Acronym tripalhip
Name trip atop lacing-orthogonal hip
Circumradius sqrt(13/8) = 1.274755
Lace city
in approx. ASCII-art
     x3o x     
               
x3x o     x3x o
x3o o     x3o o
               
     x3x x     
Confer
general polytopal classes:
segmentotera  

Incidence matrix according to Dynkin symbol

ox xo ox3xx&#x   → height = 1/sqrt(6) = 0.408248
(trip || lacing-ortho hip)

o. o. o.3o.    | 6  * | 1 2  4 0 0 0 | 2 1  2  4  2  4 0 0 0 | 1 2 1 2 2 4 2 0 | 1 2 1 2
.o o. .o3.o    | * 12 | 0 0  2 1 1 1 | 0 0  2  1  2  2 1 1 1 | 0 1 2 2 1 1 2 1 | 1 1 2 1
---------------+------+--------------+-----------------------+-----------------+--------
.. x. .. ..    | 2  0 | 3 *  * * * * | 2 0  0  4  0  0 0 0 0 | 1 2 0 0 2 4 0 0 | 1 2 0 2
.. .. .. x.    | 2  0 | * 6  * * * * | 1 1  0  0  0  2 0 0 0 | 1 0 0 1 0 2 2 0 | 0 1 1 2
oo oo oo3oo&#x | 1  1 | * * 24 * * * | 0 0  1  1  1  1 0 0 0 | 0 1 1 1 1 1 1 0 | 1 1 1 1
.x .. .. ..    | 0  2 | * *  * 6 * * | 0 0  2  0  0  0 1 1 0 | 0 1 2 2 0 0 0 1 | 1 1 2 0
.. .. .x ..    | 0  2 | * *  * * 6 * | 0 0  0  0  2  0 1 0 1 | 0 0 2 0 1 0 2 1 | 1 0 2 1
.. .. .. .x    | 0  2 | * *  * * * 6 | 0 0  0  0  0  2 0 1 1 | 0 0 0 2 0 1 2 1 | 0 1 2 1
---------------+------+--------------+-----------------------+-----------------+--------
.. x. .. x.    | 4  0 | 2 2  0 0 0 0 | 3 *  *  *  *  * * * * | 1 0 0 0 0 2 0 0 | 0 1 0 2
.. .. o.3x.    | 3  0 | 0 3  0 0 0 0 | * 2  *  *  *  * * * * | 1 0 0 0 0 0 2 0 | 0 0 1 2
ox .. .. ..&#x | 1  2 | 0 0  2 1 0 0 | * * 12  *  *  * * * * | 0 1 1 1 0 0 0 0 | 1 1 1 0
.. xo .. ..&#x | 2  1 | 1 0  2 0 0 0 | * *  * 12  *  * * * * | 0 1 0 0 1 1 0 0 | 1 1 0 1
.. .. ox ..&#x | 1  2 | 0 0  2 0 1 0 | * *  *  * 12  * * * * | 0 0 1 0 1 0 1 0 | 1 0 1 1
.. .. .. xx&#x | 2  2 | 0 1  2 0 0 1 | * *  *  *  * 12 * * * | 0 0 0 1 0 1 1 0 | 0 1 1 1
.x .. .x ..    | 0  4 | 0 0  0 2 2 0 | * *  *  *  *  * 3 * * | 0 0 2 0 0 0 0 1 | 1 0 2 0
.x .. .. .x    | 0  4 | 0 0  0 2 0 2 | * *  *  *  *  * * 3 * | 0 0 0 2 0 0 0 1 | 0 1 2 0
.. .. .x3.x    | 0  6 | 0 0  0 0 3 3 | * *  *  *  *  * * * 2 | 0 0 0 0 0 0 2 1 | 0 0 2 1
---------------+------+--------------+-----------------------+-----------------+--------
.. x. o.3x.     6  0 | 3 6  0 0 0 0 | 3 2  0  0  0  0 0 0 0 | 1 * * * * * * * | 0 0 0 2
ox xo .. ..&#x  2  2 | 1 0  4 1 0 0 | 0 0  2  2  0  0 0 0 0 | * 6 * * * * * * | 1 1 0 0
ox .. ox ..&#x  1  4 | 0 0  4 2 2 0 | 0 0  2  0  2  0 1 0 0 | * * 6 * * * * * | 1 0 1 0
