Acronym | tripal triddip | ||
Name | trip atop gyro-perp triddip | ||
Circumradius | sqrt(2/3) = 0.816497 | ||
Lace city in approx. ASCII-art |
A A B where: A = o3x o3o ({3}) B = x3o x3o (triddip) | ||
Lace hyper city in approx. ASCII-art |
where: e = x o3o t = o x3o | ||
Face vector | 15, 63, 110, 97, 46, 11 | ||
Confer |
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Incidence matrix according to Dynkin symbol
xo ox3xo ox3oo&#x → height = 1/sqrt(12) = 0.288675
(trip || gyro-perp triddip)
o. o.3o. o.3o. | 6 * | 1 2 6 0 0 | 2 1 6 3 6 6 0 0 0 | 1 3 6 6 3 3 6 2 0 0 | 3 3 6 2 3 1 2 0 | 3 1 2 1
.o .o3.o .o3.o | * 9 | 0 0 4 2 2 | 0 0 2 4 2 8 1 4 1 | 0 2 1 4 2 8 4 4 2 2 | 1 4 2 2 4 4 2 1 | 2 2 1 2
------------------+-----+------------+-----------------------+-------------------------+-----------------+--------
x. .. .. .. .. | 2 0 | 3 * * * * | 2 0 6 0 0 0 0 0 0 | 1 3 6 6 0 0 0 0 0 0 | 3 3 6 2 0 0 0 0 | 3 1 2 0
.. .. x. .. .. | 2 0 | * 6 * * * | 1 1 0 0 3 0 0 0 0 | 1 0 3 0 3 0 3 0 0 0 | 3 0 3 0 3 0 1 0 | 3 0 1 1
oo oo3oo oo3oo&#x | 1 1 | * * 36 * * | 0 0 1 1 1 2 0 0 0 | 0 1 1 2 1 2 2 1 0 0 | 1 2 2 1 2 1 1 0 | 2 1 1 1
.. .x .. .. .. | 0 2 | * * * 9 * | 0 0 0 2 0 0 1 2 0 | 0 1 0 0 2 4 0 0 2 1 | 1 2 0 0 4 2 0 1 | 2 1 0 2
.. .. .. .x .. | 0 2 | * * * * 9 | 0 0 0 0 0 4 0 2 1 | 0 0 0 2 0 4 2 4 1 2 | 0 2 1 2 2 4 2 1 | 1 2 1 2
------------------+-----+------------+-----------------------+-------------------------+-----------------+--------
x. .. x. .. .. | 4 0 | 2 2 0 0 0 | 3 * * * * * * * * | 1 0 3 0 0 0 0 0 0 0 | 3 0 3 0 0 0 0 0 | 3 0 1 0
.. o.3x. .. .. | 3 0 | 0 3 0 0 0 | * 2 * * * * * * * | 1 0 0 0 3 0 0 0 0 0 | 3 0 0 0 3 0 0 0 | 3 0 0 1
xo .. .. .. ..&#x | 2 1 | 1 0 2 0 0 | * * 18 * * * * * * | 0 1 1 2 0 0 0 0 0 0 | 1 2 2 1 0 0 0 0 | 2 1 1 0
.. ox .. .. ..&#x | 1 2 | 0 0 2 1 0 | * * * 18 * * * * * | 0 1 0 0 1 2 0 0 0 0 | 1 2 0 0 2 1 0 0 | 2 1 0 1
.. .. xo .. ..&#x | 2 1 | 0 1 2 0 0 | * * * * 18 * * * * | 0 0 1 0 1 0 2 0 0 0 | 1 0 2 0 2 0 1 0 | 2 0 1 1
.. .. .. ox ..&#x | 1 2 | 0 0 2 0 1 | * * * * * 36 * * * | 0 0 0 1 0 1 1 1 0 0 | 0 1 1 1 1 1 1 0 | 1 1 1 1
