Acronym	firp
Name	faceted rectified pentachoron, retropyrohemiperichoron, vertex figure of dah, tetrahedral cuploid
Cross sections	©
Circumradius	sqrt(3/5) = 0.774597
Inradius wrt. tet	-3/sqrt(40) = -0.474342
Inradius wrt. trip	1/sqrt(60) = 0.129099
Volume	sqrt(5)/32 = 0.069877
Surface	[5 sqrt(2)+30 sqrt(3)]/12 = 4.919383
General of army	rap
Colonel of regiment	rap
Dihedral angles (at margins)	at {3} between tet and trip:   arccos[sqrt(3/8)] = 52.238756° at {4} between trip and trip:   arccos(2/3) = 48.189685°
Face vector	10, 30, 35, 15
Confer	Grünbaumian relatives: 2firp   firp+rap+15{4}   analogs: facetorectified simplex frSn
External links

Incidence matrix according to Dynkin symbol

hemi( x3o3o3/2x )

 10 ♦  6 |  6  6 | 2  6
----+----+-------+-----
  2 | 30 |  2  2 | 1  3
----+----+-------+-----
  3 |  3 | 20  * | 1  1
  4 |  4 |  * 15 | 0  2
----+----+-------+-----
♦ 4 |  6 |  4  0 | 5  *
♦ 6 |  9 |  2  3 | * 10

reduced( xx3/2oo3ox&#x , by x3/2o3x)   → height = sqrt(5/8) = 0.790569
tet || pseudo 2thah

o.3/2o.3o.                   | 4 * ♦ 3  3  0 | 3  6  3 0 0 | 1 3 3 1
.o3/2.o3.o                   | * 6 ♦ 0  2  4 | 0  4  4 2 2 | 0 2 4 2
-----------------------------+-----+---------+-------------+--------
x.   .. ..                   | 2 0 | 6  *  * | 2  2  0 0 0 | 1 2 1 0
oo3/2oo3oo&#x                | 1 1 | * 12  * | 0  2  2 0 0 | 0 1 2 1
.x   .. ..     &  ..   .. .x | 0 2 | *  * 12 | 0  1  1 1 1 | 0 1 2 1
-----------------------------+-----+---------+-------------+--------
x.3/2o. ..                   | 3 0 | 3  0  0 | 4  *  * * * | 1 1 0 0
xx   .. ..&#x                | 2 2 | 1  2  1 | * 12  * * * | 0 1 1 0
..   .. ox&#x                | 1 2 | 0  2  1 | *  * 12 * * | 0 0 1 1
.x3/2.o ..     & ..    .o3.x | 0 3 | 0  0  3 | *  *  * 4 * | 0 1 0 1
.x   .. .x                   | 0 4 | 0  0  4 | *  *  * * 3 | 0 0 2 0
-----------------------------+-----+---------+-------------+--------
x.3/2o.3o.                   ♦ 4 0 | 6  0  0 | 4  0  0 0 0 | 1 * * *
xx3/2oo ..&#x                ♦ 3 3 | 3  3  3 | 1  3  0 1 0 | * 4 * *
xx   .. ox&#x                ♦ 2 4 | 1  4  4 | 0  2  2 0 1 | * * 6 *
..   oo3ox&#x                ♦ 1 3 | 0  3  3 | 0  0  3 1 0 | * * * 4

reduced( ox3/2oo3xx&#x , by x3/2o3x)   → height = sqrt(5/8) = 0.790569
tet || pseudo 2thah

o.3/2o.3o.                   | 4 * ♦ 3  3  0 | 3  3  6 0 0 | 1 1 3 3
.o3/2.o3.o                   | * 6 ♦ 0  2  4 | 0  4  4 2 2 | 0 2 4 2
-----------------------------+-----+---------+-------------+--------
..   .. x.                   | 2 0 | 6  *  * | 2  0  2 0 0 | 1 0 1 2
oo3/2oo3oo&#x                | 1 1 | * 12  * | 0  2  2 0 0 | 0 1 2 1
.x   .. ..     &  ..   .. .x | 0 2 | *  * 12 | 0  1  1 1 1 | 0 1 2 1
-----------------------------+-----+---------+-------------+--------
..   o.3x.                   | 3 0 | 3  0  0 | 4  *  * * * | 1 0 0 1
ox   .. ..&#x                | 1 2 | 0  2  1 | * 12  * * * | 0 1 1 0
..   .. xx&#x                | 2 2 | 1  2  1 | *  * 12 * * | 0 0 1 1
.x3/2.o ..     & ..    .o3.x | 0 3 | 0  0  3 | *  *  * 4 * | 0 1 0 1
.x   .. .x                   | 0 4 | 0  0  4 | *  *  * * 3 | 0 0 2 0
-----------------------------+-----+---------+-------------+--------
o.3/2o.3x.                   ♦ 4 0 | 6  0  0 | 4  0  0 0 0 | 1 * * *
ox3/2oo ..&#x                ♦ 1 3 | 0  3  3 | 0  3  0 1 0 | * 4 * *
ox   .. xx&#x                ♦ 2 4 | 1  4  4 | 0  2  2 0 1 | * * 6 *
..   oo3xx&#x                ♦ 3 3 | 3  3  3 | 1  0  3 1 0 | * * * 4