ox .. .. xx&#x  2  4 | 0 1  4 2 0 2 | 0 0  2  0  0  2 0 1 0 | * * * 6 * * * * | 0 1 1 0
.. xo ox ..&#x  2  2 | 1 0  4 0 1 0 | 0 0  0  2  2  0 0 0 0 | * * * * 6 * * * | 1 0 0 1
.. xo .. xx&#x  4  2 | 2 2  4 0 0 1 | 1 0  0  2  0  2 0 0 0 | * * * * * 6 * * | 0 1 0 1
.. .. ox3xx&#x  3  6 | 0 3  6 0 3 3 | 0 1  0  0  3  3 0 0 1 | * * * * * * 4 * | 0 0 1 1
.x .. .x3.x     0 12 | 0 0  0 6 6 6 | 0 0  0  0  0  0 3 3 2 | * * * * * * * 1 | 0 0 2 0
---------------+------+--------------+-----------------------+-----------------+--------
ox xo ox ..&#x  2  4 | 1 0  8 2 2 0 | 0 0  4  4  4  0 1 0 0 | 0 2 2 0 2 0 0 0 | 3 * * *
ox xo .. xx&#x  4  4 | 2 2  8 2 0 2 | 1 0  4  4  0  4 0 1 0 | 0 2 0 2 0 2 0 0 | * 3 * *
ox .. ox3xx&#x  3 12 | 0 3 12 6 6 6 | 0 1  6  0  6  6 3 3 2 | 0 0 3 3 0 0 2 1 | * * 2 *
.. xo ox3xx&#x  6  6 | 3 6 12 0 3 3 | 3 2  0  6  6  6 0 0 1 | 1 0 0 0 3 3 2 0 | * * * 2

oox oox3xxx&#x   → height(1,2) = 1
                   height(1,3) = height(2,3) = sqrt(5/12) = 0.645497

o.. o..3o..    | 3 *  * | 2 1  4 0  0 0 0 0 | 1 2 2 2 4  4 0 0 0 0 0 0 0 | 1 1 2 2 2 2 4 0 0 0 0 | 1 1 2 2 0
.o. .o.3.o.    | * 3  * | 0 1  0 2  4 0 0 0 | 0 2 0 0 0  4 1 2 2 4 0 0 0 | 1 0 0 0 2 2 4 1 2 2 0 | 0 1 2 2 1
..o ..o3..o    | * * 12 | 0 0  1 0  1 1 1 1 | 0 0 1 1 1  1 0 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 | 3 *  * *  * * * * | 1 1 0 0 2  0 0 0 0 0 0 0 0 | 1 0 1 2 0 0 2 0 0 0 0 | 1 0 1 2 0
oo. oo.3oo.&#x | 1 1  0 | * 3  * *  * * * * | 0 2 0 0 0  4 0 0 0 0 0 0 0 | 1 0 0 0 2 2 4 0 0 0 0 | 0 1 2 2 0
o.o o.o3o.o&#x | 1 0  1 | * * 12 *  * * * * | 0 0 1 1 1  1 0 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 | * *  * 3  * * * * | 0 1 0 0 0  0 1 0 0 2 0 0 0 | 1 0 0 0 0 0 2 0 1 2 0 | 0 0 1 2 1
.oo .oo3.oo&#x | 0 1  1 | * *  * * 12 * * * | 0 0 0 0 0  1 0 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 | * *  * *  * 6 * * | 0 0 1 0 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 | * *  * *  * * 6 * | 0 0 0 1 0  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 | * *  * *  * * * 6 | 0 0 0 0 1  0 0 0 0 1 0 1 1 | 0 0 1 1 0 0 1 0 1 1 1 | 1 0 1 1 1
---------------+--------+-------------------+----------------------------+-----------------------+----------
... o..3x..    | 3 0  0 | 3 0  0 0  0 0 0 0 | 1 * * * *  * * * * * * * * | 1 0 0 2 0 0 0 0 0 0 0 | 1 0 0 2 0
