Acronym triddaf
Name triangular duoantifastegium,
digonal-triangular duoantiwedge,
trip atop bidual trip
Circumradius sqrt(5/8) = 0.790569
Lace city
in approx. ASCII-art
  3		3 = o o3x (triangle)
P  		P = x x3o (gyro trip)
  3
Lace hyper city
in approx. ASCII-art
x3o           
           x3o
              
              
         o3x  
              
  o3x         
(disphenoid in configuration space)
    a    
         
         
a       a
         
         
b       b
         
         
    b    
where:
a = x o
b = o x
Coordinates
  • (1/2, 0, 1/2, -1/sqrt(12), -1/sqrt(24))   & all changes of sign in first 3 coords
  • (1/2, 0, 0, 1/sqrt(3), -1/sqrt(24))         & all changes of sign in first 3 coords
    (lower trip)
  • (0, 1/2, 1/2, 1/sqrt(12), 1/sqrt(24))     & all changes of sign in first 3 coords
  • (0, 1/2, 0, -1/sqrt(3), 1/sqrt(24))         & all changes of sign in first 3 coords
    (upper, bidual trip)
Confer
general duoantifastegia:
n/d-daf  
uniform relative:
hin  
general polytopal classes:
scaliform   segmentotera   lace simplices  
External
links
polytopewiki  

Note: it can not be seen as {3}-ap || axis-ortho {3}-ap too, as it well would be kind an disphenoid (daw) with octs for digonal bases within configuration space of lace hypercity display, but those bases then would not be orthogonal, just somehow slanted in a non-parallel way.


Incidence matrix according to Dynkin symbol

xo ox xo3ox&#x   → height = 1/sqrt(6) = 0.408248
(trip || bidual trip)

