Acronym trial triddip
Name {3} atop gyrated triddip,
{3}-first cap of rix
Circumradius sqrt(2/3) = 0.816497
Lace city
in approx. ASCII-art
  T     t
         
o     l  

where:
o = o o3o (point)
l = x o3o (line)
t = o x3o ({3})
T = x x3o (trip)
Lace hyper city
in approx. ASCII-art
      o3x      
       x3o     
x3o            
            x3o
(shallow triangular pyramid with {3}-tip and all dual {3}'s for base vertices)
    o    
         
        
o       o
         
         
3       3
        
         
    3    
where:
o = o3o
3 = x3o 
Confer
uniform relative:
rix  
variations:
spil-verf  
general polytopal classes:
segmentotera   lace simplices  

Incidence matrix according to Dynkin symbol

xo3ox ox3oo&#x   → height = 1/sqrt(3) = 0.577350
({3} || gyro triddip)

o.3o. o.3o.    | 3 * | 2  6 0 0 | 1 6 3  6 0 0 0 | 3 6 3 2 0 0 | 3 2 1 0
.o3.o .o3.o    | * 9 | 0  2 2 2 | 0 1 2  4 1 4 1 | 1 2 4 2 2 2 | 2 1 2 1
---------------+-----+----------+----------------+-------------+--------
x. .. .. ..    | 2 0 | 3  * * * | 1 3 0  0 0 0 0 | 3 3 0 0 0 0 | 3 1 0 0
oo3oo oo3oo&#x | 1 1 | * 18 * * | 0 1 1  2 0 0 0 | 1 2 2 1 0 0 | 2 1 1 0
.. .x .. ..    | 0 2 | *  * 9 * | 0 0 1  0 1 2 0 | 1 0 2 0 2 1 | 2 0 1 1
.. .. .x ..    | 0 2 | *  * * 9 | 0 0 0  2 0 2 1 | 0 1 2 2 1 2 | 1 1 2 1
---------------+-----+----------+----------------+-------------+--------
x.3o. .. ..    | 3 0 | 3  0 0 0 | 1 * *  * * * * | 3 0 0 0 0 0 | 3 0 0 0
xo .. .. ..&#x | 2 1 | 1  2 0 0 | * 9 *  * * * * | 1 2 0 0 0 0 | 2 1 0 0
.. ox .. ..&#x | 1 2 | 0  2 1 0 | * * 9  * * * * | 1 0 2 0 0 0 | 2 0 1 0
.. .. ox ..&#x | 1 2 | 0  2 0 1 | * * * 18 * * * | 0 1 1 1 0 0 | 1 1 1 0
.o3.x .. ..    | 0 3 | 0  0 3 0 | * * *  * 3 * * | 1 0 0 0 2 0 | 2 0 0 1
.. .x .x ..    | 0 4 | 0  0 2 2 | * * *  * * 9 * | 0 0 1 0 1 1 | 1 0 1 1
.. .. .x3.o    | 0 3 | 0  0 0 3 | * * *  * * * 3 | 0 0 0 2 0 2 | 0 1 2 1
---------------+-----+----------+----------------+-------------+--------
xo3ox .. ..&#x  3 3 | 3  6 3 0 | 1 3 3  0 1 0 0 | 3 * * * * * | 2 0 0 0
xo .. ox ..&#x  2 2 | 1  4 0 1 | 0 2 0  2 0 0 0 | * 9 * * * * | 1 1 0 0
.. ox ox ..&#x  1 4 | 0  4 2 2 | 0 0 2  2 0 1 0 | * * 9 * * * | 1 0 1 0
.. .. ox3oo&#x  1 3 | 0  3 0 3 | 0 0 0  3 0 0 1 | * * * 6 * * | 0 1 1 0
.o3.x .x ..     0 6 | 0  0 6 3 | 0 0 0  0 2 3 0 | * * * * 3 * | 1 0 0 1
.. .x .x3.o     0 6 | 0  0 3 6 | 0 0 0  0 0 3 2 | * * * * * 3 | 0 0 1 1
---------------+-----+----------+----------------+-------------+--------
xo3ox ox ..&#x  3 6 | 3 12 6 3 | 1 6 6  6 2 3 0 | 2 3 3 0 1 0 | 3 * * *
xo .. ox3oo&#x  2 3 | 1  6 0 3 | 0 3 0  6 0 0 1 | 0 3 0 2 0 0 | * 3 * *
.. ox ox3oo&#x  1 6 | 0  6 3 6 | 0 0 3  6 0 3 2 | 0 0 3 2 0 1 | * * 3 *
.o3.x .x3.o     0 9 | 0  0 9 9 | 0 0 0  0 3 9 3 | 0 0 0 0 3 3 | * * * 1

xoo xox3oxo&#x   → height(1,2) = height(1,3) = 1/sqrt(3) = 0.577350
                   height(2,3) = sqrt(2/3) = 0.816497

