Acronym	firx
Name	facetorectified hexateron
Field of sections	©
Circumradius	sqrt(2/3) = 0.816497
Inradius wrt. pen	2/sqrt(15) = 0.516398
Inradius wrt. tepe	1/sqrt(24) = 0.204124
Inradius wrt. triddip	0
Vertex figure	©
Surface	[30+20 sqrt(2)+sqrt(5)]/16 = 3.782521
General of army	rix
Colonel of regiment	rix
Dihedral angles (at margins)	at tet between pen and tepe:   arccos[sqrt(2/5)] = 50.768480° at trip between tepe and triddip:   45°
Face vector	15, 60, 105, 90, 31
Confer	Grünbaumian relatives: 2firx   general polytopal classes: non-orientable   analogs: facetorectified simplex frSn
External links

Incidence matrix according to Dynkin symbol

hemi( x3o3o3o3/2x )

 15 |  8 | 12 12 |  8 24 | 2  8  6
----+----+-------+-------+--------
  2 | 60 |  3  3 |  3  9 | 1  4  3
----+----+-------+-------+--------
  3 |  3 | 60  * |  2  2 | 1  2  1
  4 |  4 |  * 45 |  0  4 | 0  2  2
----+----+-------+-------+--------
♦ 4 |  6 |  4  0 | 30  * | 1  1  0
♦ 6 |  9 |  2  3 |  * 60 | 0  1  1
----+----+-------+-------+--------
♦ 5 | 10 | 10  0 |  5  0 | 6  *  *
♦ 8 | 16 |  8  6 |  2  4 | * 15  *
♦ 9 | 18 |  6  9 |  0  6 | *  * 10

reduced(xx3oo3oo3/2ox&#x, by .x3.o3.o3/2.x)   → height = sqrt(5/8) = 0.790569
(pen || pseudo 2firp)

o.3o.3o.3/2o.                         | 5  * |  4  4  0 |  6 12  6  0  0 | 4 12 12  4 0  0 | 1 4  6  4 1
.o3.o3.o3/2.o                         | * 10 |  0  2  6 |  0  6  6  6  6 | 0  6 12  6 2  6 | 0 2  6  6 2
--------------------------------------+------+----------+----------------+-----------------+------------
x. .. ..   ..                         | 2  0 | 10  *  * |  3  3  0  0  0 | 3  6  3  0 0  0 | 1 3  3  1 0
oo3oo3oo3/2oo&#x                      | 1  1 |  * 20  * |  0  3  3  0  0 | 0  3  6  3 0  0 | 0 1  3  3 1
.x .. ..   ..     &  .. .. ..   .x    | 0  2 |  *  * 30 |  0  1  1  2  2 | 0  2  4  2 1  3 | 0 1  3  3 1
--------------------------------------+------+----------+----------------+-----------------+------------
x.3o. ..   ..                         | 3  0 |  3  0  0 | 10  *  *  *  * | 2  2  0  0 0  0 | 1 2  1  0 0
xx .. ..   ..&#x                      | 2  2 |  1  2  1 |  * 30  *  *  * | 0  2  2  0 0  0 | 0 1  2  1 0
.. .. ..   ox&#x                      | 1  2 |  0  2  1 |  *  * 30  *  * | 0  0  2  2 0  0 | 0 0  1  2 1
.x3.o ..   ..     &  .. .. .o3/2.x    | 0  3 |  0  0  3 |  *  *  * 20  * | 0  1  0  1 1  1 | 0 1  1  1 1
.x .. ..   .x                         | 0  4 |  0  0  4 |  *  *  *  * 15 | 0  0  2  0 0  2 | 0 0  2  2 0
--------------------------------------+------+----------+----------------+-----------------+------------
x.3o.3o.   ..                         ♦ 4  0 |  6  0  0 |  4  0  0  0  0 | 5  *  *  * *  * | 1 1  0  0 0
xx3oo ..   ..&#x                      ♦ 3  3 |  3  3  3 |  1  3  0  1  0 | * 20  *  * *  * | 0 1  1  0 0
xx .. ..   ox&#x                      ♦ 2  4 |  1  4  4 |  0  2  2  0  1 | *  * 30  * *  * | 0 0  1  1 0
.. .. oo3/2ox&#x                      ♦ 1  3 |  0  3  3 |  0  0  3  1  0 | *  *  * 20 *  * | 0 0  0  1 1
.x3.o3.o   ..     &  .. .o3.o3/2.x    ♦ 0  4 |  0  0  6 |  0  0  0  4  0 | *  *  *  * 5  * | 0 1  0  0 1
.x3.o ..   .x     &  .x .. .o3/2.x    ♦ 0  6 |  0  0  9 |  0  0  0  2  3 | *  *  *  * * 10 | 0 0  1  1 0
--------------------------------------+------+----------+----------------+-----------------+------------
x.3o.3o.3/2o.                         ♦ 5  0 | 10  0  0 | 10  0  0  0  0 | 5  0  0  0 0  0 | 1 *  *  * *
xx3oo3oo   ..&#x                      ♦ 4  4 |  6  4  6 |  4  6  0  4  0 | 1  4  0  0 1  0 | * 5  *  * *
xx3oo ..   ox&#x                      ♦ 3  6 |  3  6  9 |  1  6  3  2  3 | 0  2  3  0 0  1 | * * 10  * *
xx .. oo3/2ox&#x                      ♦ 2  6 |  1  6  9 |  0  3  6  2  3 | 0  0  3  2 0  1 | * *  * 10 *
.. oo3oo3/2ox&#x                      ♦ 1  4 |  0  4  6 |  0  0  6  4  0 | 0  0  0  4 1  0 | * *  *  * 5