Acronym rappy
Name rectified-pentachoric pyramid,
vertex cap of hin
Circumradius sqrt(5/8) = 0.790569
Inradius
wrt. pen 		3/sqrt(40) = 0.474342
Inradius
wrt. octpy 		1/sqrt(8) = 0.353553
Inradius
wrt. rap 		-1/sqrt(40) = -0.158114
Lace city
in approx. ASCII-art 
O   o       o = o3o3o
            O = o3x3o
  T         T = x3o3o
Volume 11 sqrt(2)/480 = 0.032409
Dihedral angles
(at margins)
  • at tet between octpy and pen:   arccos[-1/sqrt(5)] = 116.565051°
  • at tet between octpy and octpy:   90°
  • at oct between octpy and rap:   arccos[1/sqrt(5)] = 63.434949°
  • at tet between pen and rap:   arccos(3/5) = 53.130102°
Face vector 11, 40, 60, 40, 11
Confer
uniform relative:
hin  
segmentotera:
bidhin   trafpy  
related CRFs:
rapt  
general polytopal classes:
segmentotera   fundamental lace prisms   lace simplices  
analogs:
rectified simplex pyramid rSn-py  

Incidence matrix according to Dynkin symbol

oo3ox3oo3oo&#x   → height = sqrt(2/5) = 0.632456
(pt || rap)

o.3o.3o.3o.    | 1  * ♦ 10  0 | 30  0  0 | 10 20 0 0 | 5 5 0
.o3.o3.o3.o    | * 10 ♦  1  6 |  6  3  6 |  3  6 3 2 | 3 2 1
---------------+------+-------+----------+-----------+------
oo3oo3oo3oo&#x | 1  1 | 10  * ♦  6  0  0 |  3  6 0 0 | 3 2 0
.. .x .. ..    | 0  2 |  * 30 |  1  1  2 |  1  2 2 1 | 2 1 1
---------------+------+-------+----------+-----------+------
.. ox .. ..&#x | 1  2 |  2  1 | 30  *  * |  1  2 0 0 | 2 1 0
.o3.x .. ..    | 0  3 |  0  3 |  * 10  * |  1  0 2 0 | 2 0 1
.. .x3.o ..    | 0  3 |  0  3 |  *  * 20 |  0  1 1 1 | 1 1 1
---------------+------+-------+----------+-----------+------
oo3ox .. ..&#x ♦ 1  3 |  3  3 |  3  1  0 | 10  * * * | 2 0 0
.. ox3oo ..&#x ♦ 1  3 |  3  3 |  3  0  1 |  * 20 * * | 1 1 0
.o3.x3.o ..    ♦ 0  6 |  0 12 |  0  4  4 |  *  * 5 * | 1 0 1
.. .x3.o3.o    ♦ 0  4 |  0  6 |  0  0  4 |  *  * * 5 | 0 1 1
---------------+------+-------+----------+-----------+------
oo3ox3oo ..&#x ♦ 1  6 |  6 12 | 12  4  4 |  4  4 1 0 | 5 * *
.. ox3oo3oo&#x ♦ 1  4 |  4  6 |  6  0  4 |  0  4 0 1 | * 5 *
.o3.x3.o3.o    ♦ 0 10 |  0 30 |  0 10 20 |  0  0 5 5 | * * 1


oxo3oox3ooo&#x   → height(1,2) = height(2,3) = sqrt(5/8) = 0.790569
                   height(1,3) = 1/sqrt(2) = 0.707107

