﻿ tutatoe augrip
 Acronym tutatoe augrip Name tutatoe-augmented grip ``` © near side view: green = top tut, transparent = hips + tricues + lateral tuts, yellow = gybefs © far side view: green = bottom tut, orange = trips, blue = toes ``` Lace cityin approx. ASCII-art ``` +-- 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) ``` ``` 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) ``` Dihedral angles 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(-sqrt[1/6]) = 114.094843° at {4} between hip and tricu:   arccos(-sqrt[1/6]) = 114.094843° at {4} between toe and trip:   arccos(-sqrt[1/6]) = 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° Confer uniform relative: grip   related segmentochora: tutatoe Externallinks

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
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