o.. o..3o..    | 6 * * | 1 2  1 2 0 0 0 | 2 1 2 2 1 1 2  2 0 0 0 0 | 1 2 1 1 2 1 2 2 1 0 | 1 1 2 1 1
.o. .o.3.o.    | * 3 * | 0 0  4 0 2 2 0 | 0 0 2 2 4 0 0  4 1 1 2 0 | 0 1 2 2 0 0 2 2 4 1 | 1 0 1 2 2
..o ..o3..o    | * * 3 | 0 0  0 2 0 2 2 | 0 0 0 0 0 1 4  4 0 2 1 1 | 0 0 0 0 2 2 2 4 2 1 | 0 1 2 1 2
---------------+-------+----------------+--------------------------+---------------------+----------
x.. ... ...    | 2 0 0 | 3 *  * * * * * | 2 0 2 0 0 1 0  0 0 0 0 0 | 1 2 1 0 2 0 2 0 0 0 | 1 1 2 1 0
... x.. ...    | 2 0 0 | * 6  * * * * * | 1 1 0 1 0 0 1  0 0 0 0 0 | 1 1 0 1 1 1 0 1 0 0 | 1 1 1 0 1
oo. oo.3oo.&#x | 1 1 0 | * * 12 * * * * | 0 0 1 1 1 0 0  1 0 0 0 0 | 0 1 1 1 0 0 1 1 1 0 | 1 0 1 1 1
o.o o.o3o.o&#x | 1 0 1 | * *  * 6 * * * | 0 0 0 0 0 1 2  2 0 0 0 0 | 0 0 0 0 2 1 2 2 1 0 | 0 1 2 1 1
... ... .x.    | 0 2 0 | * *  * * 3 * * | 0 0 0 0 2 0 0  0 1 0 1 0 | 0 0 1 2 0 0 0 0 2 1 | 1 0 0 1 2
.oo .oo3.oo&#x | 0 1 1 | * *  * * * 6 * | 0 0 0 0 0 0 0  2 0 1 1 0 | 0 0 0 0 0 0 1 2 2 1 | 0 0 1 1 2
... ..x ...    | 0 0 2 | * *  * * * * 3 | 0 0 0 0 0 0 2  0 0 1 0 1 | 0 0 0 0 1 2 0 2 0 1 | 0 1 1 0 2
---------------+-------+----------------+--------------------------+---------------------+----------
x.. x.. ...    | 4 0 0 | 2 2  0 0 0 0 0 | 3 * * * * * *  * * * * * | 1 1 0 0 1 0 0 0 0 0 | 1 1 1 0 0
... x..3o..    | 3 0 0 | 0 3  0 0 0 0 0 | * 2 * * * * *  * * * * * | 1 0 0 1 0 1 0 0 0 0 | 1 1 0 0 1
xo. ... ...&#x | 2 1 0 | 1 0  2 0 0 0 0 | * * 6 * * * *  * * * * * | 0 1 1 0 0 0 1 0 0 0 | 1 0 1 1 0
... xo. ...&#x | 2 1 0 | 0 1  2 0 0 0 0 | * * * 6 * * *  * * * * * | 0 1 0 1 0 0 0 1 0 0 | 1 0 1 0 1
... ... ox.&#x | 1 2 0 | 0 0  2 0 1 0 0 | * * * * 6 * *  * * * * * | 0 0 1 1 0 0 0 0 1 0 | 1 0 0 1 1
x.o ... ...&#x | 2 0 1 | 1 0  0 2 0 0 0 | * * * * * 3 *  * * * * * | 0 0 0 0 2 0 2 0 0 0 | 0 1 2 1 0
... x.x ...&#x | 2 0 2 | 0 1  0 2 0 0 1 | * * * * * * 6  * * * * * | 0 0 0 0 1 1 0 1 0 0 | 0 1 1 0 1
ooo ooo3ooo&#x | 1 1 1 | 0 0  1 1 0 1 0 | * * * * * * * 12 * * * * | 0 0 0 0 0 0 1 1 1 0 | 0 0 1 1 1
