Acronym	prip
Name	prismatorhombated pentachoron, runcitruncated pentachoron
Circumradius	sqrt(13/5) = 1.612452
Vertex figure	©
Vertex layers	Layer Symmetry Subsymmetries   o3o3o3o o3o3o . o3o . o o . o3o . o3o3o 1 x3x3o3x x3x3o . tut first x3x . x hip first x . o3x trip first . x3o3x co first 2a x3x3x . u3o . u u . x3x . u3o3x 2b x3u . o 3a u3o3x . u3x . x x . u3x . x3x3x 3b x3o . H H . x3o 4a x3o3x . opposite co x3x . u u . u3o . x3x3o opposite tut 4b o . x3u 5   o3x . x opposite trip x . x3x opposite hip   (H=hh=x+u)
Lace city in approx. ASCII-art	o3x x3x x3o o3x u3x u3o x3x u3x x3u x3x x3o u3o x3x
General of army	(is itself convex)
Colonel of regiment	(is itself locally convex – other uniform polychoral members: by cells: co hip oho toe trip tut prip 5 10 0 0 10 5 pittip 0 0 5 5 10 5   & others)
Confer	Grünbaumian relatives: 2prip   segmentochora: tut || toe   related CRFs: co || (u,x)-co || toe
External links

Incidence matrix according to Dynkin symbol

x3x3o3x

. . . . | 60 |  1  2  2 |  2  2  1  2  1 | 1  2  1 1
--------+----+----------+----------------+----------
x . . . |  2 | 30  *  * |  2  2  0  0  0 | 1  2  1 0
. x . . |  2 |  * 60  * |  1  0  1  1  0 | 1  1  0 1
. . . x |  2 |  *  * 60 |  0  1  0  1  1 | 0  1  1 1
--------+----+----------+----------------+----------
x3x . . |  6 |  3  3  0 | 20  *  *  *  * | 1  1  0 0
x . . x |  4 |  2  0  2 |  * 30  *  *  * | 0  1  1 0
. x3o . |  3 |  0  3  0 |  *  * 20  *  * | 1  0  0 1
. x . x |  4 |  0  2  2 |  *  *  * 30  * | 0  1  0 1
. . o3x |  3 |  0  0  3 |  *  *  *  * 20 | 0  0  1 1
--------+----+----------+----------------+----------
x3x3o . ♦ 12 |  6 12  0 |  4  0  4  0  0 | 5  *  * *
x3x . x ♦ 12 |  6  6  6 |  2  3  0  3  0 | * 10  * *
x . o3x ♦  6 |  3  0  6 |  0  3  0  0  2 | *  * 10 *
. x3o3x ♦ 12 |  0 12 12 |  0  0  4  6  4 | *  *  * 5

x3x3/2o3/2x

. .   .   . | 60 |  1  2  2 |  2  2  1  2  1 | 1  2  1 1
------------+----+----------+----------------+----------
x .   .   . |  2 | 30  *  * |  2  2  0  0  0 | 1  2  1 0
. x   .   . |  2 |  * 60  * |  1  0  1  1  0 | 1  1  0 1
. .   .   x |  2 |  *  * 60 |  0  1  0  1  1 | 0  1  1 1
------------+----+----------+----------------+----------
x3x   .   . |  6 |  3  3  0 | 20  *  *  *  * | 1  1  0 0
x .   .   x |  4 |  2  0  2 |  * 30  *  *  * | 0  1  1 0
. x3/2o   . |  3 |  0  3  0 |  *  * 20  *  * | 1  0  0 1
. x   .   x |  4 |  0  2  2 |  *  *  * 30  * | 0  1  0 1
. .   o3/2x |  3 |  0  0  3 |  *  *  *  * 20 | 0  0  1 1
------------+----+----------+----------------+----------
x3x3/2o   . ♦ 12 |  6 12  0 |  4  0  4  0  0 | 5  *  * *
x3x   .   x ♦ 12 |  6  6  6 |  2  3  0  3  0 | * 10  * *
x .   o3/2x ♦  6 |  3  0  6 |  0  3  0  0  2 | *  * 10 *
. x3/2o3/2x ♦ 12 |  0 12 12 |  0  0  4  6  4 | *  *  * 5

xxux3xxoo3oxxx&#xt   → all heights = sqrt(5/8) = 0.790569
(tut || pseudo toe || pseudo (u,x)-co || co)