o. o. o.3o.    | 6 * | 1 2  4 0 0 | 2 1  4  2  4  2 0 0 | 1 2 4 2 2 1 2 0 | 2 1 2 1
.o .o .o3.o    | * 6 | 0 0  4 1 2 | 0 0  2  4  2  4 2 1 | 0 2 1 2 2 4 2 1 | 1 2 1 2
---------------+-----+------------+---------------------+-----------------+--------
x. .. .. ..    | 2 0 | 3 *  * * * | 2 0  4  0  0  0 0 0 | 1 2 4 2 0 0 0 0 | 2 1 2 0
.. .. x. ..    | 2 0 | * 6  * * * | 1 1  0  0  2  0 0 0 | 1 0 2 0 1 0 2 0 | 1 0 2 1
oo oo oo3oo&#x | 1 1 | * * 24 * * | 0 0  1  1  1  1 0 0 | 0 1 1 1 1 1 1 0 | 1 1 1 1
.. .x .. ..    | 0 2 | * *  * 3 * | 0 0  0  4  0  0 2 0 | 0 2 0 0 2 4 0 1 | 1 2 0 2
.. .. .. .x    | 0 2 | * *  * * 6 | 0 0  0  0  0  2 1 1 | 0 0 0 1 0 2 2 1 | 0 1 1 2
---------------+-----+------------+---------------------+-----------------+--------
x. .. x. ..    | 4 0 | 2 2  0 0 0 | 3 *  *  *  *  * * * | 1 0 2 0 0 0 0 0 | 1 0 2 0
.. .. x.3o.    | 3 0 | 0 3  0 0 0 | * 2  *  *  *  * * * | 1 0 0 0 0 0 2 0 | 0 0 2 1
xo .. .. ..&#x | 2 1 | 1 0  2 0 0 | * * 12  *  *  * * * | 0 1 1 1 0 0 0 0 | 1 1 1 0
.. ox .. ..&#x | 1 2 | 0 0  2 1 0 | * *  * 12  *  * * * | 0 1 0 0 1 1 0 0 | 1 1 0 1
.. .. xo ..&#x | 2 1 | 0 1  2 0 0 | * *  *  * 12  * * * | 0 0 1 0 1 0 1 0 | 1 0 1 1
.. .. .. ox&#x | 1 2 | 0 0  2 0 1 | * *  *  *  * 12 * * | 0 0 0 1 0 1 1 0 | 0 1 1 1
.. .x .. .x    | 0 4 | 0 0  0 2 2 | * *  *  *  *  * 3 * | 0 0 0 0 0 2 0 1 | 0 1 0 2
.. .. .o3.x    | 0 3 | 0 0  0 0 3 | * *  *  *  *  * * 2 | 0 0 0 0 0 0 2 1 | 0 0 1 2
---------------+-----+------------+---------------------+-----------------+--------
x. .. x.3o.     6 0 | 3 6  0 0 0 | 3 2  0  0  0  0 0 0 | 1 * * * * * * * | 0 0 2 0
xo ox .. ..&#x  2 2 | 1 0  4 1 0 | 0 0  2  2  0  0 0 0 | * 6 * * * * * * | 1 1 0 0
xo .. xo ..&#x  4 1 | 2 2  4 0 0 | 1 0  2  0  2  0 0 0 | * * 6 * * * * * | 1 0 1 0
xo .. .. ox&#x  2 2 | 1 0  4 0 1 | 0 0  2  0  0  2 0 0 | * * * 6 * * * * | 0 1 1 0
.. ox xo ..&#x  2 2 | 0 1  4 1 0 | 0 0  0  2  2  0 0 0 | * * * * 6 * * * | 1 0 0 1
.. ox .. ox&#x  1 4 | 0 0  4 2 2 | 0 0  0  2  0  2 1 0 | * * * * * 6 * * | 0 1 0 1
.. .. xo3ox&#x  3 3 | 0 3  6 0 3 | 0 1  0  0  3  3 0 1 | * * * * * * 4 * | 0 0 1 1
.. .x .o3.x     0 6 | 0 0  0 3 6 | 0 0  0  0  0  0 3 2 | * * * * * * * 1 | 0 0 0 2
---------------+-----+------------+---------------------+-----------------+--------
xo ox xo ..&#x  4 2 | 2 2  8 1 0 | 1 0  4  4  4  0 0 0 | 0 2 2 0 2 0 0 0 | 3 * * *
xo ox .. ox&#x  2 4 | 1 0  8 2 2 | 0 0  4  4  0  4 1 0 | 0 2 0 2 0 2 0 0 | * 3 * *
xo .. xo3ox&#x  6 3 | 3 6 12 0 3 | 3 2  6  0  6  6 0 1 | 1 0 3 3 0 0 2 0 | * * 2 *
.. ox xo3ox&#x  3 6 | 0 3 12 3 6 | 0 1  0  6  6  6 3 2 | 0 0 0 0 3 3 2 1 | * * * 2
or
o. o. o.3o.    & | 12 | 1  2  4 | 2 1  6  6 | 1 2  5  4 2 | 3 3
-----------------+----+---------+-----------+-------------+----
x. .. .. ..    & |  2 | 6  *  * | 2 0  4  0 | 1 2  4  2 0 | 3 2
.. .. x. ..    & |  2 | * 12  * | 1 1  0  2 | 1 0  2  1 2 | 1 3
oo oo oo3oo&#x   |  2 | *  * 24 | 0 0  2  2 | 0 1  2  2 1 | 2 2
-----------------+----+---------+-----------+-------------+----
x. .. x. ..    & |  4 | 2  2  0 | 6 *  *  * | 1 0  2  0 0 | 1 2
.. .. x.3o.    & |  3 | 0  3  0 | * 4  *  * | 1 0  0  0 2 | 0 3
xo .. .. ..&#x & |  3 | 1  0  2 | * * 24  * | 0 1  1  1 0 | 2 1
.. .. xo ..&#x & |  3 | 0  1  2 | * *  * 24 | 0 0  1  1 1 | 1 2
-----------------+----+---------+-----------+-------------+----
x. .. x.3o.    &   6 | 3  6  0 | 3 2  0  0 | 2 *  *  * * | 0 2
xo ox .. ..&#x     4 | 2  0  4 | 0 0  4  0 | * 6  *  * * | 2 0
xo .. xo ..&#x &   5 | 2  2  4 | 1 0  2  2 | * * 12  * * | 1 1
xo .. .. ox&#x &   4 | 1  1  4 | 0 0  2  2 | * *  * 12 * | 1 1
.. .. xo3ox&#x     6 | 0  6  6 | 0 2  0  6 | * *  *  * 4 | 0 2
-----------------+----+---------+-----------+-------------+----
xo ox xo ..&#x &   6 | 3  2  8 | 1 0  8  4 | 0 2  2  2 0 | 6 *
xo .. xo3ox&#x &   9 | 3  9 12 | 3 3  6 12 | 1 0  3  3 2 | * 4