.. .x3.o .. .. | 0 3 | 0 0 0 3 0 | * * * * * * 3 * * | 0 0 0 0 2 0 0 0 2 0 | 1 0 0 0 4 0 0 1 | 2 0 0 2
.. .x .. .x .. | 0 4 | 0 0 0 2 2 | * * * * * * * 9 * | 0 0 0 0 0 2 0 0 1 1 | 0 1 0 0 2 2 0 1 | 1 1 0 2
.. .. .. .x3.o | 0 3 | 0 0 0 0 3 | * * * * * * * * 3 | 0 0 0 0 0 0 0 4 0 2 | 0 0 0 2 0 4 2 1 | 0 2 1 2
------------------+-----+------------+-----------------------+-------------------------+-----------------+--------
x. o.3x. .. .. ♦ 6 0 | 3 6 0 0 0 | 3 2 0 0 0 0 0 0 0 | 1 * * * * * * * * * | 3 0 0 0 0 0 0 0 | 3 0 0 0
xo ox .. .. ..&#x ♦ 2 2 | 1 0 4 1 0 | 0 0 2 2 0 0 0 0 0 | * 9 * * * * * * * * | 1 2 0 0 0 0 0 0 | 2 1 0 0
xo .. xo .. ..&#x ♦ 4 1 | 2 2 4 0 0 | 1 0 2 0 2 0 0 0 0 | * * 9 * * * * * * * | 1 0 2 0 0 0 0 0 | 2 0 1 0
xo .. .. ox ..&#x ♦ 2 2 | 1 0 4 0 1 | 0 0 2 0 0 2 0 0 0 | * * * 18 * * * * * * | 0 1 1 1 0 0 0 0 | 1 1 1 0
.. ox3xo .. ..&#x ♦ 3 3 | 0 3 6 3 0 | 0 1 0 3 3 0 1 0 0 | * * * * 6 * * * * * | 1 0 0 0 2 0 0 0 | 2 0 0 1
.. ox .. ox ..&#x ♦ 1 4 | 0 0 4 2 2 | 0 0 0 2 0 2 0 1 0 | * * * * * 18 * * * * | 0 1 0 0 1 1 0 0 | 1 1 0 1
.. .. xo ox ..&#x ♦ 2 2 | 0 1 4 0 1 | 0 0 0 0 2 2 0 0 0 | * * * * * * 18 * * * | 0 0 1 0 1 0 1 0 | 1 0 1 1
.. .. .. ox3oo&#x ♦ 1 3 | 0 0 3 0 3 | 0 0 0 0 0 3 0 0 1 | * * * * * * * 12 * * | 0 0 0 1 0 1 1 0 | 0 1 1 1
.. .x3.o .x .. ♦ 0 6 | 0 0 0 6 3 | 0 0 0 0 0 0 2 3 0 | * * * * * * * * 3 * | 0 0 0 0 2 0 0 1 | 1 0 0 2
.. .x .. .x3.o ♦ 0 6 | 0 0 0 3 6 | 0 0 0 0 0 0 0 3 2 | * * * * * * * * * 3 | 0 0 0 0 0 2 0 1 | 0 1 0 2
------------------+-----+------------+-----------------------+-------------------------+-----------------+--------
xo ox3xo .. ..&#x ♦ 6 3 | 3 6 12 3 0 | 3 2 6 6 6 0 1 0 0 | 1 3 3 0 2 0 0 0 0 0 | 3 * * * * * * * | 2 0 0 0
xo ox .. ox ..&#x ♦ 2 4 | 1 0 8 2 2 | 0 0 4 4 0 4 0 1 0 | 0 2 0 2 0 2 0 0 0 0 | * 9 * * * * * * | 1 1 0 0
xo .. xo ox ..&#x ♦ 4 2 | 2 2 8 0 1 | 1 0 4 0 4 4 0 0 0 | 0 0 2 2 0 0 2 0 0 0 | * * 9 * * * * * | 1 0 1 0
xo .. .. ox3oo&#x ♦ 2 3 | 1 0 6 0 3 | 0 0 3 0 0 6 0 0 1 | 0 0 0 3 0 0 0 2 0 0 | * * * 6 * * * * | 0 1 1 0