... ... xx.&#x | 2 2  0 | 1 2  0 1  0 0 0 0 | * 3 * * *  * * * * * * * * | 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 | * * 6 * *  * * * * * * * * | 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 | * * * 6 *  * * * * * * * * | 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 | * * * * 6  * * * * * * * * | 0 0 1 1 0 0 1 0 0 0 0 | 1 0 1 1 0
ooo ooo3ooo&#x | 1 1  1 | 0 1  1 0  1 0 0 0 | * * * * * 12 * * * * * * * | 0 0 0 0 1 1 1 0 0 0 0 | 0 1 1 1 0
... .o.3.x.    | 0 3  0 | 0 0  0 3  0 0 0 0 | * * * * *  * 1 * * * * * * | 1 0 0 0 0 0 0 0 0 2 0 | 0 0 0 2 1
.ox ... ...&#x | 0 1  2 | 0 0  0 0  2 1 0 0 | * * * * *  * * 6 * * * * * | 0 0 0 0 1 0 0 1 1 0 0 | 0 1 1 0 1
... .ox ...&#x | 0 1  2 | 0 0  0 0  2 0 1 0 | * * * * *  * * * 6 * * * * | 0 0 0 0 0 1 0 1 0 1 0 | 0 1 0 1 1
... ... .xx&#x | 0 2  2 | 0 0  0 1  2 0 0 1 | * * * * *  * * * * 6 * * * | 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 | * * * * *  * * * * * 3 * * | 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 | * * * * *  * * * * * * 3 * | 0 0 1 0 0 0 0 0 1 0 1 | 1 0 1 0 1
... ..x3..x    | 0 0  6 | 0 0  0 0  0 0 3 3 | * * * * *  * * * * * * * 2 | 0 0 0 1 0 0 0 0 0 1 1 | 1 0 0 1 1
---------------+--------+-------------------+----------------------------+-----------------------+----------
... oo.3xx.&#x  3 3  0 | 3 3  0 3  0 0 0 0 | 1 3 0 0 0  0 1 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 0 1 0 0 | * 3 * * * * * * * * * | 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 0 1 0 | * * 3 * * * * * * * * | 1 0 1 0 0
... o.x3x.x&#x  3 0  6 | 3 0  6 0  0 0 3 3 | 1 0 0 3 3  0 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 0 1 0 0 0 0 0 | * * * * 6 * * * * * * | 0 1 1 0 0
... oox ...&#x  1 1  2 | 0 1  2 0  2 0 1 0 | 0 0 0 1 0  2 0 0 1 0 0 0 0 | * * * * * 6 * * * * * | 0 1 0 1 0
... ... xxx&#x  2 2  2 | 1 2  2 1  2 0 0 1 | 0 1 0 0 1  2 0 0 0 1 0 0 0 | * * * * * * 6 * * * * | 0 0 1 1 0
.ox .ox ...&#x  0 1  4 | 0 0  0 0  4 2 2 0 | 0 0 0 0 0  0 0 2 2 0 1 0 0 | * * * * * * * 3 * * * | 0 1 0 0 1
.ox ... .xx&#x  0 2  4 | 0 0  0 1  4 2 0 2 | 0 0 0 0 0  0 0 2 0 2 0 1 0 | * * * * * * * * 3 * * | 0 0 1 0 1
... .ox3.xx&#x  0 3  6 | 0 0  0 3  6 0 3 3 | 0 0 0 0 0  0 1 0 3 3 0 0 1 | * * * * * * * * * 2 * | 0 0 0 1 1
..x ..x3..x     0 0 12 | 0 0  0 0  0 6 6 6 | 0 0 0 0 0  0 0 0 0 0 3 3 2 | * * * * * * * * * * 1 | 1 0 0 0 1
---------------+--------+-------------------+----------------------------+-----------------------+----------
o.x o.x3x.x&#x  3 0 12 | 3 0 12 0  0 6 6 6 | 1 0 6 6 6  0 0 0 0 0 3 3 2 | 0 3 3 2 0 0 0 0 0 0 1 | 1 * * * *
