Acronym tetasquip
Name 1/6-lune of dodecateron,
tetrahedron atop lacing-orthogonal square prism
Circumradius sqrt(3)/2 = 0.866025
Lace city
in approx. ASCII-art
o o x     o x o		-- oo xo ox&#x (tet)
               
               
               
               
     x x x     		--  x x x  (cube)
Confer
uniform relative:
dot  
general polytopal classes:
segmentotera  

Incidence matrix according to Dynkin symbol

oox oxx xox&#x   → all lacing heights = 1/sqrt(2) = 0.707107
(tet || lacing-orthogonal square prism)

o.. o.. o..    | 2 * * | 1 2 4 0 0 0 0 0 | 1 2 2 2 4 4 0 0 0 0 0 0 | 1 1 2 2 2 2 4 0 0 0 0 | 1 1 2 2 0
.o. .o. .o.    | * 2 * | 0 2 0 1 4 0 0 0 | 2 1 0 0 0 4 2 4 2 0 0 0 | 1 0 0 0 2 4 2 2 1 2 0 | 0 2 1 2 1
..o ..o ..o    | * * 8 | 0 0 1 0 1 1 1 1 | 0 0 1 1 1 1 1 1 1 1 1 1 | 0 1 1 1 1 1 1 1 1 1 1 | 1 1 1 1 1
---------------+-------+-----------------+-------------------------+-----------------------+----------
... ... x..    | 2 0 0 | 1 * * * * * * * | 0 2 0 0 4 0 0 0 0 0 0 0 | 1 0 2 2 0 0 4 0 0 0 0 | 1 0 2 2 0
oo. oo. oo.&#x | 1 1 0 | * 4 * * * * * * | 1 1 0 0 0 2 0 0 0 0 0 0 | 1 0 0 0 1 2 2 0 0 0 0 | 0 1 1 2 0
o.o o.o o.o&#x | 1 0 1 | * * 8 * * * * * | 0 0 1 1 1 1 0 0 0 0 0 0 | 0 1 1 1 1 1 1 0 0 0 0 | 1 1 1 1 0
... .x. ...    | 0 2 0 | * * * 1 * * * * | 2 0 0 0 0 0 0 4 0 0 0 0 | 1 0 0 0 0 4 0 2 0 2 0 | 0 2 0 2 1
.oo .oo .oo&#x | 0 1 1 | * * * * 8 * * * | 0 0 0 0 0 1 1 1 1 0 0 0 | 0 0 0 0 1 1 1 1 1 1 0 | 0 1 1 1 1
..x ... ...    | 0 0 2 | * * * * * 4 * * | 0 0 1 0 0 0 1 0 0 1 1 0 | 0 1 1 0 1 0 0 1 1 0 1 | 1 1 1 0 1
... ..x ...    | 0 0 2 | * * * * * * 4 * | 0 0 0 1 0 0 0 1 0 1 0 1 | 0 1 0 1 0 1 0 1 0 1 1 | 1 1 0 1 1
... ... ..x    | 0 0 2 | * * * * * * * 4 | 0 0 0 0 1 0 0 0 1 0 1 1 | 0 0 1 1 0 0 1 0 1 1 1 | 1 0 1 1 1
---------------+-------+-----------------+-------------------------+-----------------------+----------
... ox. ...&#x | 1 2 0 | 0 2 0 1 0 0 0 0 | 2 * * * * * * * * * * * | 1 0 0 0 0 2 0 0 0 0 0 | 0 1 0 2 0
... ... xo.&#x | 2 1 0 | 1 2 0 0 0 0 0 0 | * 2 * * * * * * * * * * | 1 0 0 0 0 0 2 0 0 0 0 | 0 0 1 2 0
o.x ... ...&#x | 1 0 2 | 0 0 2 0 0 1 0 0 | * * 4 * * * * * * * * * | 0 1 1 0 1 0 0 0 0 0 0 | 1 1 1 0 0
... o.x ...&#x | 1 0 2 | 0 0 2 0 0 0 1 0 | * * * 4 * * * * * * * * | 0 1 0 1 0 1 0 0 0 0 0 | 1 1 0 1 0
... ... x.x&#x | 2 0 2 | 1 0 2 0 0 0 0 1 | * * * * 4 * * * * * * * | 0 0 1 1 0 0 1 0 0 0 0 | 1 0 1 1 0
ooo ooo ooo&#x | 1 1 1 | 0 1 1 0 1 0 0 0 | * * * * * 8 * * * * * * | 0 0 0 0 1 1 1 0 0 0 0 | 0 1 1 1 0