.. ox3xo ox ..&#x ♦ 3 6 | 0 3 12 6 3 | 0 1 0 6 6 6 2 3 0 | 0 0 0 0 2 3 3 0 1 0 | * * * * 6 * * * | 1 0 0 1
.. ox .. ox3oo&#x ♦ 1 6 | 0 0 6 3 6 | 0 0 0 3 0 6 0 3 2 | 0 0 0 0 0 3 0 2 0 1 | * * * * * 6 * * | 0 1 0 1
.. .. xo ox3oo&#x ♦ 2 3 | 0 1 6 0 3 | 0 0 0 0 3 6 0 0 1 | 0 0 0 0 0 0 3 2 0 0 | * * * * * * 6 * | 0 0 1 1
.. .x3.o .x3.o ♦ 0 9 | 0 0 0 9 9 | 0 0 0 0 0 0 3 9 3 | 0 0 0 0 0 0 0 0 3 3 | * * * * * * * 1 | 0 0 0 2
------------------+-----+------------+-----------------------+-------------------------+-----------------+--------
xo ox3xo ox ..&#x ♦ 6 6 | 3 6 24 6 3 | 3 2 12 12 12 12 2 3 0 | 1 6 6 6 4 6 6 0 1 0 | 2 3 3 0 2 0 0 0 | 3 * * *
xo ox .. ox3oo&#x ♦ 2 6 | 1 0 12 3 6 | 0 0 6 6 0 12 0 3 2 | 0 3 0 6 0 6 0 4 0 1 | 0 3 0 2 0 2 0 0 | * 3 * *
xo .. xo ox3oo&#x ♦ 4 3 | 2 2 12 0 3 | 1 0 6 0 6 12 0 0 1 | 0 0 3 6 0 0 6 4 0 0 | 0 0 3 2 0 0 2 0 | * * 3 *
.. ox3xo ox3oo&#x ♦ 3 9 | 0 3 18 9 9 | 0 1 0 9 9 18 3 9 3 | 0 0 0 0 3 9 9 6 3 3 | 0 0 0 0 3 3 3 1 | * * * 2
xoxoxo3oooooo oxoxox&#xr → all consecutive pairwise heights = sqrt(5/12) = 0.645497 all alternating pairwise heights = 1 Note: these lengths show that this cycle is not flat, rather it is wobbling up and down! o.....3o..... o..... & | 9 * | 2 4 2 0 0 | 1 8 2 4 4 1 2 0 0 | 4 4 8 2 2 2 2 4 1 0 | 2 4 4 4 1 1 2 2 | 2 2 2 1 .o....3.o.... .o.... & | * 6 | 0 6 0 1 2 | 0 6 6 3 0 0 6 2 1 | 2 6 3 3 3 0 0 6 6 1 | 2 1 3 3 3 0 2 6 | 1 1 3 2 ---------------------------+-----+------------+-----------------------+-------------------------+-----------------+-------- x..... ...... ...... & | 2 0 | 9 * * * * | 1 4 0 0 2 0 0 0 0 | 4 2 4 0 0 2 1 2 0 0 | 2 4 2 2 0 1 2 2 | 2 2 1 1 oo....3oo.... oo....&#x & | 1 1 | * 36 * * * | 0 2 1 1 0 0 1 0 0 | 1 2 2 1 1 0 0 2 1 0 | 1 1 2 2 1 0 1 2 | 1 1 2 1 o.o...3o.o... o.o...&#x & | 2 0 | * * 9 * * | 0 0 0 2 2 1 0 0 0 | 0 0 4 1 2 1 2 0 0 0 | 0 2 2 4 1 1 0 0 | 1 2 2 0 ...... ...... .x.... & | 0 2 | * * * 3 * | 0 0 6 0 0 0 0 2 0 | 0 6 0 3 0 0 0 0 6 1 | 2 0 3 0 3 0 0 6 | 1 0 3 2 .o.o..3.o.o.. .o.o..