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Acronym
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tutatoe augrip
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Name
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tutatoe-augmented grip
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 ©
near side view: green = top tut, transparent = hips + tricues + lateral tuts, yellow = gybefs
 ©
far side view: green = bottom tut, orange = trips, blue = toes
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Lace city
in approx. ASCII-art
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+-- xxo oxx&#xt (gybef)
/
o x x u u x x o -- o3x3x (inv tut)
x x u u xw wx u u x x -- x3x3x (toe)
x o w u u w o x -- x3u3o ((x,u)-tut)
u o w x x w o u -- u3x3o ((u,x)-tut)
x o u x x u o x -- x3x3o (tut)
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o3x o3u x3x -- o3x3x (inv tut)
x3x x3u u3x x3x -- x3x3x (toe)
x3u H3o u3o -- x3u3o ((x,u)-tut)
u3x H3o x3o -- u3x3o ((u,x)-tut)
x3x u3o x3o -- x3x3o (tut)
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Dihedral angles
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- at {6} between hip and tut (across rim): arccos(-sqrt[27/32]) = 156.716268°
- at {6} between toe and tricu: arccos(-7/8) = 151.044976°
- at {4} between gybef and hip: arccos(-2/3) = 131.810315°
- at {3} between gybef and tricu: arccos[-sqrt(3/8)] = 127.761244°
- at {3} between gybef and tut: arccos[-sqrt(3/8)] = 127.761244°
- at {3} between trip and tut: arccos[-sqrt(3/8)] = 127.761244°
- at {6} between hip and tut (on tutatoe part): arccos[-sqrt(3/8)] = 127.761244°
- at {4} between gybef and toe: arccos[-1/sqrt(6)] = 114.094843°
- at {4} between hip and tricu: arccos[-1/sqrt(6)] = 114.094843°
- at {4} between toe and trip: arccos[-1/sqrt(6)] = 114.094843°
- at {3} between tricu and tut: arccos(-1/4) = 104.477512°
- at {6} between toe and tut: arccos(-1/4) = 104.477512°
- at {6} between toe and toe: arccos(1/4) = 75.522488°
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Face vector
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72, 162, 118, 28
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Confer
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- uniform relative:
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grip
- related segmentochora:
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tutatoe
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External
links
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A multi-augmentation with further tutatoees surely is possible, but that one would no longer be CRF,
