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) | |
where: a = x o b = o x | ||
Coordinates |
| |
Face vector | 12, 42, 58, 36, 10 | |
Confer |
| |
External links |
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
oxxo oxox xoxo&#xt → height(1,2) = height(3,4) = 1/sqrt(12) = 0.288675 height(2,3) = 1/sqrt(3) = 0.577350 Note: these lengths show that this tower is not flat, rather it has additional leporello folds! o... o... o... & | 4 * | 1 4 2 0 0 0 | 2 2 4 4 1 2 0 0 | 1 2 2 2 2 4 1 0 | 1 3 2 .o.. .o.. .o.. & | * 8 | 0 2 1 1 1 2 | 2 2 1 4 1 1 1 3 | 2 1 1 2 3 3 1 1 | 1 3 2 ---------------------+-----+--------------+------------------+-----------------+------ .... .... x... & | 2 0 | 2 * * * * * | 0 0 4 0 0 2 0 0 | 0 2 2 0 0 4 1 0 | 1 2 2 oo.. oo.. oo..&#x & | 1 1 | * 16 * * * * | 1 1 1 1 0 0 0 0 | 1 1 1 1 1 1 0 0 | 1 2 1 o.o. o.o. o.o.&#x & | 1 1 | * * 8 * * * | 0 0 0 2 1 1 0 0 | 0 0 0 2 1 2 1 0 | 0 3 1 .x.. .... .... & | 0 2 | * * * 4 * * | 2 0 0 0 1 0 1 0 | 2 1 0 2 0 0 1 0 | 1 3 0 .... .x.. .... & | 0 2 | * * * * 4 * | 0 2 0 0 0 1 1 2 | 2 0 1 0 2 2 1 1 | 1 2 2 .oo. .oo. .oo.&#x | 0 2 | * * * * * 8 | 0 0 0 2 0 0 0 2 | 0 0 0 1 2 2 0 1 | 0 2 2 ---------------------+-----+--------------+------------------+-----------------+------ ox.. .... ....&#x & | 1 2 | 0 2 0 1 0 0 | 8 * * * * * * * | 1 1 0 1 0 0 0 0 | 1 2 0 .... ox.. ....&#x & | 1 2 | 0 2 0 0 1 0 | * 8 * * * * * * | 1 0 1 0 1 0 0 0 | 1 1 1 .... .... xo..&#x & | 2 1 | 1 2 0 0 0 0 | * * 8 * * * * * | 0 1 1 0 0 1 0 0 | 1 1 1 ooo. ooo. ooo.&#x & | 1 2 | 0 1 1 0 0 1 | * * * 16 * * * * | 0 0 0 1 1 1 0 0 | 0 2 1 o.x. .... ....&#x & | 1 2 | 0 0 2 1 0 0 | * * * * 4 * * * | 0 0 0 2 0 0 1 0 | 0 3 0 .... .... x.x.&#x & | 2 2 | 1 0 2 0 1 0 | * * * * * 4 * * | 0 0 0 0 0 2 1 0 | 0 2 1 .x.. .x.. .... & | 0 4 | 0 0 0 2 2 0 | * * * * * * 2 * | 2 0 0 0 0 0 1 0 | 1 2 0 .... .xo. ....&#x & | 0 3 | 0 0 0 0 1 2 | * * * * * * * 8 | 0 0 0 0 1 1 0 1 | 0 1 2 ---------------------+-----+--------------+------------------+-----------------+------ ox.. ox.. ....&#x & ♦ 1 4 | 0 4 0 2 2 0 | 2 2 0 0 0 0 1 0 | 4 * * * * * * * | 1 1 0 ox.. .... xo..&#x & ♦ 2 2 | 1 4 0 1 0 0 | 2 0 2 0 0 0 0 0 | * 4 * * * * * * | 1 1 0 .... ox.. xo..&#x & ♦ 2 2 | 1 4 0 0 1 0 | 0 2 2 0 0 0 0 0 | * * 4 * * * * * | 1 0 1 oxxo .... ....&#xt ♦ 2 4 | 0 4 4 2 0 2 | 2 0 0 4 2 0 0 0 | * * * 4 * * * * | 0 2 0 (as non-flat lace tower) .... oxo. ....&#x & ♦ 1 3 | 0 2 1 0 1 2 | 0 1 0 2 0 0 0 1 | * * * * 8 * * * | 0 1 1 .... .... xox.&#x & ♦ 2 3 | 1 2 2 0 1 2 | 0 0 1 2 0 1 0 1 | * * * * * 8 * * | 0 1 1 o.x. .... x.x.&#x & ♦ 2 4 | 1 0 4 2 2 0 | 0 0 0 0 2 2 1 0 | * * * * * * 2 * | 0 2 0 .... .xo. .ox.&#x ♦ 0 4 | 0 0 0 0 2 4 | 0 0 0 0 0 0 0 4 | * * * * * * * 2 | 0 0 2 ---------------------+-----+--------------+------------------+-----------------+------ ox.. ox.. xo..&#x & ♦ 2 4 | 1 8 0 2 2 0 | 4 4 4 0 0 0 1 0 | 2 2 2 0 0 0 0 0 | 2 * * oxxo .... xoxo&#xt & ♦ 3 6 | 1 8 6 3 2 4 | 4 2 2 8 3 2 1 2 | 1 1 0 2 2 2 1 0 | * 4 * (as non-flat lace tower) .... oxo. xox.&#x & ♦ 2 4 | 1 4 2 0 2 4 | 0 2 2 4 0 1 0 4 | 0 0 1 0 2 2 0 1 | * * 4
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