&#x & | 0 2 | * * * * 6 | 0 0 0 0 0 0 3 1 1 | 0 0 0 0 3 0 0 3 3 1 | 0 0 0 3 3 0 1 3 | 0 1 3 1 ---------------------------+-----+------------+-----------------------+-------------------------+-----------------+-------- x.....3o..... ...... & | 3 0 | 3 0 0 0 0 | 3 * * * * * * * * | 4 0 0 0 0 2 0 0 0 0 | 2 4 0 0 0 1 2 0 | 2 2 0 1 xo.... ...... ......&#x & | 2 1 | 1 2 0 0 0 | * 36 * * * * * * * | 1 1 1 0 0 0 0 1 0 0 | 1 1 1 1 0 0 1 1 | 1 1 1 1 ...... ...... ox....&#x & | 1 2 | 0 2 0 1 0 | * * 18 * * * * * * | 0 2 0 1 0 0 0 0 1 0 | 1 0 2 0 1 0 0 2 | 1 0 2 1 ooo...3ooo... ooo...&#x & | 2 1 | 0 2 1 0 0 | * * * 18 * * * * * | 0 0 2 1 1 0 0 0 0 0 | 0 1 2 2 1 0 0 0 | 1 1 2 0 x.x... ...... ......&#x & | 4 0 | 2 0 2 0 0 | * * * * 9 * * * * | 0 0 2 0 0 1 1 0 0 0 | 0 2 1 2 0 1 0 0 | 1 2 1 0 o.o.o.3o.o.o. o.o.o.&#x | 3 0 | 0 0 3 0 0 | * * * * * 3 * * * | 0 0 0 0 2 0 2 0 0 0 | 0 0 0 4 1 1 0 0 | 0 2 2 0 .ooo..3.ooo.. .ooo..&#x & | 1 2 | 0 2 0 0 1 | * * * * * * 18 * * | 0 0 0 0 1 0 0 2 1 0 | 0 0 0 2 1 0 1 2 | 0 1 2 1 ...... ...... .x.x..&#x & | 0 4 | 0 0 0 2 2 | * * * * * * * 3 * | 0 0 0 0 0 0 0 0 3 1 | 0 0 0 0 3 0 0 3 | 0 0 3 1 .o.o.o3.o.o.o .o.o.o&#x | 0 3 | 0 0 0 0 3 | * * * * * * * * 2 | 0 0 0 0 3 0 0 0 0 1 | 0 0 0 3 3 0 0 0 | 0 1 3 0 ---------------------------+-----+------------+-----------------------+-------------------------+-----------------+-------- xo....3oo.... ......&#x & ♦ 3 1 | 3 3 0 0 0 | 1 3 0 0 0 0 0 0 0 | 12 * * * * * * * * * | 1 1 0 0 0 0 1 0 | 1 1 0 1 xo.... ...... ox....&#x & ♦ 2 2 | 1 4 0 1 0 | 0 2 2 0 0 0 0 0 0 | * 18 * * * * * * * * | 1 0 1 0 0 0 0 1 | 1 0 1 1 xox... ...... ......&#x & ♦ 4 1 | 2 4 2 0 0 | 0 2 0 2 1 0 0 0 0 | * * 18 * * * * * * * | 0 1 1 1 0 0 0 0 | 1 1 1 0 ...... ...... oxo...&#x & ♦ 2 2 | 0 4 1 1 0 | 0 0 2 2 0 0 0 0 0 | * * * 9 * * * * * * | 0 0 2 0 1 0 0 0 | 1 0 2 0 oooooo3oooooo oooooo&#xr ♦ 3 3 | 0 6 3 0 3 | 0 0 0 3 0 1 3 0 1 | * * * * 6 * * * * * | 0 0 0 2 1 0 0 0 | 0 1 2 0 x.x...3o.o... ......&#x & ♦ 6 0 | 6 0 3 0 0 | 2 0 0 0 3 0 0 0 0 | * * * * * 3 * * * * | 0 2 0 0 0 1 0 0 | 1 2 0 0 x.x.x. ...... ......