oox oox ...&#x  1 1  4 | 0 1  4 0  4 2 2 0 | 0 0 2 2 0  4 0 2 2 0 1 0 0 | 0 1 0 0 2 2 0 1 0 0 0 | * 3 * * *
oox ... xxx&#x  2 2  4 | 1 2  4 1  4 2 0 2 | 0 1 2 0 2  4 0 2 0 2 0 1 0 | 0 0 1 0 2 0 2 0 1 0 0 | * * 3 * *
... oox3xxx&#x  3 3  6 | 3 3  6 3  6 0 3 3 | 1 3 0 3 3  6 1 0 3 3 0 0 1 | 1 0 0 1 0 3 3 0 0 1 0 | * * * 2 *
.ox .ox3.xx&#x  0 3 12 | 0 0  0 1 12 6 6 6 | 0 0 0 0 0  0 1 6 6 6 3 3 2 | 0 0 0 0 0 0 0 3 3 2 1 | * * * * 1

oox xxo3xxx&#x   → height(1,2) = 1
                   height(1,3) = height(2,3) = sqrt(5/12) = 0.645497

o.. o..3o..    | 6 * * | 1 1 1  2 0 0  0 0 0 | 1 1 1 1 2 2  2 0 0 0 0 0 0 | 1 1 1 2 1 2 2 0 0 0 0 | 1 1 1 2 0
.o. .o.3.o.    | * 6 * | 0 0 1  0 1 1  2 0 0 | 0 1 1 0 0 0  2 1 1 2 2 0 0 | 1 0 0 0 1 2 2 1 1 2 0 | 0 1 1 2 1
..o ..o3..o    | * * 6 | 0 0 0  2 0 0  2 1 2 | 0 0 0 2 1 2  2 0 2 1 2 2 1 | 0 1 2 1 2 1 2 1 2 1 1 | 1 1 2 1 1
---------------+-------+---------------------+----------------------------+-----------------------+----------
... x.. ...    | 2 0 0 | 3 * *  * * *  * * * | 1 1 0 0 2 0  0 0 0 0 0 0 0 | 1 1 0 2 0 2 0 0 0 0 0 | 1 1 0 2 0
... ... x..    | 2 0 0 | * 3 *  * * *  * * * | 1 0 1 0 0 2  0 0 0 0 0 0 0 | 1 0 1 2 0 0 2 0 0 0 0 | 1 0 1 2 0
oo. oo.3oo.&#x | 1 1 0 | * * 6  * * *  * * * | 0 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.o3o.o&#x | 1 0 1 | * * * 12 * *  * * * | 0 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 | * * *  * 3 *  * * * | 0 1 0 0 0 0  0 1 0 2 0 0 0 | 1 0 0 0 0 2 0 1 0 2 0 | 0 1 0 2 1
... ... .x.    | 0 2 0 | * * *  * * 3  * * * | 0 0 1 0 0 0  0 1 0 0 2 0 0 | 1 0 0 0 0 0 2 0 1 2 0 | 0 0 1 2 1
.oo .oo3.oo&#x | 0 1 1 | * * *  * * * 12 * * | 0 0 0 0 0 0  1 0 1 1 1 0 0 | 0 0 0 0 1 1 1 1 1 1 0 | 0 1 1 1 1
..x ... ...    | 0 0 2 | * * *  * * *  * 3 * | 0 0 0 2 0 0  0 0 2 0 0 2 0 | 0 1 2 0 2 0 0 1 2 0 1 | 1 1 2 0 1
... ... ..x    | 0 0 2 | * * *  * * *  * * 6 | 0 0 0 0 0 1  0 0 0 0 1 1 1 | 0 0 1 1 0 0 1 0 1 1 1 | 1 0 1 1 1
---------------+-------+---------------------+----------------------------+-----------------------+----------
... x..3x..    | 6 0 0 | 3 3 0  0 0 0  0 0 0 | 1 * * * * *  * * * * * * * | 1 0 0 2 0 0 0 0 0 0 0 | 1 0 0 2 0
... xx. ...&#x | 2 2 0 | 1 0 2  0 1 0  0 0 0 | * 3 * * * *  * * * * * * * | 1 0 0 0 0 2 0 0 0 0 0 | 0 1 0 2 0
... ... xx.&#x | 2 2 0 | 0 1 2  0 0 1  0 0 0 | * * 3 * * *  * * * * * * * | 1 0 0 0 0 0 2 0 0 0 0 | 0 0 1 2 0