.ox ... ...&#x | 0 1 2 | 0 0 0 0 2 1 0 0 | * * * * * * 4 * * * * * | 0 0 0 0 1 0 0 1 1 0 0 | 0 1 1 0 1
... .xx ...&#x | 0 2 2 | 0 0 0 1 2 0 1 0 | * * * * * * * 4 * * * * | 0 0 0 0 0 1 0 1 0 1 0 | 0 1 0 1 1
... ... .ox&#x | 0 1 2 | 0 0 0 0 2 0 0 1 | * * * * * * * * 4 * * * | 0 0 0 0 0 0 1 0 1 1 0 | 0 0 1 1 1
..x ..x ...    | 0 0 4 | 0 0 0 0 0 2 2 0 | * * * * * * * * * 2 * * | 0 1 0 0 0 0 0 1 0 0 1 | 1 1 0 0 1
..x ... ..x    | 0 0 4 | 0 0 0 0 0 2 0 2 | * * * * * * * * * * 2 * | 0 0 1 0 0 0 0 0 1 0 1 | 1 0 1 0 1
... ..x ..x    | 0 0 4 | 0 0 0 0 0 0 2 2 | * * * * * * * * * * * 2 | 0 0 0 1 0 0 0 0 0 1 1 | 1 0 0 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 0 0 0 | 1 * * * * * * * * * * | 0 0 0 2 0
o.x o.x ...&#x  1 0 4 | 0 0 4 0 0 2 2 0 | 0 0 2 2 0 0 0 0 0 1 0 0 | * 2 * * * * * * * * * | 1 1 0 0 0
o.x ... x.x&#x  2 0 4 | 1 0 4 0 0 2 0 2 | 0 0 2 0 2 0 0 0 0 0 1 0 | * * 2 * * * * * * * * | 1 0 1 0 0
... o.x x.x&#x  2 0 4 | 1 0 4 0 0 0 2 2 | 0 0 0 2 2 0 0 0 0 0 0 1 | * * * 2 * * * * * * * | 1 0 0 1 0
oox ... ...&#x  1 1 2 | 0 1 2 0 2 1 0 0 | 0 0 1 0 0 2 1 0 0 0 0 0 | * * * * 4 * * * * * * | 0 1 1 0 0
... oxx ...&#x  1 2 2 | 0 2 2 1 2 0 1 0 | 1 0 0 1 0 2 0 1 0 0 0 0 | * * * * * 4 * * * * * | 0 1 0 1 0
... ... xox&#x  2 1 2 | 1 2 2 0 2 0 0 1 | 0 1 0 0 1 2 0 0 1 0 0 0 | * * * * * * 4 * * * * | 0 0 1 1 0
.ox .xx ...&#x  0 2 4 | 0 0 0 1 4 2 2 0 | 0 0 0 0 0 0 2 2 0 1 0 0 | * * * * * * * 2 * * * | 0 1 0 0 1
.ox ... .ox&#x  0 1 4 | 0 0 0 0 4 2 0 2 | 0 0 0 0 0 0 2 0 2 0 1 0 | * * * * * * * * 2 * * | 0 0 1 0 1
... .xx .ox&#x  0 2 4 | 0 0 0 1 4 0 2 2 | 0 0 0 0 0 0 0 2 2 0 0 1 | * * * * * * * * * 2 * | 0 0 0 1 1
..x ..x ..x     0 0 8 | 0 0 0 0 0 4 4 4 | 0 0 0 0 0 0 0 0 0 2 2 2 | * * * * * * * * * * 1 | 1 0 0 0 1
---------------+-------+-----------------+-------------------------+-----------------------+----------
o.x o.x x.x&#x  2 0 8 | 1 0 8 0 0 4 4 4 | 0 0 4 4 4 0 0 0 0 2 2 2 | 0 2 2 2 0 0 0 0 0 0 1 | 1 * * * *
oox oxx ...&#x  1 2 4 | 0 2 4 1 4 2 2 0 | 1 0 2 2 0 4 2 2 0 1 0 0 | 0 1 0 0 2 2 0 1 0 0 0 | * 2 * * *
oox ... xox&#x  2 1 4 | 1 2 4 0 4 2 0 2 | 0 1 2 0 2 4 2 0 2 0 1 0 | 0 0 1 0 2 0 2 0 1 0 0 | * * 2 * *
... oxx xox&#x  2 2 4 | 1 4 4 1 4 0 2 2 | 2 2 0 2 2 4 0 2 2 0 0 1 | 1 0 0 1 0 2 2 0 0 1 0 | * * * 2 *
.ox .xx .ox&#x  0 2 8 | 0 0 0 1 8 4 4 4 | 0 0 0 0 0 0 4 4 4 2 2 2 | 0 0 0 0 0 0 0 2 2 2 1 | * * * * 1

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