oox oox3xxo&#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 | 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.3.o.    | * 3 * | 0 1  0 2  4 0 0 | 0 2 0 0 0  4 1 2 2 4 0 0 | 1 0 0 0 2 2 4 1 2 2 0 | 0 1 2 2 1
..o ..o3..o    | * * 6 | 0 0  2 0  2 1 2 | 0 0 2 2 1  2 0 2 2 1 2 1 | 0 2 1 1 2 2 1 2 1 1 1 | 1 2 1 1 1
---------------+-------+-----------------+--------------------------+-----------------------+----------
... ... x..    | 2 0 0 | 3 *  * *  * * * | 1 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 | * 3  * *  * * * | 0 2 0 0 0  4 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 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 | 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 1 1 1 1 1 1 0 | 0 1 1 1 1
..x ... ...    | 0 0 2 | * *  * *  * 3 * | 0 0 2 0 0  0 0 2 0 0 2 0 | 0 2 1 0 2 0 0 2 1 0 1 | 1 2 1 0 1
... ..x ...    | 0 0 2 | * *  * *  * * 6 | 0 0 0 1 0  0 0 0 1 0 1 1 | 0 1 0 1 0 1 0 1 0 1 1 | 1 1 0 1 1
---------------+-------+-----------------+--------------------------+-----------------------+----------
... o..3x..    | 3 0 0 | 3 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 | * 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 | * * 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 | * * * 6 *  * * * * * * * | 0 1 0 1 0 1 0 0 0 0 0 | 1 1 0 1 0
... ... x.o&#x | 2 0 1 | 1 0  2 0  0 0 0 | * * * * 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 | * * * * * 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 | * * * * *  * 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 | * * * * *  * * 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 | * * * * *  * * * 6 * * * | 0 0 0 0 0 1 0 1 0 1 0 | 0 1 0 1 1
... ... .xo&#x | 0 2 1 | 0 0  0 1  2 0 0 | * * * * *  * * * * 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 | * * * * *  * * * * * 3 * | 0 1 0 0 0 0 0 1 0 0 1 | 1 1 0 0 1
... ..x3..o    | 0 0 3 | 0 0  0 0  0 0 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 | 1 3 0 0 0  0 1 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 2 2 0  0 0 0 0 0 1 0 | * 3 * * * * * * * * * | 1 1 0 0 0
o.x ... x.o&#x  2 0 2 | 1 0  4 0  0 1 0 | 0 0 2 0 2  0 0 0 0 0 0 0 | * * 3 * * * * * * * * | 1 0 1 0 0
... o.x3x.o&#x  3 0 3 | 3 0  6 0  0 0 3 | 1 0 0 3 3  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 1 0 0  2 0 1 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 1 0  2 0 0 1 0 0 0 | * * * * * 6 * * * * * | 0 1 0 1 0
... ... xxo&#x  2 2 1 | 1 2  2 1  2 0 0 | 0 1 0 0 1  2 0 0 0 1 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 2 2 0 1 0 | * * * * * * * 3 * * * | 0 1 0 0 1
.ox ... .xo&#x  0 2 2 | 0 0  0 1  4 1 0 | 0 0 0 0 0  0 0 2 0 2 0 0 | * * * * * * * * 3 * * | 0 0 1 0 1
... .ox3.xo&#x  0 3 3 | 0 0  0 3  6 0 3 | 0 0 0 0 0  0 1 0 3 3 0 1 | * * * * * * * * * 2 * | 0 0 0 1 1
..x ..x3..o     0 0 6 | 0 0  0 0  0 3 6 | 0 0 0 0 0  0 0 0 0 0 3 2 | * * * * * * * * * * 1 | 1 0 0 0 1
---------------+-------+-----------------+--------------------------+-----------------------+----------
o.x o.x3x.o&#x  3 0 6 | 3 0 12 0  0 3 6 | 1 0 6 6 6  0 0 0 0 0 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 2 2 0  4 0 2 2 0 1 0 | 0 1 0 0 2 2 0 1 0 0 0 | * 3 * * *
oox ... xxo&#x  2 2 2 | 1 2  4 1  4 1 0 | 0 1 2 0 2  4 0 2 0 2 0 0 | 0 0 1 0 2 0 2 0 1 0 0 | * * 3 * *
... oox3xxo&#x  3 3 3 | 3 3  6 3  6 0 3 | 1 3 0 3 3  6 1 0 3 3 0 1 | 1 0 0 1 0 3 3 0 0 1 0 | * * * 2 *
.ox .ox3.xo&#x  0 3 6 | 0 0  0 3 12 3 6 | 0 0 0 0 0  0 1 6 6 6 3 2 | 0 0 0 0 0 0 0 3 3 2 1 | * * * * 1

ooxx3xxoo&#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 || bidual trip)

