Acronym penatrip
Name pentachoron atop trigonal prism,
(edge,perp triangle,trip)-trigonic
Circumradius 1
Lace city
in approx. ASCII-art
x o3o   o o3x
             
             
             
    x o3x     
Confer
uniform relative:
scad  
segmentotera:
penaspid  
general polytopal classes:
segmentotera   lace simplices  

This polychoron can be obtained as a wedge of scad. In fact it is a diminishing of its pen-first rotunda, i.e. of penaspid. There the spid base gets diminished down to its trip facet only, while the other base (pen) just gets scratched tangentially only.


Incidence matrix according to Dynkin symbol

oxx ooo3xox&#x   → height(1,2) = sqrt(5/12) = 0.645497
                   height(1,3) = sqrt(3)/2 = 0.866025
                   height(2,3) = sqrt(2/3) = 0.816497
                   height(12,3) = sqrt(3/5) = 0.774597

o.. o..3o..    | 3 * * | 2 2 2 0 0 0 0 | 1 1 4 2 1 4 0 0 0 0 | 2 2 1 4 2 2 0 0 0 | 1 2 2 1 0
.o. .o.3.o.    | * 2 * | 0 3 0 1 3 0 0 | 0 3 3 3 0 0 3 3 0 0 | 3 1 3 3 0 0 3 1 0 | 1 3 1 0 1
..o ..o3..o    | * * 6 | 0 0 1 0 1 1 2 | 0 0 0 1 1 2 1 2 2 1 | 0 0 1 2 2 1 2 1 1 | 0 2 1 1 1
---------------+-------+---------------+---------------------+-------------------+----------
... ... x..    | 2 0 0 | 3 * * * * * * | 1 0 2 0 0 2 0 0 0 0 | 1 2 0 2 1 2 0 0 0 | 1 1 2 1 0
oo. oo.3oo.&#x | 1 1 0 | * 6 * * * * * | 0 1 2 1 0 0 0 0 0 0 | 2 1 1 2 0 0 0 0 0 | 1 2 1 0 0
o.o o.o3o.o&#x | 1 0 1 | * * 6 * * * * | 0 0 0 1 1 2 0 0 0 0 | 0 0 1 2 2 1 0 0 0 | 0 2 1 1 0
.x. ... ...    | 0 2 0 | * * * 1 * * * | 0 1 0 0 0 0 3 0 0 0 | 3 0 3 0 0 0 3 0 0 | 1 3 0 0 1
.oo .oo3.oo&#x | 0 1 1 | * * * * 6 * * | 0 0 0 1 0 0 1 2 0 0 | 0 0 1 2 0 0 2 1 0 | 0 2 1 0 1
..x ... ...    | 0 0 2 | * * * * * 3 * | 0 0 0 0 1 0 1 0 2 0 | 0 0 1 0 2 0 2 0 1 | 0 2 0 1 1
... ... ..x    | 0 0 2 | * * * * * * 6 | 0 0 0 0 0 1 0 1 1 1 | 0 0 0 1 1 1 1 1 1 | 0 1 1 1 1
---------------+-------+---------------+---------------------+-------------------+----------
... o..3x..    | 3 0 0 | 3 0 0 0 0 0 0 | 1 * * * * * * * * * | 0 2 0 0 0 2 0 0 0 | 1 0 2 1 0
ox. ... ...&#x | 1 2 0 | 0 2 0 1 0 0 0 | * 3 * * * * * * * * | 2 0 1 0 0 0 0 0 0 | 1 2 0 0 0
... ... xo.&#x | 2 1 0 | 1 2 0 0 0 0 0 | * * 6 * * * * * * * | 1 1 0 1 0 0 0 0 0 | 1 1 1 0 0