as tricu-6-toe (of tutatoe) + toe-6-toe (of grip) + tricu-6-toe (of tutatoe) = 3x 75.522488° will be concave.
Incidence matrix according to Dynkin symbol
oxxux3xxuxx3xxooo&#xt → all heights = sqrt(5/8) = 0.790569
(tut || toe || inv (x,u)-tut || inv (u,x)-tut || inv tut)
o....3o....3o.... | 12 * * * * | 2 1 2 0 0 0 0 0 0 0 0 0 0 | 1 2 1 2 2 0 0 0 0 0 0 0 0 0 0 | 1 1 1 2 0 0 0 0
.o...3.o...3.o... | * 24 * * * | 0 0 1 1 1 1 1 0 0 0 0 0 0 | 0 0 1 1 1 1 1 1 1 1 0 0 0 0 0 | 0 1 1 1 1 1 0 0
..o..3..o..3..o.. | * * 12 * * | 0 0 0 0 0 0 2 1 1 0 0 0 0 | 0 0 0 0 0 0 0 2 2 1 1 0 0 0 0 | 0 0 1 0 2 1 0 0
...o.3...o.3...o. | * * * 12 * | 0 0 0 0 0 0 0 0 1 2 1 0 0 | 0 0 0 0 0 0 0 0 2 0 1 1 2 0 0 | 0 0 0 0 2 1 1 0
....o3....o3....o | * * * * 12 | 0 0 0 0 0 0 0 0 0 0 1 1 2 | 0 0 0 0 0 0 0 0 0 0 1 0 2 2 1 | 0 0 0 0 2 0 1 1
----------------------+----------------+-------------------------------------+--------------------------------------+----------------
..... x.... ..... | 2 0 0 0 0 | 12 * * * * * * * * * * * * | 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 | 1 1 0 1 0 0 0 0
..... ..... x.... | 2 0 0 0 0 | * 6 * * * * * * * * * * * | 0 2 0 0 2 0 0 0 0 0 0 0 0 0 0 | 1 0 1 2 0 0 0 0
oo...3oo...3oo...&#x | 1 1 0 0 0 | * * 24 * * * * * * * * * * | 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 | 0 1 1 1 0 0 0 0
.x... ..... ..... | 0 2 0 0 0 | * * * 12 * * * * * * * * * | 0 0 1 0 0 1 0 1 0 0 0 0 0 0 0 | 0 1 1 0 1 0 0 0
..... .x... ..... | 0 2 0 0 0 | * * * * 12 * * * * * * * * | 0 0 0 1 0 1 1 0 1 0 0 0 0 0 0 | 0 1 0 1 1 1 0 0
..... ..... .x... | 0 2 0 0 0 | * * * * * 12 * * * * * * * | 0 0 0 0 1 0 1 0 0 1 0 0 0 0 0 | 0 0 1 1 0 1 0 0
.oo..3.oo..3.oo..&#x | 0 1 1 0 0 | * * * * * * 24 * * * * * * | 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 | 0 0 1 0 1 1 0 0
..x.. ..... ..... | 0 0 2 0 0 | * * * * * * * 6 * * * * * | 0 0 0 0 0 0 0 2 0 0 1 0 0 0 0 | 0 0 1 0 2 0 0 0
..oo.3..oo.3..oo.&#x | 0 0 1 1 0 | * * * * * * * * 12 * * * * | 0 0 0 0 0 0 0 0 2 0 1 0 0 0 0 | 0 0 0 0 2 1 0 0
..... ...x. ..... | 0 0 0 2 0 | * * * * * * * * * 12 * * * | 0 0 0 0 0 0 0 0 1 0 0 1 1 0 0 | 0 0 0 0 1 1 1 0
...oo3...oo3...oo&#x | 0 0 0 1 1 | * * * * * * * * * * 12 * * | 0 0 0 0 0 0 0 0 0 0 1 0 2 0 0 | 0 0 0 0 2 0 1 0
....x ..... ..... | 0 0 0 0 2 | * * * * * * * * * * * 6 * | 0 0 0 0 0 0 0 0 0 0 1 0 0 2 0 | 0 0 0 0 2 0 0 1
..... ....x ..... | 0 0 0 0 2 | * * * * * * * * * * * * 12 | 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 | 0 0 0 0 1 0 1 1
----------------------+----------------+-------------------------------------+--------------------------------------+----------------