o...3o...    | 3 * * * | 2 1 2 2 0 0 0 0 0 0 | 1 2 2 2 1 2 2 1 2 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 2 2 2 0 0 0 0 0 1 1 2 2 1 2 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.    | * * 3 * | 0 0 2 0 0 2 0 2 1 0 | 0 0 2 0 2 1 2 0 0 0 2 1 2 0 0 1 2 0 | 0 2 1 2 0 0 1 2 1 0 1 2 1 0 1 | 1 2 1 0 1 1
...o3...o    | * * * 3 | 0 0 0 2 0 0 2 0 1 2 | 0 0 0 2 0 0 2 2 1 0 0 0 2 2 1 0 2 1 | 0 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 0 1 0 0 1 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 | 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 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 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 | 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 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 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 1 0 0 0 0 1 1 0 0 1 1 0 0 1 | 1 1 0 0 1 1
..oo3..oo&#x | 0 0 1 1 | * * * * * * * * 3 * | 0 0 0 0 0 0 2 0 0 0 0 0 2 0 0 0 2 0 | 0 0 0 2 0 0 0 2 1 0 0 2 1 0 1 | 0 2 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 1 | 0 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 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 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 | * * 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 | * * * 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 | * * * * 3 * * * * * * * * * * * * * | 0 1 0 0 0 0 1 1 0 0 0 0 0 0 0 | 1 1 0 0 1 0
.... x.o.&#x | 2 0 1 0 | 1 0 2 0 0 0 0 0 0 0 | * * * * * 3 * * * * * * * * * * * * | 0 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 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 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 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 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 | * * * * * * * * * * 3 * * * * * * * | 0 1 0 0 0 0 0 0 0 0 1 1 0 0 0 | 1 1 0 0 0 1
.... .xo.&#x | 0 2 1 0 | 0 0 0 0 1 2 0 0 0 0 | * * * * * * * * * * * 3 * * * * * * | 0 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 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 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 0 1 0 0 0 0 0 0 1 1 0 | 0 0 1 1 0 1
..x.3..o.    | 0 0 3 0 | 0 0 0 0 0 0 0 3 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 2 1 | * * * * * * * * * * * * * * * * 3 * | 0 0 0 0 0 0 0 1 0 0 0 1 0 0 1 | 0 1 0 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 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 0 1 0 0 0 0 0 0 0 0 | 1 * * * * * * * * * * * * * * | 1 0 0 1 0 0
oox. ....&#x  1 1 2 0 | 0 1 2 0 0 2 0 1 0 0 | 0 0 2 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 | * 3 * * * * * * * * * * * * * | 1 1 0 0 0 0
.... xxo.&#x  2 2 1 0 | 1 2 2 0 1 2 0 0 0 0 | 0 1 2 0 0 1 0 0 0 0 0 1 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 0 1 0 0 0 0 0 1 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 0 1 0 0 0 0 0 1 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 0 1 0 0 0 0 0 1 0 0 0 | * * * * * 3 * * * * * * * * * | 0 0 1 1 0 0
o.x.3x.o.&#x  3 0 3 0 | 3 0 6 0 0 0 0 3 0 0 | 1 0 0 0 3 3 0 0 0 0 0 0 0 0 0 1 0 0 | * * * * * * 1 * * * * * * * * | 1 0 0 0 1 0
o.xx ....&#x  1 0 2 2 | 0 0 2 2 0 0 0 1 2 1 | 0 0 0 0 1 0 2 1 0 0 0 0 0 0 0 0 1 0 | * * * * * * * 3 * * * * * * * | 0 1 0 0 1 0
.... x.oo&#x  2 0 1 1 | 1 0 2 2 0 0 0 0 1 0 | 0 0 0 0 0 1 2 0 1 0 0 0 0 0 0 0 0 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 0 3 3 0 0 0 0 0 0 0 0 1 | * * * * * * * * * 1 * * * * * | 0 0 0 1 1 0
.ox.3.xo.&#x  0 3 3 0 | 0 0 0 0 3 6 0 3 0 0 | 0 0 0 0 0 0 0 0 0 1 3 3 0 0 0 1 0 0 | * * * * * * * * * * 1 * * * * | 1 0 0 0 0 1
.oxx ....&#x  0 1 2 2 | 0 0 0 0 0 2 2 1 2 1 | 0 0 0 0 0 0 0 0 0 0 1 0 2 1 0 0 1 0 | * * * * * * * * * * * 3 * * * | 0 1 0 0 0 1
.... .xoo&#x  0 2 1 1 | 0 0 0 0 1 2 2 0 1 0 | 0 0 0 0 0 0 0 0 0 0 0 1 2 0 1 0 0 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 0 1 0 0 0 3 3 0 0 1 | * * * * * * * * * * * * * 1 * | 0 0 0 1 0 1
..xx3..oo&#x  0 0 3 3 | 0 0 0 0 0 0 0 3 3 3 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 3 1 | * * * * * * * * * * * * * * 1 | 0 0 0 0 1 1
-------------+---------+---------------------+-------------------------------------+-------------------------------+------------
oox.3xxo.&#x  3 3 3 0 | 3 3 6 0 3 6 0 3 0 0 | 1 3 6 0 3 3 0 0 0 1 3 3 0 0 0 1 0 0 | 1 3 3 0 0 0 1 0 0 0 1 0 0 0 0 | 1 * * * * *
ooxx ....&#x  1 1 2 2 | 0 1 2 2 0 2 2 1 2 1 | 0 0 2 2 1 0 2 1 0 0 1 0 2 1 0 0 1 0 | 0 1 0 2 1 0 0 1 0 0 0 1 0 0 0 | * 3 * * * *
.... xxoo&#x  2 2 1 1 | 1 2 2 2 1 2 2 0 1 0 | 0 1 2 2 0 1 2 0 1 0 0 1 2 0 1 0 0 0 | 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 0 3 3 1 0 0 0 3 3 0 0 1 | 1 0 0 0 3 3 0 0 0 1 0 0 0 1 0 | * * * 1 * *
o.xx3x.oo&#x  3 0 3 3 | 3 0 6 6 0 0 0 3 3 3 | 1 0 0 0 3 3 6 3 3 0 0 0 0 0 0 1 3 1 | 0 0 0 0 0 0 1 3 3 1 0 0 0 0 1 | * * * * 1 *
.oxx3.xoo&#x  0 3 3 3 | 0 0 0 0 3 6 6 3 3 3 | 0 0 0 0 0 0 0 0 0 1 3 3 6 3 3 1 3 1 | 0 0 0 0 0 0 0 0 0 0 1 3 3 1 1 | * * * * * 1