... .o.3.x.    | 0 3 0 | 0 0  0 0 3 0 0 | * * * * * * *  * 1 * * * | 0 0 0 2 0 0 0 0 0 1 | 1 0 0 0 2
... .ox ...&#x | 0 1 2 | 0 0  0 0 0 2 1 | * * * * * * *  * * 3 * * | 0 0 0 0 0 0 0 2 0 1 | 0 0 1 0 2
... ... .xo&#x | 0 2 1 | 0 0  0 0 1 2 0 | * * * * * * *  * * * 3 * | 0 0 0 0 0 0 0 0 2 1 | 0 0 0 1 2
... ..x3..o    | 0 0 3 | 0 0  0 0 0 0 3 | * * * * * * *  * * * * 1 | 0 0 0 0 0 2 0 0 0 1 | 0 1 0 0 2
---------------+-------+----------------+--------------------------+---------------------+----------
x.. x..3o..     6 0 0 | 3 6  0 0 0 0 0 | 3 2 0 0 0 0 0  0 0 0 0 0 | 1 * * * * * * * * * | 1 1 0 0 0
xo. xo. ...&#x  4 1 0 | 2 2  4 0 0 0 0 | 1 0 2 2 0 0 0  0 0 0 0 0 | * 3 * * * * * * * * | 1 0 1 0 0
xo. ... ox.&#x  2 2 0 | 1 0  4 0 1 0 0 | 0 0 2 0 2 0 0  0 0 0 0 0 | * * 3 * * * * * * * | 1 0 0 1 0
... xo.3ox.&#x  3 3 0 | 0 3  6 0 3 0 0 | 0 1 0 3 3 0 0  0 1 0 0 0 | * * * 2 * * * * * * | 1 0 0 0 1
x.o x.x ...&#x  4 0 2 | 2 2  0 4 0 0 1 | 1 0 0 0 0 2 2  0 0 0 0 0 | * * * * 3 * * * * * | 0 1 1 0 0
... x.x3o.o&#x  3 0 3 | 0 3  0 3 0 0 3 | 0 1 0 0 0 0 3  0 0 0 0 1 | * * * * * 2 * * * * | 0 1 0 0 1
xoo ... ...&#x  2 1 1 | 1 0  2 2 0 1 0 | 0 0 1 0 0 1 0  2 0 0 0 0 | * * * * * * 6 * * * | 0 0 1 1 0
... xox ...&#x  2 1 2 | 0 1  2 2 0 2 1 | 0 0 0 1 0 0 1  2 0 1 0 0 | * * * * * * * 6 * * | 0 0 1 0 1
... ... oxo&#x  1 2 1 | 0 0  2 1 1 2 0 | 0 0 0 0 1 0 0  2 0 0 1 0 | * * * * * * * * 6 * | 0 0 0 1 1
... .ox3.xo&#x  0 3 3 | 0 0  0 0 3 6 3 | 0 0 0 0 0 0 0  0 1 3 3 1 | * * * * * * * * * 1 | 0 0 0 0 2
---------------+-------+----------------+--------------------------+---------------------+----------
xo. xo.3ox.&#x  6 3 0 | 3 6 12 0 3 0 0 | 3 2 6 6 6 0 0  0 1 0 0 0 | 1 3 3 2 0 0 0 0 0 0 | 1 * * * *
x.o x.x3o.o&#x  6 0 3 | 3 6  0 6 0 0 3 | 3 2 0 0 0 3 6  0 0 0 0 1 | 1 0 0 0 3 2 0 0 0 0 | * 1 * * *
xoo xox ...&#x  4 1 2 | 2 2  4 4 0 2 1 | 1 0 2 2 0 2 2  4 0 1 0 0 | 0 1 0 0 1 0 2 2 0 0 | * * 3 * *
xoo ... oxo&#x  2 2 1 | 1 0  4 2 1 2 0 | 0 0 2 0 2 1 0  4 0 0 1 0 | 0 0 1 0 0 0 2 0 2 0 | * * * 3 *
... xox3oxo&#x  3 3 3 | 0 3  6 3 3 6 3 | 0 1 0 3 3 0 3  6 1 3 3 1 | 0 0 0 1 0 1 0 3 3 1 | * * * * 2