o.x ... ...&#x | 1 0 2 | 0 0 0  2 0 0  0 1 0 | * * * 6 * *  * * * * * * * | 0 1 1 0 1 0 0 0 0 0 0 | 1 1 1 0 0
... x.o ...&#x | 2 0 1 | 1 0 0  2 0 0  0 0 0 | * * * * 6 *  * * * * * * * | 0 1 0 1 0 1 0 0 0 0 0 | 1 1 0 1 0
... ... x.x&#x | 2 0 2 | 0 1 0  2 0 0  0 0 1 | * * * * * 6  * * * * * * * | 0 0 1 1 0 0 1 0 0 0 0 | 1 0 1 1 0
ooo ooo3ooo&#x | 1 1 1 | 0 0 1  1 0 0  1 0 0 | * * * * * * 12 * * * * * * | 0 0 0 0 1 1 1 0 0 0 0 | 0 1 1 1 0
... .x.3.x.    | 0 6 0 | 0 0 0  0 3 3  0 0 0 | * * * * * *  * 1 * * * * * | 1 0 0 0 0 0 0 0 0 2 0 | 0 0 0 2 1
.ox ... ...&#x | 0 1 2 | 0 0 0  0 0 0  2 1 0 | * * * * * *  * * 6 * * * * | 0 0 0 0 1 0 0 1 1 0 0 | 0 1 1 0 1
... .xo ...&#x | 0 2 1 | 0 0 0  0 1 0  2 0 0 | * * * * * *  * * * 6 * * * | 0 0 0 0 0 1 0 1 0 1 0 | 0 1 0 1 1
... ... .xx&#x | 0 2 2 | 0 0 0  0 0 1  2 0 1 | * * * * * *  * * * * 6 * * | 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 0  0 2 2 | * * * * * *  * * * * * 3 * | 0 0 1 0 0 0 0 0 1 0 1 | 1 0 1 0 1
... ..o3..x    | 0 0 3 | 0 0 0  0 0 0  0 0 3 | * * * * * *  * * * * * * 2 | 0 0 0 1 0 0 0 0 0 1 1 | 1 0 0 1 1
---------------+-------+---------------------+----------------------------+-----------------------+----------
... xx.3xx.&#x  6 6 0 | 3 3 6  0 3 3  0 0 0 | 1 3 3 0 0 0  0 1 0 0 0 0 0 | 1 * * * * * * * * * * | 0 0 0 2 0
o.x x.o ...&#x  2 0 2 | 1 0 0  4 0 0  0 1 0 | 0 0 0 2 2 0  0 0 0 0 0 0 0 | * 3 * * * * * * * * * | 1 1 0 0 0
o.x ... x.x&#x  2 0 4 | 0 1 0  4 0 0  0 2 2 | 0 0 0 2 0 2  0 0 0 0 0 1 0 | * * 3 * * * * * * * * | 1 0 1 0 0
... x.o3x.x&#x  6 0 3 | 3 3 0  6 0 0  0 0 3 | 1 0 0 0 3 3  0 0 0 0 0 0 1 | * * * 2 * * * * * * * | 1 0 0 1 0
oox ... ...&#x  1 1 2 | 0 0 1  2 0 0  2 1 0 | 0 0 0 1 0 0  2 0 1 0 0 0 0 | * * * * 6 * * * * * * | 0 1 1 0 0
... xxo ...&#x  2 2 1 | 1 0 2  2 1 0  2 0 0 | 0 1 0 0 1 0  2 0 0 1 0 0 0 | * * * * * 6 * * * * * | 0 1 0 1 0
... ... xxx&#x  2 2 2 | 0 1 2  2 0 1  2 0 1 | 0 0 1 0 0 1  2 0 0 0 1 0 0 | * * * * * * 6 * * * * | 0 0 1 1 0
.ox .xo ...&#x  0 2 2 | 0 0 0  0 1 0  4 1 0 | 0 0 0 0 0 0  0 0 2 2 0 0 0 | * * * * * * * 3 * * * | 0 1 0 0 1
.ox ... .xx&#x  0 2 4 | 0 0 0  0 0 1  4 2 2 | 0 0 0 0 0 0  0 0 2 0 2 1 0 | * * * * * * * * 3 * * | 0 0 1 0 1
... .xo3.xx&#x  0 6 3 | 0 0 0  0 3 3  6 0 3 | 0 0 0 0 0 0  0 1 0 3 3 0 1 | * * * * * * * * * 2 * | 0 0 0 1 1
..x ..o3..x     0 0 6 | 0 0 0  0 0 0  0 3 6 | 0 0 0 0 0 0  0 0 0 0 0 3 2 | * * * * * * * * * * 1 | 1 0 0 0 1
---------------+-------+---------------------+----------------------------+-----------------------+----------
