o.     |  * 10  * |  0  0  6  1  0 |  0  0  0  0  3  6  6  0  0 | 0  0 0  3  3  6  2 0 0 | 0 3  1 2 0
..o3..o3..o3..o     |  *  * 10 |  0  0  0  1  6 |  0  0  0  0  0  6  0  3  6 | 0  0 0  3  0  6  0 3 2 | 0 3  0 2 1
--------------------+----------+----------------+----------------------------+------------------------+-----------
x.. ... ... ...     |  2  0  0 | 30  *  *  *  * |  1  2  0  0  1  0  0  0  0 | 2  1 0  1  2  0  0 0 0 | 1 2  1 0 0
... ... x.. ...     |  2  0  0 |  * 60  *  *  * |  0  1  1  1  0  0  1  0  0 | 1  1 1  0  1  1  1 0 0 | 1 1  1 1 0
oo.3oo.3oo.3oo.&#x  |  1  1  0 |  *  * 60  *  * |  0  0  0  0  1  1  2  0  0 | 0  0 0  1  2  2  1 0 0 | 0 2  1 1 0
.oo3.oo3.oo3.oo&#x  |  0  1  1 |  *  *  * 10  *   0  0  0  0  0  6  0  0  0 | 0  0 0  3  0  6  0 0 0 | 0 3  0 2 0
... ..x ... ...     |  0  0  2 |  *  *  *  * 30 |  0  0  0  0  0  1  0  1  2 | 0  0 0  1  0  2  0 2 1 | 0 2  0 1 1
--------------------+----------+----------------+----------------------------+------------------------+-----------
x..3o.. ... ...     |  3  0  0 |  3  0  0  0  0 | 10  *  *  *  *  *  *  *  * | 2  0 0  1  0  0  0 0 0 | 1 2  0 0 0
x.. ... x.. ...     |  4  0  0 |  2  2  0  0  0 |  * 30  *  *  *  *  *  *  * | 1  1 0  0  1  0  0 0 0 | 1 1  1 0 0
... o..3x.. ...     |  3  0  0 |  0  3  0  0  0 |  *  * 20  *  *  *  *  *  * | 1  0 1  0  0  1  0 0 0 | 1 1  0 1 0
... ... x..3o..     |  3  0  0 |  0  3  0  0  0 |  *  *  * 20  *  *  *  *  * | 0  1 1  0  0  0  1 0 0 | 1 0  1 1 0
xo. ... ... ...&#x  |  2  1  0 |  1  0  2  0  0 |  *  *  *  * 30  *  *  *  * | 0  0 0  1  2  0  0 0 0 | 0 2  1 0 0
... ofx ... ...&#xt |  1  2  2 |  0  0  2  2  1 |  *  *  *  *  * 30  *  *  * | 0  0 0  1  0  2  0 0 0 | 0 2  0 1 0
... ... xo. ...&#x  |  2  1  0 |  0  1  2  0  0 |  *  *  *  *  *  * 60  *  * | 0  0 0  0  1  1  1 0 0 | 0 1  1 1 0
..o3..x ... ...     |  0  0  3 |  0  0  0  0  3 |  *  *  *  *  *  *  * 10  * | 0  0 0  1  0  0  0 2 0 | 0 2  0 0 1
... ..x3..o ...     |  0  0  3 |  0  0  0  0  3 |  *  *  *  *  *  *  *  * 20 | 0  0 0  0  0  1  0 1 1 | 0 1  0 1 1
--------------------+----------+----------------+----------------------------+------------------------+-----------
x..3o..3x.. ...      12  0  0 | 12 12  0  0  0 |  4  6  4  0  0  0  0  0  0 | 5  * *  *  *  *  * * * | 1 1  0 0 0
x.. ... x..3o..       6  0  0 |  3  6  0  0  0 |  0  3  0  2  0  0  0  0  0 | * 10 *  *  *  *  * * * | 1 0  1 0 0
... o..3x..3o..       6  0  0 |  0 12  0  0  0 |  0  0  4  4  0  0  0  0  0 | *  * 5  *  *  *  * * * | 1 0  0 1 0
xoo3ofx ... ...&#xt   3  3  3 |  3  0  6  3  3 |  1  0  0  0  3  3  0  1  0 | *  * * 10  *  *  * * * | 0 2  0 0 0
xo. ... xo. ...&#x    4  1  0 |  2  2  4  0  0 |  0  1  0  0  2  0  2  0  0 | *  * *  * 30  *  * * * | 0 1  1 0 0
... ofx3xoo ...&#xt   3  3  3 |  0  3  6  3  3 |  0  0  1  0  0  3  3  0  1 | *  * *  *  * 20  * * * | 0 1  0 1 0
... ... xo.3oo.&#x    3  1  0 |  0  3  3  0  0 |  0  0  0  1  0  0  3  0  0 | *  * *  *  *  * 20 * * | 0 0  1 1 0
..o3..x3..o ...       0  0  6 |  0  0  0  0 12 |  0  0  0  0  0  0  0  4  4 | *  * *  *  *  *  * 5 * | 0 1  0 0 1
... ..x3..o3..o       0  0  4 |  0  0  0  0  6 |  0  0  0  0  0  0  0  0  4 | *  * *  *  *  *  * * 5 | 0 0  0 1 1
--------------------+----------+----------------+----------------------------+------------------------+-----------
x..3o..3x..3o..      30  0  0 | 30 60  0  0  0 | 10 30 20 20  0  0  0  0  0 | 5 10 5  0  0  0  0 0 0 | 1 *  * * *
xoo3ofx3xoo ...&#xt  12  6  6 | 12 12 24  6 12 |  4  6  4  0 12 12 12  4  4 | 1  0 0  4  6  4  0 1 0 | * 5  * * *
xo. ... xo.3oo.&#x    6  1  0 |  3  6  6  0  0 |  0  3  0  2  3  0  6  0  0 | 0  1 0  0  3  0  2 0 0 | * * 10 * *
... ofx3xoo3ooo&#xt   6  4  4 |  0 12 12  4  6 |  0  0  4  4  0  6 12  0  4 | 0  0 1  0  0  4  4 0 1 | * *  * 5 *
..o3..x3..o3..o       0  0 10 |  0  0  0  0 30 |  0  0  0  0  0  0  0 10 20 | 0  0 0  0  0  0  0 5 5 | * *  * * 1

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