&#x ♦ 6 0 | 3 0 6 0 0 | 0 0 0 0 3 2 0 0 0 | * * * * * * 3 * * * | 0 0 0 2 0 1 0 0 | 0 2 1 0 .oxo.. ...... ......&#x & ♦ 2 2 | 1 4 0 0 1 | 0 2 0 0 0 0 2 0 0 | * * * * * * * 18 * * | 0 0 0 1 0 0 1 1 | 0 1 1 1 ...... ...... .xox..&#x & ♦ 1 4 | 0 4 0 2 2 | 0 0 2 0 0 0 2 1 0 | * * * * * * * * 9 * | 0 0 0 0 1 0 0 2 | 0 0 2 1 ...... ...... .x.x.x&#x ♦ 0 6 | 0 0 0 3 6 | 0 0 0 0 0 0 0 3 2 | * * * * * * * * * 1 | 0 0 0 0 3 0 0 0 | 0 0 3 0 ---------------------------+-----+------------+-----------------------+-------------------------+-----------------+-------- xo....3oo.... ox....&#x & ♦ 3 2 | 3 6 0 1 0 | 1 6 3 0 0 0 0 0 0 | 2 3 0 0 0 0 0 0 0 0 | 6 * * * * * * * | 1 0 0 1 xox...3ooo... ......&#x & ♦ 6 1 | 6 6 3 0 0 | 2 6 0 3 3 0 0 0 0 | 2 0 3 0 0 1 0 0 0 0 | * 6 * * * * * * | 1 1 0 0 xox... ...... oxo...&#x & ♦ 4 2 | 2 8 2 1 0 | 0 4 4 4 1 0 0 0 0 | 0 2 2 2 0 0 0 0 0 0 | * * 9 * * * * * | 1 0 1 0 xoxoxo ...... ......&#xr ♦ 6 3 | 3 12 6 0 3 | 0 6 0 6 3 2 6 0 1 | 0 0 3 0 2 0 1 3 0 0 | * * * 6 * * * * | 0 1 1 0 ...... ...... oxoxox&#xr ♦ 3 6 | 0 12 3 3 6 | 0 0 6 6 0 1 6 3 2 | 0 0 0 3 2 0 0 0 3 1 | * * * * 3 * * * | 0 0 2 0 x.x.x.3o.o.o. ......&#x ♦ 9 0 | 9 0 9 0 0 | 3 0 0 0 9 3 0 0 0 | 0 0 0 0 0 3 3 0 0 0 | * * * * * 1 * * | 0 2 0 0 .oxo..3.ooo.. ......&#x & ♦ 3 2 | 3 6 0 0 1 | 1 6 0 0 0 0 3 0 0 | 2 0 0 0 0 0 0 3 0 0 | * * * * * * 6 * | 0 1 0 1 .oxo.. ...... .xox..&#x & ♦ 2 4 | 1 8 0 2 2 | 0 4 4 0 0 0 4 1 0 | 0 2 0 0 0 0 0 2 2 0 | * * * * * * * 9 | 0 0 1 1 ---------------------------+-----+------------+-----------------------+-------------------------+-----------------+-------- xox...3ooo... oxo...&#x & ♦ 6 2 | 6 12 3 1 0 | 2 12 6 6 3 0 0 0 0 | 4 6 6 3 0 1 0 0 0 0 | 2 2 3 0 0 0 0 0 | 3 * * * xoxoxo3oooooo ......&#xr ♦ 9 3 | 9 18 9 0 3 | 3 18 0 9 9 3 9 0 1 | 6 0 9 0 3 3 3 9 0 0 | 0 3 0 3 0 1 3 0 | * 2 * * xoxoxo ...... oxoxox&#xr ♦ 6 6 | 3 24 6 3 6 | 0 12 12 12 3 2 12 3 2 | 0 6 6 6 4 0 1 6 6 1 | 0 0 3 2 2 0 0 3 | * * 3 * .oxo..3.ooo.. .xox..&#x & ♦ 3 4 | 3 12 0 2 2 | 1 12 6 0 0 0 6 1 0 | 4 6 0 0 0 0 0 6 3 0 | 2 0 0 0 0 0 2 3 | * * * 3
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