x o3o   o o3x
             
             
             
    x o3x     

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