ooox3xxxo&#x   → height(1,2) = height(1,3) = height(2,3) = 1
                 height(1,4) = height(2,4) = height(3,4) = sqrt(2/3) = sqrt(2/3) = 0.816497

o...3o...    | 3 * * * | 2 1 1 2 0 0 0 0 0 0 | 1 2 1 2 2 2 1 2 0 0 0 0 0 0 0 0 0 | 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 1 2 0 0 0 | 0 2 1 2 0 0 0 0 1 2 2 1 2 0 0 0 0 | 1 2 2 1 2 0 0 0 0 1 1 2 1 0 | 1 1 2 1 0 1
..o.3..o.    | * * 3 * | 0 0 1 0 0 1 0 2 2 0 | 0 0 1 0 2 2 0 0 0 2 2 0 0 1 1 2 0 | 0 2 2 0 0 1 1 2 0 1 1 2 0 1 | 1 1 2 0 1 1
...o3...o    | * * * 3 | 0 0 0 2 0 0 2 0 2 2 | 0 0 0 2 0 2 2 1 0 0 2 2 1 0 2 1 1 | 0 0 2 2 1 0 2 1 1 0 2 1 1 1 | 0 2 1 1 1 1
-------------+---------+---------------------+-----------------------------------+-----------------------------+------------
.... x...    | 2 0 0 0 | 3 * * * * * * * * * | 1 1 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 | 1 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 1 2 0 0 0 0 0 0 0 0 0 0 0 0 0 | 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 | * * 3 * * * * * * * | 0 0 1 0 2 2 0 0 0 0 0 0 0 0 0 0 0 | 0 2 2 0 0 1 1 2 0 0 0 0 0 0 | 1 1 2 0 1 0
o..o3o..o&#x | 1 0 0 1 | * * * 6 * * * * * * | 0 0 0 1 0 1 1 1 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 1 1 0 0 1 0 0 0 0 | 1 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 | * * * * * 3 * * * * | 0 0 1 0 0 0 0 0 0 2 2 0 0 0 0 0 0 | 0 2 2 0 0 0 0 0 0 1 1 2 0 0 | 1 1 2 0 0 1
.o.o3.o.o&#x | 0 1 0 1 | * * * * * * 6 * * * | 0 0 0 1 0 0 0 0 0 0 1 1 1 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 1 0 0 0 1 0 1 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 1 0 0 0 0 1 0 0 0 1 1 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 1 0 0 0 0 1 0 0 1 0 1 | 0 0 0 1 0 0 1 0 1 0 1 0 1 1 | 0 1 0 1 1 1
-------------+---------+---------------------+-----------------------------------+-----------------------------+------------
o...3x...    | 3 0 0 0 | 3 0 0 0 0 0 0 0 0 0 | 1 * * * * * * * * * * * * * * * * | 1 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 | * 3 * * * * * * * * * * * * * * * | 1 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 | * * 3 * * * * * * * * * * * * * * | 0 2 2 0 0 0 0 0 0 0 0 0 0 0 | 1 1 2 0 0 0
oo.o3oo.o&#x | 1 1 0 1 | 0 1 0 1 0 0 1 0 0 0 | * * * 6 * * * * * * * * * * * * * | 0 0 1 1 1 0 0 0 0 0 0 0 0 0 | 0 1 1 1 0 0
.... x.x.&#x | 2 0 2 0 | 1 0 2 0 0 0 0 1 0 0 | * * * * 3 * * * * * * * * * * * * | 0 1 0 0 0 1 0 1 0 0 0 0 0 0 | 1 0 1 0 1 0
o.oo3o.oo&#x | 1 0 1 1 | 0 0 1 1 0 0 0 0 1 0 | * * * * * 6 * * * * * * * * * * * | 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 1 | * * * * * * 3 * * * * * * * * * * | 0 0 0 1 0 0 1 0 1 0 0 0 0 0 | 0 1 0 1 1 0
.... x..o&#x | 2 0 0 1 | 1 0 0 2 0 0 0 0 0 0 | * * * * * * * 3 * * * * * * * * * | 0 0 0 0 1 0 0 1 1 0 0 0 0 0 | 0 0 1 1 1 0
.o..3.x..    | 0 3 0 0 | 0 0 0 0 3 0 0 0 0 0 | * * * * * * * * 1 * * * * * * * * | 1 0 0 0 0 0 0 0 0 1 0 0 1 0 | 1 0 0 1 0 1
.... .xx.&#x | 0 2 2 0 | 0 0 0 0 1 2 0 1 0 0 | * * * * * * * * * 3 * * * * * * * | 0 1 0 0 0 0 0 0 0 1 0 1 0 0 | 1 0 1 0 0 1
.ooo3.ooo&#x | 0 1 1 1 | 0 0 0 0 0 1 1 0 1 0 | * * * * * * * * * * 6 * * * * * * | 0 0 1 0 0 0 0 0 0 0 1 1 0 0 | 0 1 1 0 0 1
.o.x ....&#x | 0 1 0 2 | 0 0 0 0 0 0 2 0 0 1 | * * * * * * * * * * * 3 * * * * * | 0 0 0 1 0 0 0 0 0 0 1 0 1 0 | 0 1 0 1 0 1
.... .x.o&#x | 0 2 0 1 | 0 0 0 0 1 0 2 0 0 0 | * * * * * * * * * * * * 3 * * * * | 0 0 0 0 1 0 0 0 0 0 0 1 1 0 | 0 0 1 1 0 1