o..3o..3o..    | 1 * * ♦ 4 6 0  0  0 | 6 12 12 0 0  0 0 0 | 4 4 4 6 12 0 0 0 0 | 1 1 4 4 0
.o.3.o.3.o.    | * 4 * ♦ 1 0 3  3  0 | 3  0  3 3 3  3 0 0 | 3 0 0 3  3 1 3 1 0 | 1 0 3 1 1
..o3..o3..o    | * * 6 ♦ 0 1 0  2  4 | 0  4  2 0 1  4 2 2 | 0 2 2 1  4 0 2 2 1 | 0 1 2 2 1
---------------+-------+-------------+--------------------+--------------------+----------
oo.3oo.3oo.&#x | 1 1 0 | 4 * *  *  * ♦ 3  0  3 0 0  0 0 0 | 3 0 0 3  3 0 0 0 0 | 1 0 3 1 0
o.o3o.o3o.o&#x | 1 0 1 | * 6 *  *  * ♦ 0  4  2 0 0  0 0 0 | 0 2 2 1  4 0 0 0 0 | 0 1 2 2 0
.x. ... ...    | 0 2 0 | * * 6  *  * | 1  0  0 2 1  0 0 0 | 2 0 0 1  0 1 2 0 0 | 1 0 2 0 1
.oo3.oo3.oo&#x | 0 1 1 | * * * 12  * | 0  0  1 0 1  2 0 0 | 0 0 0 1  2 0 2 1 0 | 0 0 2 1 1
... ..x ...    | 0 0 2 | * * *  * 12 | 0  1  0 0 0  1 1 1 | 0 1 1 0  1 0 1 1 1 | 0 1 1 1 1
---------------+-------+-------------+--------------------+--------------------+----------
ox. ... ...&#x | 1 2 0 | 2 0 1  0  0 | 6  *  * * *  * * * | 2 0 0 1  0 0 0 0 0 | 1 0 2 0 0
... o.x ...&#x | 1 0 2 | 0 2 0  0  1 | * 12  * * *  * * * | 0 1 1 0  1 0 0 0 0 | 0 1 1 1 0
ooo3ooo3ooo&#x | 1 1 1 | 1 1 0  1  0 | *  * 12 * *  * * * | 0 0 0 1  2 0 0 0 0 | 0 0 2 1 0
.x.3.o. ...    | 0 3 0 | 0 0 3  0  0 | *  *  * 4 *  * * * | 1 0 0 0  0 1 1 0 0 | 1 0 1 0 1
.xo ... ...&#x | 0 2 1 | 0 0 1  2  0 | *  *  * * 6  * * * | 0 0 0 1  0 0 2 0 0 | 0 0 2 0 1
... .ox ...&#x | 0 1 2 | 0 0 0  2  1 | *  *  * * * 12 * * | 0 0 0 0  1 0 1 1 0 | 0 0 1 1 1
..o3..x ...    | 0 0 3 | 0 0 0  0  3 | *  *  * * *  * 4 * | 0 1 0 0  0 0 1 0 1 | 0 1 1 0 1
... ..x3..o    | 0 0 3 | 0 0 0  0  3 | *  *  * * *  * * 4 | 0 0 1 0  0 0 0 1 1 | 0 1 0 1 1
---------------+-------+-------------+--------------------+--------------------+----------
ox.3oo. ...&#x ♦ 1 3 0 | 3 0 3  0  0 | 3  0  0 1 0  0 0 0 | 4 * * *  * * * * * | 1 0 1 0 0
o.o3o.x ...&#x ♦ 1 0 3 | 0 3 0  0  3 | 0  3  0 0 0  0 1 0 | * 4 * *  * * * * * | 0 1 1 0 0
... o.x3o.o&#x ♦ 1 0 3 | 0 3 0  0  3 | 0  3  0 0 0  0 0 1 | * * 4 *  * * * * * | 0 1 0 1 0
oxo ... ...&#x ♦ 1 2 1 | 2 1 1  2  0 | 1  0  2 0 1  0 0 0 | * * * 6  * * * * * | 0 0 2 0 0
... oox ...&#x ♦ 1 1 2 | 1 2 0  2  1 | 0  1  2 0 0  1 0 0 | * * * * 12 * * * * | 0 0 1 1 0
.x.3.o.3.o.    ♦ 0 4 0 | 0 0 6  0  0 | 0  0  0 4 0  0 0 0 | * * * *  * 1 * * * | 1 0 0 0 1
.xo3.ox ...&#x ♦ 0 3 3 | 0 0 3  6  3 | 0  0  0 1 3  3 1 0 | * * * *  * * 4 * * | 0 0 1 0 1
... .ox3.oo&#x ♦ 0 1 3 | 0 0 0  3  3 | 0  0  0 0 0  3 0 1 | * * * *  * * * 4 * | 0 0 0 1 1
..o3..x3..o    ♦ 0 0 6 | 0 0 0  0 12 | 0  0  0 0 0  0 4 4 | * * * *  * * * * 1 | 0 1 0 0 1
---------------+-------+-------------+--------------------+--------------------+----------
ox.3oo.3oo.&#x ♦ 1 4 0 | 4 0 6  0  0 | 6  0  0 4 0  0 0 0 | 4 0 0 0  0 1 0 0 0 | 1 * * * *
o.o3o.x3o.o&#x ♦ 1 0 6 | 0 6 0  0 12 | 0 12  0 0 0  0 4 4 | 0 4 4 0  0 0 0 0 1 | * 1 * * *
oxo3oox ...&#x ♦ 1 3 3 | 3 3 3  6  3 | 3  3  6 1 3  3 1 0 | 1 1 0 3  3 0 1 0 0 | * * 4 * *
... oox3ooo&#x ♦ 1 1 3 | 1 3 0  3  3 | 0  3  3 0 0  3 0 1 | 0 0 1 0  3 0 0 1 0 | * * * 4 *
.xo3.ox3.oo&#x ♦ 0 4 6 | 0 0 6 12 12 | 0  0  0 4 6 12 4 4 | 0 0 0 0  0 1 4 4 1 | * * * * 1

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