o...3o...3o...     | 12  *  *  * | 1  2  2  0  0  0  0  0  0  0  0 | 2 1  2  2  1 0 0  0  0  0 0  0 0 0 0 | 1 2 1 1 0 0 0 0
.o..3.o..3.o..     |  * 24  *  * | 0  0  1  1  1  1  1  0  0  0  0 | 0 0  1  1  1 1 1  1  1  1 0  0 0 0 0 | 0 1 1 1 1 1 0 0
..o.3..o.3..o.     |  *  * 12  * | 0  0  0  0  0  0  2  2  1  0  0 | 0 0  0  0  0 0 0  1  2  2 1  2 0 0 0 | 0 0 0 1 1 2 1 0
...o3...o3...o     |  *  *  * 12 | 0  0  0  0  0  0  0  0  1  2  2 | 0 0  0  0  0 0 0  0  0  2 0  2 1 2 1 | 0 0 0 0 1 2 1 1
-------------------+-------------+---------------------------------+--------------------------------------+----------------
x... .... ....     |  2  0  0  0 | 6  *  *  *  *  *  *  *  *  *  * | 2 0  2  0  0 0 0  0  0  0 0  0 0 0 0 | 1 2 1 0 0 0 0 0
.... x... ....     |  2  0  0  0 | * 12  *  *  *  *  *  *  *  *  * | 1 1  0  1  0 0 0  0  0  0 0  0 0 0 0 | 1 1 0 1 0 0 0 0
oo..3oo..3oo..&#x  |  1  1  0  0 | *  * 24  *  *  *  *  *  *  *  * | 0 0  1  1  1 0 0  0  0  0 0  0 0 0 0 | 0 1 1 1 0 0 0 0
.x.. .... ....     |  0  2  0  0 | *  *  * 12  *  *  *  *  *  *  * | 0 0  1  0  0 1 1  0  0  1 0  0 0 0 0 | 0 1 1 0 1 1 0 0
.... .x.. ....     |  0  2  0  0 | *  *  *  * 12  *  *  *  *  *  * | 0 0  0  1  0 1 0  1  0  0 0  0 0 0 0 | 0 1 0 1 1 0 0 0
.... .... .x..     |  0  2  0  0 | *  *  *  *  * 12  *  *  *  *  * | 0 0  0  0  1 0 1  0  1  0 0  0 0 0 0 | 0 0 1 1 0 1 0 0
.oo.3.oo.3.oo.&#x  |  0  1  1  0 | *  *  *  *  *  * 24  *  *  *  * | 0 0  0  0  0 0 0  1  1  1 0  0 0 0 0 | 0 0 0 1 1 1 0 0
.... .... ..x.     |  0  0  2  0 | *  *  *  *  *  *  * 12  *  *  * | 0 0  0  0  0 0 0  0  1  0 1  1 0 0 0 | 0 0 0 1 0 1 1 0
..oo3..oo3..oo&#x  |  0  0  1  1 | *  *  *  *  *  *  *  * 12  *  * | 0 0  0  0  0 0 0  0  0  2 0  2 0 0 0 | 0 0 0 0 1 2 1 0
...x .... ....     |  0  0  0  2 | *  *  *  *  *  *  *  *  * 12  * | 0 0  0  0  0 0 0  0  0  1 0  0 1 1 0 | 0 0 0 0 1 1 0 1
.... .... ...x     |  0  0  0  2 | *  *  *  *  *  *  *  *  *  * 12 | 0 0  0  0  0 0 0  0  0  0 0  1 0 1 1 | 0 0 0 0 0 1 1 1
-------------------+-------------+---------------------------------+--------------------------------------+----------------
x...3x... ....     |  6  0  0  0 | 3  3  0  0  0  0  0  0  0  0  0 | 4 *  *  *  * * *  *  *  * *  * * * * | 1 1 0 0 0 0 0 0
.... x...3o...     |  3  0  0  0 | 0  3  0  0  0  0  0  0  0  0  0 | * 4  *  *  * * *  *  *  * *  * * * * | 1 0 0 1 0 0 0 0
xx.. .... ....&#x  |  2  2  0  0 | 1  0  2  1  0  0  0  0  0  0  0 | * * 12  *  * * *  *  *  * *  * * * * | 0 1 1 0 0 0 0 0