..o.3..x.    | 0 0 3 0 | 0 0 0 0 0 0 0 3 0 0 | * * * * * * * * * * * * * 1 * * * | 0 0 0 0 0 1 0 0 0 1 0 0 0 1 | 1 0 0 0 1 1
..ox ....&#x | 0 0 1 2 | 0 0 0 0 0 0 0 0 2 1 | * * * * * * * * * * * * * * 3 * * | 0 0 0 0 0 0 1 0 0 0 1 0 0 1 | 0 1 0 0 1 1
.... ..xo&#x | 0 0 2 1 | 0 0 0 0 0 0 0 1 2 0 | * * * * * * * * * * * * * * * 3 * | 0 0 0 0 0 0 0 1 0 0 0 1 0 1 | 0 0 1 0 1 1
...x3...o    | 0 0 0 3 | 0 0 0 0 0 0 0 0 0 3 | * * * * * * * * * * * * * * * * 1 | 0 0 0 0 0 0 0 0 1 0 0 0 1 1 | 0 0 0 1 1 1
-------------+---------+---------------------+-----------------------------------+-----------------------------+------------
oo..3xx..&#x  3 3 0 0 | 3 3 0 0 3 0 0 0 0 0 | 1 3 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 | 1 * * * * * * * * * * * * * | 1 0 0 1 0 0
.... xxx.&#x  2 2 2 0 | 1 2 2 0 1 2 0 1 0 0 | 0 1 2 0 1 0 0 0 0 1 0 0 0 0 0 0 0 | * 3 * * * * * * * * * * * * | 1 0 1 0 0 0
oooo3oooo&#x  1 1 1 1 | 0 1 1 1 0 1 1 0 1 0 | 0 0 1 1 0 1 0 0 0 0 1 0 0 0 0 0 0 | * * 6 * * * * * * * * * * * | 0 1 1 0 0 0
oo.x ....&#x  1 1 0 2 | 0 1 0 2 0 0 2 0 0 1 | 0 0 0 2 0 0 1 0 0 0 0 1 0 0 0 0 0 | * * * 3 * * * * * * * * * * | 0 1 0 1 0 0
.... xx.o&#x  2 2 0 1 | 1 2 0 2 1 0 2 0 0 0 | 0 1 0 2 0 0 0 1 0 0 0 0 1 0 0 0 0 | * * * * 3 * * * * * * * * * | 0 0 1 1 0 0
o.o.3x.x.&#x  3 0 3 0 | 3 0 3 0 0 0 0 3 0 0 | 1 0 0 0 3 0 0 0 0 0 0 0 0 1 0 0 0 | * * * * * 1 * * * * * * * * | 1 0 0 0 1 0
o.ox ....&#x  1 0 1 2 | 0 0 1 2 0 0 0 0 2 1 | 0 0 0 0 0 2 1 0 0 0 0 0 0 0 1 0 0 | * * * * * * 3 * * * * * * * | 0 1 0 0 1 0
.... x.xo&#x  2 0 2 1 | 1 0 2 2 0 0 0 1 2 0 | 0 0 0 0 1 2 0 1 0 0 0 0 0 0 0 1 0 | * * * * * * * 3 * * * * * * | 0 0 1 0 1 0
o..x3x..o&#x  3 0 0 3 | 3 0 0 6 0 0 0 0 0 3 | 1 0 0 0 0 0 3 3 0 0 0 0 0 0 0 0 1 | * * * * * * * * 1 * * * * * | 0 0 0 1 1 0
.oo.3.xx.&#x  0 3 3 0 | 0 0 0 0 3 3 0 3 0 0 | 0 0 0 0 0 0 0 0 1 3 0 0 0 1 0 0 0 | * * * * * * * * * 1 * * * * | 1 0 0 0 0 1
.oox ....&#x  0 1 1 2 | 0 0 0 0 0 1 2 0 2 1 | 0 0 0 0 0 0 0 0 0 0 2 1 0 0 1 0 0 | * * * * * * * * * * 3 * * * | 0 1 0 0 0 1
.... .xxo&#x  0 2 2 1 | 0 0 0 0 1 2 2 1 2 0 | 0 0 0 0 0 0 0 0 0 1 2 0 1 0 0 1 0 | * * * * * * * * * * * 3 * * | 0 0 1 0 0 1
.o.x3.x.o&#x  0 3 0 3 | 0 0 0 0 3 0 6 0 0 3 | 0 0 0 0 0 0 0 0 1 0 0 3 3 0 0 0 1 | * * * * * * * * * * * * 1 * | 0 0 0 1 0 1
..ox3..xo&#x  0 0 3 3 | 0 0 0 0 0 0 0 3 6 3 | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 3 3 1 | * * * * * * * * * * * * * 1 | 0 0 0 0 1 1
-------------+---------+---------------------+-----------------------------------+-----------------------------+------------
ooo.3xxx.&#x  3 3 3 0 | 3 3 3 0 3 3 0 3 0 0 | 1 3 3 0 3 0 0 0 1 3 0 0 0 1 0 0 0 | 1 3 0 0 0 1 0 0 0 1 0 0 0 0 | 1 * * * * *
ooox ....&#x  1 1 1 2 | 0 1 1 2 0 1 2 0 2 1 | 0 0 1 2 0 2 1 0 0 0 2 1 0 0 1 0 0 | 0 0 2 1 0 0 1 0 0 0 1 0 0 0 | * 3 * * * *
.... xxxo&#x  2 2 2 1 | 1 2 2 2 1 2 2 1 2 0 | 0 1 2 2 1 2 0 1 0 1 2 0 1 0 0 1 0 | 0 1 2 0 1 0 0 1 0 0 0 1 0 0 | * * 3 * * *
oo.x3xx.o&#x  3 3 0 3 | 3 3 0 6 3 0 6 0 0 3 | 1 3 0 6 0 0 3 3 1 0 0 3 3 0 0 0 1 | 1 0 0 3 3 0 0 0 1 0 0 0 1 0 | * * * 1 * *
o.ox3x.xo&#x  3 0 3 3 | 3 0 3 6 0 0 0 3 6 3 | 1 0 0 0 3 6 3 3 0 0 0 0 0 1 3 3 1 | 0 0 0 0 0 1 3 3 1 0 0 0 0 1 | * * * * 1 *
.oox3.xxo&#x  0 3 3 3 | 0 0 0 0 3 3 6 3 6 3 | 0 0 0 0 0 0 0 0 1 3 6 3 3 1 3 3 1 | 0 0 0 0 0 0 0 0 0 1 3 3 1 1 | * * * * * 1