ooo ooo3ooo&#x | 1 1 1 | 0 1 1 0 1 0 0 | * * * 6 * * * * * * | 0 0 1 2 0 0 0 0 0 | 0 2 1 0 0
o.x ... ...&#x | 1 0 2 | 0 0 2 0 0 1 0 | * * * * 3 * * * * * | 0 0 1 0 2 0 0 0 0 | 0 2 0 1 0
... ... x.x&#x | 2 0 2 | 1 0 2 0 0 0 1 | * * * * * 6 * * * * | 0 0 0 1 1 1 0 0 0 | 0 1 1 1 0
.xx ... ...&#x | 0 2 2 | 0 0 0 1 2 1 0 | * * * * * * 3 * * * | 0 0 1 0 0 0 2 0 0 | 0 2 0 0 1
... ... .ox&#x | 0 1 2 | 0 0 0 0 2 0 1 | * * * * * * * 6 * * | 0 0 0 1 0 0 1 1 0 | 0 1 1 0 1
..x ... ..x    | 0 0 4 | 0 0 0 0 0 2 2 | * * * * * * * * 3 * | 0 0 0 0 1 0 1 0 1 | 0 1 0 1 1
... ..o3..x    | 0 0 3 | 0 0 0 0 0 0 3 | * * * * * * * * * 2 | 0 0 0 0 0 1 0 1 1 | 0 0 1 1 1
---------------+-------+---------------+---------------------+-------------------+----------
ox. ... xo.&#x  2 2 0 | 1 4 0 1 0 0 0 | 0 2 2 0 0 0 0 0 0 0 | 3 * * * * * * * * | 1 1 0 0 0
... oo.3xo.&#x  3 1 0 | 3 3 0 0 0 0 0 | 1 0 3 0 0 0 0 0 0 0 | * 2 * * * * * * * | 1 0 1 0 0
oxx ... ...&#x  1 2 2 | 0 2 2 1 2 1 0 | 0 1 0 2 1 0 1 0 0 0 | * * 3 * * * * * * | 0 2 0 0 0
... ... xox&#x  2 1 2 | 1 2 2 0 2 0 1 | 0 0 1 2 0 1 0 1 0 0 | * * * 6 * * * * * | 0 1 1 0 0
o.x ... x.x&#x  2 0 4 | 1 0 4 0 0 2 2 | 0 0 0 0 2 2 0 0 1 0 | * * * * 3 * * * * | 0 1 0 1 0
... o.o3x.x&#x  3 0 3 | 3 0 3 0 0 0 3 | 1 0 0 0 0 3 0 0 0 1 | * * * * * 2 * * * | 0 0 1 1 0
.xx ... .ox&#x  0 2 4 | 0 0 0 1 4 2 2 | 0 0 0 0 0 0 2 2 1 0 | * * * * * * 3 * * | 0 1 0 0 1
... .oo3.ox&#x  0 1 3 | 0 0 0 0 3 0 3 | 0 0 0 0 0 0 0 3 0 1 | * * * * * * * 2 * | 0 0 1 0 1
..x ..o3..x     0 0 6 | 0 0 0 0 0 3 6 | 0 0 0 0 0 0 0 0 3 2 | * * * * * * * * 1 | 0 0 0 1 1
---------------+-------+---------------+---------------------+-------------------+----------
ox. oo.3xo.&#x  3 2 0 | 3 6 0 1 0 0 0 | 1 3 6 0 0 0 0 0 0 0 | 3 2 0 0 0 0 0 0 0 | 1 * * * *
oxx ... xox&#x  2 2 4 | 1 4 4 1 4 2 2 | 0 2 2 4 2 2 2 2 1 0 | 1 0 2 2 1 0 1 0 0 | * 3 * * *
... ooo3xox&#x  3 1 3 | 3 3 3 0 3 0 3 | 1 0 3 3 0 3 0 3 0 1 | 0 1 0 3 0 1 0 1 0 | * * 2 * *
o.x o.o3x.x&#x  3 0 6 | 3 0 6 0 0 3 6 | 1 0 0 0 3 6 0 0 3 2 | 0 0 0 0 3 2 0 0 1 | * * * 1 *
.xx .oo3.ox&#x  0 2 6 | 0 0 0 1 6 3 6 | 0 0 0 0 0 0 3 6 3 2 | 0 0 0 0 0 0 3 2 1 | * * * * 1

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