xoxoxo oxoxox&#xr   → all consecutive pairwise heights = 1/sqrt(2) = 0.707107
                      all alternating pairwise heights = 1
                      Note: these lengths show that this cycle is not flat, rather it is wobbling up and down!

o..... o.....     & | 12 | 1  4  2 |  6  6 2 1 | 2  5  4 2 1 | 3 3
--------------------+----+---------+-----------+-------------+----
x..... ......     & |  2 | 6  *  * |  4  0 2 0 | 2  4  2 0 1 | 3 2
oo.... oo....&#x  & |  2 | * 24  * |  2  2 0 0 | 1  2  2 1 0 | 2 2
o.o... o.o...&#x  & |  2 | *  * 12 |  0  2 1 1 | 0  2  1 2 1 | 1 3
--------------------+----+---------+-----------+-------------+----
xo.... ......&#x  & |  3 | 1  2  0 | 24  * * * | 1  1  1 0 0 | 2 1
ooo... ooo...&#x  & |  3 | 0  2  1 |  * 24 * * | 0  1  1 1 0 | 1 2
x.x... ......&#x  & |  4 | 2  0  2 |  *  * 6 * | 0  2  0 0 1 | 1 2
o.o.o. o.o.o.&#x  & |  3 | 0  0  3 |  *  * * 4 | 0  0  0 2 1 | 0 3
--------------------+----+---------+-----------+-------------+----
xo.... ox....&#x  &   4 | 2  4  0 |  4  0 0 0 | 6  *  * * * | 2 0
xox... ......&#x  &   5 | 2  4  2 |  2  2 1 0 | * 12  * * * | 1 1
...... oxo...&#x  &   4 | 1  4  1 |  2  2 0 0 | *  * 12 * * | 1 1
oooooo oooooo&#xr     6 | 0  6  6 |  0  6 0 2 | *  *  * 4 * | 0 2
x.x.x. ......&#x  &   6 | 3  0  6 |  0  0 3 2 | *  *  * * 2 | 0 2
--------------------+----+---------+-----------+-------------+----
xox... oxo...&#x  &   6 | 3  8  2 |  8  4 1 0 | 2  2  2 0 0 | 6 *
xoxoxo ......&#xr &   9 | 3 12  9 |  6 12 3 3 | 0  3  3 2 1 | * 4

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