o....3x.... ..... | 3 0 0 0 0 | 3 0 0 0 0 0 0 0 0 0 0 0 0 | 4 * * * * * * * * * * * * * * | 1 1 0 0 0 0 0 0
..... x....3x.... | 6 0 0 0 0 | 3 3 0 0 0 0 0 0 0 0 0 0 0 | * 4 * * * * * * * * * * * * * | 1 0 0 1 0 0 0 0
ox... ..... .....&#x | 1 2 0 0 0 | 0 0 2 1 0 0 0 0 0 0 0 0 0 | * * 12 * * * * * * * * * * * * | 0 1 1 0 0 0 0 0
..... xx... .....&#x | 2 2 0 0 0 | 1 0 2 0 1 0 0 0 0 0 0 0 0 | * * * 12 * * * * * * * * * * * | 0 1 0 1 0 0 0 0
..... ..... xx...&#x | 2 2 0 0 0 | 0 1 2 0 0 1 0 0 0 0 0 0 0 | * * * * 12 * * * * * * * * * * | 0 0 1 1 0 0 0 0
.x...3.x... ..... | 0 6 0 0 0 | 0 0 0 3 3 0 0 0 0 0 0 0 0 | * * * * * 4 * * * * * * * * * | 0 1 0 0 1 0 0 0
..... .x...3.x...&#x | 0 6 0 0 0 | 0 0 0 0 3 3 0 0 0 0 0 0 0 | * * * * * * 4 * * * * * * * * | 0 0 0 1 0 1 0 0
.xx.. ..... .....&#x | 0 2 2 0 0 | 0 0 0 1 0 0 2 1 0 0 0 0 0 | * * * * * * * 12 * * * * * * * | 0 0 1 0 1 0 0 0
..... .xux. .....&#xt | 0 2 2 2 0 | 0 0 0 0 1 0 2 0 2 1 0 0 0 | * * * * * * * * 12 * * * * * * | 0 0 0 0 1 1 0 0
..... ..... .xo..&#x | 0 2 1 0 0 | 0 0 0 0 0 1 2 0 0 0 0 0 0 | * * * * * * * * * 12 * * * * * | 0 0 1 0 0 1 0 0
..xux ..... .....&#x | 0 0 2 2 2 | 0 0 0 0 0 0 0 1 2 0 2 1 0 | * * * * * * * * * * 6 * * * * | 0 0 0 0 2 0 0 0
..... ...x.3...o. | 0 0 0 3 0 | 0 0 0 0 0 0 0 0 0 3 0 0 0 | * * * * * * * * * * * 4 * * * | 0 0 0 0 0 1 1 0
..... ...xx .....&#x | 0 0 0 2 2 | 0 0 0 0 0 0 0 0 0 1 2 0 1 | * * * * * * * * * * * * 12 * * | 0 0 0 0 1 0 1 0
....x3....x ..... | 0 0 0 0 6 | 0 0 0 0 0 0 0 0 0 0 0 3 3 | * * * * * * * * * * * * * 4 * | 0 0 0 0 1 0 0 1
..... ....x3....o | 0 0 0 0 3 | 0 0 0 0 0 0 0 0 0 0 0 0 3 | * * * * * * * * * * * * * * 4 | 0 0 0 0 0 0 1 1
----------------------+----------------+-------------------------------------+--------------------------------------+----------------
o....3x....3x.... ♦ 12 0 0 0 0 | 12 6 0 0 0 0 0 0 0 0 0 0 0 | 4 4 0 0 0 0 0 0 0 0 0 0 0 0 0 | 1 * * * * * * *
ox...3xx... .....&#x ♦ 3 6 0 0 0 | 3 0 6 3 3 0 0 0 0 0 0 0 0 | 1 0 3 3 0 1 0 0 0 0 0 0 0 0 0 | * 4 * * * * * *
oxx.. ..... xxo..&#xt ♦ 2 4 2 0 0 | 0 1 4 2 0 2 4 1 0 0 0 0 0 | 0 0 2 0 2 0 0 2 0 2 0 0 0 0 0 | * * 6 * * * * *
..... xx...3xx...&#x ♦ 6 6 0 0 0 | 3 3 6 0 3 3 0 0 0 0 0 0 0 | 0 1 0 3 3 0 1 0 0 0 0 0 0 0 0 | * * * 4 * * * *
.xxux3.xuxx .....&#xt ♦ 0 6 6 6 6 | 0 0 0 3 3 0 6 3 6 3 6 3 3 | 0 0 0 0 0 1 0 3 3 0 3 0 3 1 0 | * * * * 4 * * *
..... .xux.3.xoo.&#xt ♦ 0 6 3 3 0 | 0 0 0 0 3 3 6 0 3 3 0 0 0 | 0 0 0 0 0 0 1 0 3 3 0 1 0 0 0 | * * * * * 4 * *
..... ...xx3...oo&#x ♦ 0 0 0 3 3 | 0 0 0 0 0 0 0 0 0 3 3 0 3 | 0 0 0 0 0 0 0 0 0 0 0 1 3 0 1 | * * * * * * 4 *
....x3....x3....o ♦ 0 0 0 0 12 | 0 0 0 0 0 0 0 0 0 0 0 6 12 | 0 0 0 0 0 0 0 0 0 0 0 0 0 4 4 | * * * * * * * 1