﻿ penatrip
 Acronym penatrip Name pentachoron atop trigonal prism,(edge,perp triangle,trip)-trigonic Circumradius 1 Lace cityin 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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