xoxoxo3oooooo&#xr   → all consecutive pairwise heights = sqrt(2/3) = 0.816497
                      all alternating pairwise heights = 1
                      Note: these lengths show that this cycle is not flat, rather it is wobbling up and down!

o.....3o.....     & | 9 * | 2  2 2 0 | 1  4 2 4 1 1 0 | 2 4 1 2 2 2 | 2 2 1 1
.o....3.o....     & | * 3 | 0  6 0 2 | 0  6 3 0 0 6 1 | 2 3 3 0 0 6 | 1 3 0 2
--------------------+-----+----------+----------------+-------------+--------
x..... ......     & | 2 0 | 9  * * * | 1  2 0 2 0 0 0 | 2 2 0 2 1 1 | 2 1 1 1
oo....3oo....&#x  & | 1 1 | * 18 * * | 0  2 1 0 0 1 0 | 1 2 1 0 0 2 | 1 2 0 1
o.o...3o.o...&#x  & | 2 0 | *  * 9 * | 0  0 1 2 1 0 0 | 0 2 1 1 2 0 | 1 2 1 0
.o.o..3.o.o..&#x  & | 0 2 | *  * * 3 | 0  0 0 0 0 3 1 | 0 0 3 0 0 3 | 0 3 0 1
--------------------+-----+----------+----------------+-------------+--------
x.....3o.....     & | 3 0 | 3  0 0 0 | 3  * * * * * * | 2 0 0 2 0 0 | 2 0 1 1
xo.... ......&#x  & | 2 1 | 1  2 0 0 | * 18 * * * * * | 1 1 0 0 0 1 | 1 1 0 1
ooo...3ooo...&#x  & | 2 1 | 0  2 1 0 | *  * 9 * * * * | 0 2 1 0 0 0 | 1 2 0 0
x.x... ......&#x  & | 4 0 | 2  0 2 0 | *  * * 9 * * * | 0 1 0 1 1 0 | 1 1 1 0
o.o.o.3o.o.o.&#x    | 3 0 | 0  0 3 0 | *  * * * 3 * * | 0 0 1 0 2 0 | 0 2 1 0
.ooo..3.ooo..&#x  & | 1 2 | 0  2 0 1 | *  * * * * 9 * | 0 0 1 0 0 2 | 0 2 0 1
.o.o.o3.o.o.o&#x    | 0 3 | 0  0 0 3 | *  * * * * * 1 | 0 0 3 0 0 0 | 0 3 0 0
--------------------+-----+----------+----------------+-------------+--------
xo....3oo....&#x  &  3 1 | 3  3 0 0 | 1  3 0 0 0 0 0 | 6 * * * * * | 1 0 0 1
xox... ......&#x  &  4 1 | 2  4 2 0 | 0  2 2 1 0 0 0 | * 9 * * * * | 1 1 0 0
oooooo3oooooo&#xr    3 3 | 0  6 3 3 | 0  0 3 0 1 3 1 | * * 3 * * * | 0 2 0 0
x.x...3o.o...&#x  &  6 0 | 6  0 3 0 | 2  0 0 3 0 0 0 | * * * 3 * * | 1 0 1 0
x.x.x. ......&#x     6 0 | 3  0 6 0 | 0  0 0 3 2 0 0 | * * * * 3 * | 0 1 1 0
.oxo.. ......&#x  &  2 2 | 1  4 0 1 | 0  2 0 0 0 2 0 | * * * * * 9 | 0 1 0 1
--------------------+-----+----------+----------------+-------------+--------
xox...3ooo...&#x  &  6 1 | 6  6 3 0 | 2  6 3 3 0 0 0 | 2 3 0 1 0 0 | 3 * * *
xoxoxo ......&#x     6 3 | 3 12 6 3 | 0  6 6 3 2 6 1 | 0 3 2 0 1 3 | * 3 * *
x.x.x.3o.o.o.&#x     9 0 | 9  0 9 0 | 3  0 0 9 3 0 0 | 0 0 0 3 3 0 | * * 1 *
.oxo..3.ooo..&#x  &  3 2 | 3  6 0 1 | 1  6 0 0 0 3 0 | 2 0 0 0 0 3 | * * * 3

oxox ooxx3oooo&#xr   → height(1,2) = height(3,4) = sqrt(3)/2 = 0.866025
                       height(1,4) = height(2,3) = sqrt(5/12) = 0.645497