o.x x.o3x.x&#x  6 0 6 | 3 3 0 12 0 0  0 3 6 | 1 0 0 6 6 6  0 0 0 0 0 3 2 | 0 3 3 2 0 0 0 0 0 0 1 | 1 * * * *
oox xxo ...&#x  2 2 2 | 1 0 2  4 1 0  4 1 0 | 0 1 0 2 2 0  4 0 2 2 0 0 0 | 0 1 0 0 2 2 0 1 0 0 0 | * 3 * * *
oox ... xxx&#x  2 2 4 | 0 1 2  4 0 1  4 2 2 | 0 0 1 2 0 2  4 0 2 0 2 1 0 | 0 0 1 0 2 0 2 0 1 0 0 | * * 3 * *
... xxo3xxx&#x  6 6 3 | 3 3 6  6 3 3  6 0 3 | 1 3 3 0 3 3  6 1 0 3 3 0 1 | 1 0 0 1 0 3 3 0 0 1 0 | * * * 2 *
.ox .xo3.xx&#x  0 6 6 | 0 0 0  0 3 3 12 3 6 | 0 0 0 0 0 0  0 1 6 6 6 3 2 | 0 0 0 0 0 0 0 3 3 2 1 | * * * * 1

ooxx3xxxx&#x   → height(1,2) = height(3,4) = 1
                 height(1,3) = height(1,4) = height(2,3) = height(2,4) = sqrt(2/3) = 0.816497
                 height(12,34) = 1/sqrt(6) = 0.408248
(trip || lacing-ortho hip)

o...3o...    | 3 * * * | 2 1 2 2 0 0 0 0 0 0 0 0 | 1 2 2 2 1 2 2 1 2 0 0 0 0 0 0 0 0 0 0 | 1 1 2 2 1 2 1 1 2 1 0 0 0 0 0 | 1 1 2 1 1 0
.o..3.o..    | * 3 * * | 0 1 0 0 2 2 2 0 0 0 0 0 | 0 2 2 2 0 0 0 0 0 1 1 2 2 1 2 0 0 0 0 | 1 1 2 2 1 2 0 0 0 0 1 1 2 1 0 | 1 1 2 1 0 1
..o.3..o.    | * * 6 * | 0 0 1 0 0 1 0 1 1 1 0 0 | 0 0 1 0 1 1 1 0 0 0 1 1 1 0 0 1 1 1 0 | 0 1 1 1 0 0 1 1 1 0 1 1 1 0 1 | 1 1 1 0 1 1
...o3...o    | * * * 6 | 0 0 0 1 0 0 1 0 0 1 1 1 | 0 0 0 1 0 0 1 1 1 0 0 0 1 1 1 0 1 1 1 | 0 0 0 1 1 1 0 1 1 1 0 1 1 1 1 | 0 1 1 1 1 1
-------------+---------+-------------------------+---------------------------------------+-------------------------------+------------
.... x...    | 2 0 0 0 | 3 * * * * * * * * * * * | 1 1 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 | 1 0 1 0 0 1 1 0 1 1 0 0 0 0 0 | 1 0 1 1 1 0
oo..3oo..&#x | 1 1 0 0 | * 3 * * * * * * * * * * | 0 2 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 1 1 2 2 1 2 0 0 0 0 0 0 0 0 0 | 1 1 2 1 0 0
o.o.3o.o.&#x | 1 0 1 0 | * * 6 * * * * * * * * * | 0 0 1 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 | 0 1 1 1 0 0 1 1 1 0 0 0 0 0 0 | 1 1 1 0 1 0
o..o3o..o&#x | 1 0 0 1 | * * * 6 * * * * * * * * | 0 0 0 1 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 | 0 0 0 1 1 1 0 1 1 1 0 0 0 0 0 | 0 1 1 1 1 0
.... .x..    | 0 2 0 0 | * * * * 3 * * * * * * * | 0 1 0 0 0 0 0 0 0 1 0 1 0 0 1 0 0 0 0 | 1 0 1 0 0 1 0 0 0 0 1 0 1 1 0 | 1 0 1 1 0 1
.oo.3.oo.&#x | 0 1 1 0 | * * * * * 6 * * * * * * | 0 0 1 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 | 0 1 1 1 0 0 0 0 0 0 1 1 1 0 0 | 1 1 1 0 0 1
