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Acronym
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triddaf
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Name
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triangular duoantifastegium,
digonal-triangular duoantiwedge,
trip atop bidual trip
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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
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x3o
x3o
o3x
o3x
(disphenoid in configuration space)
|
where:
a = x o
b = o x
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Coordinates
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-
(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)
|
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Face vector
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12, 42, 58, 36, 10
|
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Confer
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- general duoantifastegia:
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n/d-daf
- uniform relative:
-
hin
- general polytopal classes:
-
scaliform
segmentotera
lace simplices
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External
links
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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
oxox xxoo ooxx&#xr → height(1,2) = height(3,4) = 1/sqrt(12) = 0.288675
height(1,4) = height(2,3) = 1/2
height(2,4) = 1/sqrt(3) = 0.577350
o... o... o... & | 4 * | 1 2 4 0 0 0 | 1 2 4 2 4 2 0 0 | 1 2 4 2 2 1 2 0 | 3 2 1
.o.. .o.. .o.. & | * 8 | 0 1 2 1 1 2 | 1 1 4 2 1 2 1 3 | 1 2 3 3 1 2 1 1 | 3 2 1
---------------------+-----+--------------+------------------+-----------------+------
.... x... .... & | 2 0 | 2 * * * * * | 0 2 0 0 4 0 0 0 | 1 0 4 0 2 0 2 0 | 2 2 1
oo.. oo.. oo..&#x & | 1 1 | * 8 * * * * | 1 1 2 0 0 0 0 0 | 1 2 2 1 0 0 0 0 | 3 1 0
o..o o..o o..o&#x & | 1 1 | * * 16 * * * | 0 0 1 1 1 1 0 0 | 0 1 1 1 1 1 1 0 | 2 1 1
.x.. .... .... & | 0 2 | * * * 4 * * | 1 0 0 2 0 0 1 0 | 1 2 0 0 1 2 0 0 | 3 0 1
.... .x.. .... & | 0 2 | * * * * 4 * | 0 1 0 0 0 2 1 2 | 1 0 2 2 0 2 1 1 | 2 1 1
.o.o .o.o .o.o&#x | 0 2 | * * * * * 8 | 0 0 2 0 0 0 0 2 | 0 1 2 2 0 0 0 1 | 2 2 0
---------------------+-----+--------------+------------------+-----------------+------
ox.. .... ....&#x & | 1 2 | 0 2 0 1 0 0 | 4 * * * * * * * | 1 2 0 0 0 0 0 0 | 3 0 0
.... xx.. ....&#x & | 2 2 | 1 2 0 0 1 0 | * 4 * * * * * * | 1 0 2 0 0 0 0 0 | 2 1 0
oo.o oo.o oo.o&#x & | 1 2 | 0 1 1 0 0 1 | * * 16 * * * * * | 0 1 1 1 0 0 0 0 | 2 1 0
o..x .... ....&#x & | 1 2 | 0 0 2 1 0 0 | * * * 8 * * * * | 0 1 0 0 1 1 0 0 | 2 0 1
.... x..o ....&#x & | 2 1 | 1 0 2 0 0 0 | * * * * 8 * * * | 0 0 1 0 1 0 1 0 | 1 1 1
.... .... o..x&#x & | 1 2 | 0 0 2 0 1 0 | * * * * * 8 * * | 0 0 0 1 0 1 1 0 | 1 1 1
.x.. .x.. .... & | 0 4 | 0 0 0 2 2 0 | * * * * * * 2 * | 1 0 0 0 0 2 0 0 | 2 0 1
.... .x.o ....&#x & | 0 3 | 0 0 0 0 1 2 | * * * * * * * 8 | 0 0 1 1 0 0 0 1 | 1 2 0
---------------------+-----+--------------+------------------+-----------------+------
ox.. xx.. ....&#x & ♦ 2 4 | 1 4 0 2 2 0 | 2 2 0 0 0 0 1 0 | 2 * * * * * * * | 2 0 0
oxox .... ....&#xr ♦ 2 4 | 0 4 4 2 0 2 | 2 0 4 2 0 0 0 0 | * 4 * * * * * * | 2 0 0
.... xx.o ....&#x & ♦ 2 3 | 1 2 2 0 1 2 | 0 1 2 0 1 0 0 1 | * * 8 * * * * * | 1 1 0
.... .... oo.x&#x & ♦ 1 3 | 0 1 2 0 1 2 | 0 0 2 0 0 1 0 1 | * * * 8 * * * * | 1 1 0
o..x x..o ....&#x & ♦ 2 2 | 1 0 4 1 0 0 | 0 0 0 2 2 0 0 0 | * * * * 4 * * * | 1 0 1
o..x .... o..x&#x & ♦ 1 4 | 0 0 4 2 2 0 | 0 0 0 2 0 2 1 0 | * * * * * 4 * * | 1 0 1
.... x..o o..x&#x & ♦ 2 2 | 1 0 4 0 1 0 | 0 0 0 0 2 2 0 0 | * * * * * * 4 * | 0 1 1
.... .x.o .o.x&#x ♦ 0 4 | 0 0 0 0 2 4 | 0 0 0 0 0 0 0 4 | * * * * * * * 2 | 0 2 0
---------------------+-----+--------------+------------------+-----------------+------
oxox xxoo ....&#xr & ♦ 3 6 | 1 6 8 3 2 4 | 3 2 8 4 2 2 1 2 | 1 2 2 2 1 1 0 0 | 4 * *
.... xx.o oo.x&#x & ♦ 2 4 | 1 2 4 0 1 4 | 0 1 4 0 2 2 0 4 | 0 0 2 2 0 0 1 1 | * 4 *
o..x x..o o..x&#x & ♦ 2 4 | 1 0 8 2 2 0 | 0 0 0 4 4 4 1 0 | 0 0 0 0 2 2 2 0 | * * 2
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