.... xx.. ....&#x  |  2  2  0  0 | 0  1  2  0  1  0  0  0  0  0  0 | * *  * 12  * * *  *  *  * *  * * * * | 0 1 0 1 0 0 0 0
.... .... ox..&#x  |  1  2  0  0 | 0  0  2  0  0  1  0  0  0  0  0 | * *  *  * 12 * *  *  *  * *  * * * * | 0 0 1 1 0 0 0 0
.x..3.x.. ....     |  0  6  0  0 | 0  0  0  3  3  0  0  0  0  0  0 | * *  *  *  * 4 *  *  *  * *  * * * * | 0 1 0 0 1 0 0 0
.x.. .... .x..     |  0  4  0  0 | 0  0  0  2  0  2  0  0  0  0  0 | * *  *  *  * * 6  *  *  * *  * * * * | 0 0 1 0 0 1 0 0
.... .xo. ....&#x  |  0  2  1  0 | 0  0  0  0  1  0  2  0  0  0  0 | * *  *  *  * * * 12  *  * *  * * * * | 0 0 0 1 1 0 0 0
.... .... .xx.&#x  |  0  2  2  0 | 0  0  0  0  0  1  2  1  0  0  0 | * *  *  *  * * *  * 12  * *  * * * * | 0 0 0 1 0 1 0 0
.xux .... ....&#xt |  0  2  2  2 | 0  0  0  1  0  0  2  0  2  1  0 | * *  *  *  * * *  *  * 12 *  * * * * | 0 0 0 0 1 1 0 0
.... ..o.3..x.     |  0  0  3  0 | 0  0  0  0  0  0  0  3  0  0  0 | * *  *  *  * * *  *  *  * 4  * * * * | 0 0 0 1 0 0 1 0
.... .... ..xx&#x  |  0  0  2  2 | 0  0  0  0  0  0  0  1  2  0  1 | * *  *  *  * * *  *  *  * * 12 * * * | 0 0 0 0 0 1 1 0
...x3...o ....     |  0  0  0  3 | 0  0  0  0  0  0  0  0  0  3  0 | * *  *  *  * * *  *  *  * *  * 4 * * | 0 0 0 0 1 0 0 1
...x .... ...x     |  0  0  0  4 | 0  0  0  0  0  0  0  0  0  2  2 | * *  *  *  * * *  *  *  * *  * * 6 * | 0 0 0 0 0 1 0 1
.... ...o3...x     |  0  0  0  3 | 0  0  0  0  0  0  0  0  0  0  3 | * *  *  *  * * *  *  *  * *  * * * 4 | 0 0 0 0 0 0 1 1
-------------------+-------------+---------------------------------+--------------------------------------+----------------
x...3x...3o...     ♦ 12  0  0  0 | 6 12  0  0  0  0  0  0  0  0  0 | 4 4  0  0  0 0 0  0  0  0 0  0 0 0 0 | 1 * * * * * * *
xx..3xx.. ....&#x  ♦  6  6  0  0 | 3  3  6  3  3  0  0  0  0  0  0 | 1 0  3  3  0 1 0  0  0  0 0  0 0 0 0 | * 4 * * * * * *
xx.. .... ox..&#x  ♦  2  4  0  0 | 1  0  4  2  0  2  0  0  0  0  0 | 0 0  2  0  2 0 1  0  0  0 0  0 0 0 0 | * * 6 * * * * *
.... xxo.3oxx.&#xt ♦  3  6  3  0 | 0  3  6  0  3  3  6  3  0  0  0 | 0 1  0  3  3 0 0  3  3  0 1  0 0 0 0 | * * * 4 * * * *
.xux3.xoo ....&#xt ♦  0  6  3  3 | 0  0  0  3  3  0  6  0  3  3  0 | 0 0  0  0  0 1 0  3  0  3 0  0 1 0 0 | * * * * 4 * * *
.xux .... .xxx&#xt ♦  0  4  4  4 | 0  0  0  2  0  2  4  2  4  2  2 | 0 0  0  0  0 0 1  0  2  2 0  2 0 1 0 | * * * * * 6 * *
.... ..oo3..xx&#x  ♦  0  0  3  3 | 0  0  0  0  0  0  0  3  3  0  3 | 0 0  0  0  0 0 0  0  0  0 1  3 0 0 1 | * * * * * * 4 *
...x3...o3...x     ♦  0  0  0 12 | 0  0  0  0  0  0  0  0  0 12 12 | 0 0  0  0  0 0 0  0  0  0 0  0 4 6 4 | * * * * * * * 1