o... o...3o...     | 1 * * * | 2 6 0 0 0 0 0 0 0 | 1 6 3 6 0 0 0 0 0 0 0 0 0 | 3 6 3 2 0 0 0 0 0 0 0 | 3 2 1 0 0 0
.o.. .o..3.o..     | * 2 * * | 1 0 1 3 3 0 0 0 0 | 1 3 0 0 3 3 3 3 0 0 0 0 0 | 3 3 0 0 3 1 3 1 0 0 0 | 3 1 0 1 1 0
..o. ..o.3..o.     | * * 3 * | 0 0 0 2 0 2 2 0 0 | 0 0 0 0 1 4 2 0 1 1 4 0 0 | 1 0 0 0 2 2 4 0 2 2 0 | 2 0 0 1 2 1
...o ...o3...o     | * * * 6 | 0 1 0 0 1 0 1 1 2 | 0 1 1 2 0 0 1 2 0 1 2 2 1 | 1 2 2 1 0 0 2 1 2 1 1 | 2 1 1 0 1 1
-------------------+---------+-------------------+---------------------------+-----------------------+------------
oo.. oo..3oo..&#x  | 1 1 0 0 | 2 * * * * * * * * | 1 3 0 0 0 0 0 0 0 0 0 0 0 | 3 3 0 0 0 0 0 0 0 0 0 | 3 1 0 0 0 0
o..o o..o3o..o&#x  | 1 0 0 1 | * 6 * * * * * * * | 0 1 1 2 0 0 0 0 0 0 0 0 0 | 1 2 2 1 0 0 0 0 0 0 0 | 2 1 1 0 0 0
.x.. .... ....     | 0 2 0 0 | * * 1 * * * * * * | 1 0 0 0 3 0 0 0 0 0 0 0 0 | 3 0 0 0 3 0 0 0 0 0 0 | 3 0 0 1 0 0
.oo. .oo.3.oo.&#x  | 0 1 1 0 | * * * 6 * * * * * | 0 0 0 0 1 2 1 0 0 0 0 0 0 | 1 0 0 0 2 1 2 0 0 0 0 | 2 0 0 1 1 0
.o.o .o.o3.o.o&#x  | 0 1 0 1 | * * * * 6 * * * * | 0 1 0 0 0 0 1 2 0 0 0 0 0 | 1 2 0 0 0 0 2 1 0 0 0 | 2 1 0 0 1 0
.... ..x. ....     | 0 0 2 0 | * * * * * 3 * * * | 0 0 0 0 0 2 0 0 1 0 2 0 0 | 0 0 0 0 1 2 2 0 1 2 0 | 1 0 0 1 2 1
..oo ..oo3..oo&#x  | 0 0 1 1 | * * * * * * 6 * * | 0 0 0 0 0 0 1 0 0 1 2 0 0 | 1 0 0 0 0 0 2 0 2 1 0 | 2 0 0 0 1 1
...x .... ....     | 0 0 0 2 | * * * * * * * 3 * | 0 0 1 0 0 0 0 0 0 1 0 2 0 | 1 0 2 0 0 0 0 0 2 0 1 | 2 0 1 0 0 1
.... ...x ....     | 0 0 0 2 | * * * * * * * * 6 | 0 0 0 1 0 0 0 1 0 0 1 1 1 | 0 1 1 1 0 0 1 1 1 1 1 | 1 1 1 0 1 1
-------------------+---------+-------------------+---------------------------+-----------------------+------------
ox.. .... ....&#x  | 1 2 0 0 | 2 0 1 0 0 0 0 0 0 | 1 * * * * * * * * * * * * | 3 0 0 0 0 0 0 0 0 0 0 | 3 0 0 0 0 0
oo.o oo.o3oo.o&#x  | 1 1 0 1 | 1 1 0 0 1 0 0 0 0 | * 6 * * * * * * * * * * * | 1 2 0 0 0 0 0 0 0 0 0 | 2 1 0 0 0 0
o..x .... ....&#x  | 1 0 0 2 | 0 2 0 0 0 0 0 1 0 | * * 3 * * * * * * * * * * | 1 0 2 0 0 0 0 0 0 0 0 | 2 0 1 0 0 0
.... o..x ....&#x  | 1 0 0 2 | 0 2 0 0 0 0 0 0 1 | * * * 6 * * * * * * * * * | 0 1 1 1 0 0 0 0 0 0 0 | 1 1 1 0 0 0
.xo. .... ....&#x  | 0 2 1 0 | 0 0 1 2 0 0 0 0 0 | * * * * 3 * * * * * * * * | 1 0 0 0 2 0 0 0 0 0 0 | 2 0 0 1 0 0
.... .ox. ....&#x  | 0 1 2 0 | 0 0 0 2 0 1 0 0 0 | * * * * * 6 * * * * * * * | 0 0 0 0 1 1 1 0 0 0 0 | 1 0 0 1 1 0
.ooo .ooo3.ooo&#x  | 0 1 1 1 | 0 0 0 1 1 0 1 0 0 | * * * * * * 6 * * * * * * | 1 0 0 0 0 0 2 0 0 0 0 | 2 0 0 0 1 0
.... .o.x ....&#x  | 0 1 0 2 | 0 0 0 0 2 0 0 0 1 | * * * * * * * 6 * * * * * | 0 1 0 0 0 0 1 1 0 0 0 | 1 1 0 0 1 0
