Acronym ...
Name q x3o3o3o,
variation of pentachoron prism,
vertex figure of rectified hexeract
Circumradius sqrt(9/10) = 0.948683
Confer
uniform variant:
penp  

using edge sizes x = 1 and q = sqrt(2) = 1.414214


Incidence matrix according to Dynkin symbol

q x3o3o3o

. . . . . | 10 | 1  4 |  4  6 |  6  4 | 4 1
----------+----+------+-------+-------+----
q . . . . |  2 | 5  *   4  0 |  6  0 | 4 0
. x . . . |  2 | * 20 |  1  3 |  3  3 | 3 1
----------+----+------+-------+-------+----
q x . . . |  4 | 2  2 | 10  * |  3  0 | 3 0
. x3o . . |  3 | 0  3 |  * 20 |  1  2 | 2 1
----------+----+------+-------+-------+----
q x3o . .   6 | 3  6 |  3  2 | 10  * | 2 0
. x3o3o .   4 | 0  6 |  0  4 |  * 10 | 1 1
----------+----+------+-------+-------+----
q x3o3o .   8 | 4 12 |  6  8 |  4  2 | 5 *
. x3o3o3o   5 | 0 10 |  0 10 |  0  5 | * 2

xx3oo3oo3oo&#q   → height = sqrt(2) = 1.414214
(pen || pen)

o.3o.3o.3o.    | 5 * |  4 1  0 |  6  4  0 | 4  6 0 | 1 4 0
.o3.o3.o3.o    | * 5 |  0 1  4 |  0  4  6 | 0  6 4 | 0 4 1
---------------+-----+---------+----------+--------+------
x. .. .. ..    | 2 0 | 10 *  * |  3  1  0 | 3  3 0 | 1 3 0
oo3oo3oo3oo&#q | 1 1 |  * 5  *   0  4  0 | 0  6 0 | 0 4 0
.x .. .. ..    | 0 2 |  * * 10 |  0  1  3 | 0  3 3 | 0 3 1
---------------+-----+---------+----------+--------+------
x.3o. .. ..    | 3 0 |  3 0  0 | 10  *  * | 2  1 0 | 1 2 0
xx .. .. ..&#q | 2 2 |  1 2  1 |  * 10  * | 0  3 0 | 0 3 0
.x3.o .. ..    | 0 3 |  0 0  3 |  *  * 10 | 0  1 2 | 0 2 1
---------------+-----+---------+----------+--------+------
x.3o.3o. ..     4 0 |  6 0  0 |  4  0  0 | 5  * * | 1 1 0
xx3oo .. ..&#q  3 3 |  3 3  3 |  1  3  1 | * 10 * | 0 2 0
.x3.o3.o ..     0 4 |  0 0  6 |  0  0  4 | *  * 5 | 0 1 1
---------------+-----+---------+----------+--------+------
x.3o.3o.3o.     5 0 | 10 0  0 | 10  0  0 | 5  0 0 | 1 * *
xx3oo3oo ..&#q  4 4 |  6 4  6 |  4  6  4 | 1  4 1 | * 5 *
.x3.o3.o3.o     0 5 |  0 0 10 |  0  0 10 | 0  0 5 | * * 1

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