.o.o3.o.o&#x | 0 1 0 1 | * * * * * * 6 * * * * * | 0 0 0 1 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 | 0 0 0 1 1 1 0 0 0 0 0 1 1 1 0 | 0 1 1 1 0 1
..x. ....    | 0 0 2 0 | * * * * * * * 3 * * * * | 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 1 1 0 0 | 0 1 0 0 0 0 1 1 0 0 1 1 0 0 1 | 1 1 0 0 1 1
.... ..x.    | 0 0 2 0 | * * * * * * * * 3 * * * | 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 1 0 1 0 | 0 0 1 0 0 0 1 0 1 0 1 0 1 0 1 | 1 0 1 0 1 1
..oo3..oo&#x | 0 0 1 1 | * * * * * * * * * 6 * * | 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 1 1 0 | 0 0 0 1 0 0 0 1 1 0 0 1 1 0 1 | 0 1 1 0 1 1
...x ....    | 0 0 0 2 | * * * * * * * * * * 3 * | 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 1 0 1 | 0 0 0 0 1 0 0 1 0 1 0 1 0 1 1 | 0 1 0 1 1 1
.... ...x    | 0 0 0 2 | * * * * * * * * * * * 3 | 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 1 1 | 0 0 0 0 0 1 0 0 1 1 0 0 1 1 1 | 0 0 1 1 1 1
-------------+---------+-------------------------+---------------------------------------+-------------------------------+------------
o...3x...    | 3 0 0 0 | 3 0 0 0 0 0 0 0 0 0 0 0 | 1 * * * * * * * * * * * * * * * * * * | 1 0 0 0 0 0 1 0 0 1 0 0 0 0 0 | 1 0 0 1 1 0
.... xx..&#x | 2 2 0 0 | 1 2 0 0 1 0 0 0 0 0 0 0 | * 3 * * * * * * * * * * * * * * * * * | 1 0 1 0 0 1 0 0 0 0 0 0 0 0 0 | 1 0 1 1 0 0
ooo.3ooo.&#x | 1 1 1 0 | 0 1 1 0 0 1 0 0 0 0 0 0 | * * 6 * * * * * * * * * * * * * * * * | 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 | 1 1 1 0 0 0
oo.o3oo.o&#x | 1 1 0 1 | 0 1 0 1 0 0 1 0 0 0 0 0 | * * * 6 * * * * * * * * * * * * * * * | 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 | 0 1 1 1 0 0
o.x. ....&#x | 1 0 2 0 | 0 0 2 0 0 0 0 1 0 0 0 0 | * * * * 3 * * * * * * * * * * * * * * | 0 1 0 0 0 0 1 1 0 0 0 0 0 0 0 | 1 1 0 0 1 0
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o.oo3o.oo&#x | 1 0 1 1 | 0 0 1 1 0 0 0 0 0 1 0 0 | * * * * * * 6 * * * * * * * * * * * * | 0 0 0 1 0 0 0 1 1 0 0 0 0 0 0 | 0 1 1 0 1 0
o..x ....&#x | 1 0 0 2 | 0 0 0 2 0 0 0 0 0 0 1 0 | * * * * * * * 3 * * * * * * * * * * * | 0 0 0 0 1 0 0 1 0 1 0 0 0 0 0 | 0 1 0 1 1 0
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.o..3.x..    | 0 3 0 0 | 0 0 0 0 3 0 0 0 0 0 0 0 | * * * * * * * * * 1 * * * * * * * * * | 1 0 0 0 0 0 0 0 0 0 1 0 0 1 0 | 1 0 0 1 0 1
.ox. ....&#x | 0 1 2 0 | 0 0 0 0 0 2 0 1 0 0 0 0 | * * * * * * * * * * 3 * * * * * * * * | 0 1 0 0 0 0 0 0 0 0 1 1 0 0 0 | 1 1 0 0 0 1