.... ..x.3..o.     | 0 0 3 0 | 0 0 0 0 0 3 0 0 0 | * * * * * * * * 1 * * * * | 0 0 0 0 0 2 0 0 0 2 0 | 0 0 0 1 2 1
..ox .... ....&#x  | 0 0 1 2 | 0 0 0 0 0 0 2 1 0 | * * * * * * * * * 3 * * * | 1 0 0 0 0 0 0 0 2 0 0 | 2 0 0 0 0 1
.... ..xx ....&#x  | 0 0 2 2 | 0 0 0 0 0 1 2 0 1 | * * * * * * * * * * 6 * * | 0 0 0 0 0 0 1 0 1 1 0 | 1 0 0 0 1 1
...x ...x ....     | 0 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 0 1
.... ...x3...o     | 0 0 0 3 | 0 0 0 0 0 0 0 0 3 | * * * * * * * * * * * * 2 | 0 0 0 1 0 0 0 1 0 1 1 | 0 1 1 0 1 1
-------------------+---------+-------------------+---------------------------+-----------------------+------------
oxox .... ....&#xr  1 2 1 2 | 2 2 1 2 2 0 2 1 0 | 1 2 1 0 1 0 2 0 0 1 0 0 0 | 3 * * * * * * * * * * | 2 0 0 0 0 0
.... oo.x ....&#x   1 1 0 2 | 1 2 0 0 2 0 0 0 1 | 0 2 0 1 0 0 0 1 0 0 0 0 0 | * 6 * * * * * * * * * | 1 1 0 0 0 0
o..x o..x ....&#x   1 0 0 4 | 0 4 0 0 0 0 0 2 2 | 0 0 2 2 0 0 0 0 0 0 0 1 0 | * * 3 * * * * * * * * | 1 0 1 0 0 0
.... o..x3o..o&#x   1 0 0 3 | 0 3 0 0 0 0 0 0 3 | 0 0 0 3 0 0 0 0 0 0 0 0 1 | * * * 2 * * * * * * * | 0 1 1 0 0 0
.xo. .ox. ....&#x   0 2 2 0 | 0 0 1 4 0 1 0 0 0 | 0 0 0 0 2 2 0 0 0 0 0 0 0 | * * * * 3 * * * * * * | 1 0 0 1 0 0
.... .ox.3.oo.&#x   0 1 3 0 | 0 0 0 3 0 3 0 0 0 | 0 0 0 0 0 3 0 0 1 0 0 0 0 | * * * * * 2 * * * * * | 0 0 0 1 1 0
.... .oxx ....&#x   0 1 2 2 | 0 0 0 2 2 1 2 0 1 | 0 0 0 0 0 1 2 1 0 0 1 0 0 | * * * * * * 6 * * * * | 1 0 0 0 1 0
.... .o.x3.o.o&#x   0 1 0 3 | 0 0 0 0 3 0 0 0 3 | 0 0 0 0 0 0 0 3 0 0 0 0 1 | * * * * * * * 2 * * * | 0 1 0 0 1 0
..ox ..xx ....&#x   0 0 2 4 | 0 0 0 0 0 1 4 2 2 | 0 0 0 0 0 0 0 0 0 2 2 1 0 | * * * * * * * * 3 * * | 1 0 0 0 0 1
.... ..xx3..oo&#x   0 0 3 3 | 0 0 0 0 0 3 3 0 3 | 0 0 0 0 0 0 0 0 1 0 3 0 1 | * * * * * * * * * 2 * | 0 0 0 0 1 1
...x ...x3...o      0 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 | 0 0 1 0 0 1
-------------------+---------+-------------------+---------------------------+-----------------------+------------
oxox ooxx ....&#xr  1 2 2 4 | 2 4 1 4 4 1 4 2 2 | 1 4 2 2 2 2 4 2 0 2 2 1 0 | 2 2 1 0 1 0 2 0 1 0 0 | 3 * * * * *
.... oo.x3oo.o&#x   1 1 0 3 | 1 3 0 0 3 0 0 0 3 | 0 3 0 3 0 0 0 3 0 0 0 0 1 | 0 3 0 1 0 0 0 1 0 0 0 | * 2 * * * *
o..x o..x3o..o&#x   1 0 0 6 | 0 6 0 0 0 0 0 3 6 | 0 0 3 6 0 0 0 0 0 0 0 3 2 | 0 0 3 2 0 0 0 0 0 0 1 | * * 1 * * *
.xo. .ox.3.oo.&#x   0 2 3 0 | 0 0 1 6 0 3 0 0 0 | 0 0 0 0 3 6 0 0 1 0 0 0 0 | 0 0 0 0 3 2 0 0 0 0 0 | * * * 1 * *
.... .oxx3.ooo&#x   0 1 3 3 | 0 0 0 3 3 3 3 0 3 | 0 0 0 0 0 3 3 3 1 0 3 0 1 | 0 0 0 0 0 1 3 1 0 1 0 | * * * * 2 *
..ox ..xx3..oo&#x   0 0 3 6 | 0 0 0 0 0 3 6 3 6 | 0 0 0 0 0 0 0 0 1 3 6 3 2 | 0 0 0 0 0 0 0 0 3 2 1 | * * * * * 1

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