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.o.x ....&#x | 0 1 0 2 | 0 0 0 0 0 0 2 0 0 0 1 0 | * * * * * * * * * * * * * 3 * * * * * | 0 0 0 0 1 0 0 0 0 0 0 1 0 1 0 | 0 1 0 1 0 1
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..x.3..x.    | 0 0 6 0 | 0 0 0 0 0 0 0 3 3 0 0 0 | * * * * * * * * * * * * * * * 1 * * * | 0 0 0 0 0 0 1 0 0 0 1 0 0 0 1 | 1 0 0 0 1 1
..xx ....&#x | 0 0 2 2 | 0 0 0 0 0 0 0 1 0 2 1 0 | * * * * * * * * * * * * * * * * 3 * * | 0 0 0 0 0 0 0 1 0 0 0 1 0 0 1 | 0 1 0 0 1 1
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...x3...x    | 0 0 0 6 | 0 0 0 0 0 0 0 0 0 0 3 3 | * * * * * * * * * * * * * * * * * * 1 | 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 | 0 0 0 1 1 1
-------------+---------+-------------------------+---------------------------------------+-------------------------------+------------
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oo.x ....&#x  1 1 0 2 | 0 1 0 2 0 0 2 0 0 0 1 0 | 0 0 0 2 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 | * * * * 3 * * * * * * * * * * | 0 1 0 1 0 0
.... xx.x&#x  2 2 0 2 | 1 2 0 2 1 0 2 0 0 0 0 1 | 0 1 0 2 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 | * * * * * 3 * * * * * * * * * | 0 0 1 1 0 0
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.ox.3.xx.&#x  0 3 6 0 | 0 0 0 0 3 6 0 3 3 0 0 0 | 0 0 0 0 0 0 0 0 0 1 3 3 0 0 0 1 0 0 0 | * * * * * * * * * * 1 * * * * | 1 0 0 0 0 1
.oxx ....&#x  0 1 2 2 | 0 0 0 0 0 2 2 1 0 2 1 0 | 0 0 0 0 0 0 0 0 0 0 1 0 2 1 0 0 1 0 0 | * * * * * * * * * * * 3 * * * | 0 1 0 0 0 1
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..xx3..xx&#x  0 0 6 6 | 0 0 0 0 0 0 0 3 3 6 3 3 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 3 3 1 | * * * * * * * * * * * * * * 1 | 0 0 0 0 1 1
-------------+---------+-------------------------+---------------------------------------+-------------------------------+------------
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.... xxxx&#x  2 2 2 2 | 1 2 2 2 1 2 2 0 1 2 0 1 | 0 1 2 2 0 1 2 0 1 0 0 1 2 0 1 0 0 1 0 | 0 0 1 2 0 1 0 0 1 0 0 0 1 0 0 | * * 3 * * *
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o.xx3x.xx&#x  3 0 6 6 | 3 0 6 6 0 0 0 3 3 6 3 3 | 1 0 0 0 3 3 6 3 3 0 0 0 0 0 0 1 3 3 1 | 0 0 0 0 0 0 1 3 3 1 0 0 0 0 1 | * * * * 1 *
.oxx3.xxx&#x  0 3 6 6 | 0 0 0 0 3 6 6 3 3 6 3 3 | 0 0 0 0 0 0 0 0 0 1 3 3 6 3 3 1 3 3 1 | 0 0 0 0 0 0 0 0 0 0 1 3 3 1 1 | * * * * * 1

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