﻿ tetaco ausrip
 Acronym tetaco ausrip Name tetaco-augmented srip Lace cityin approx. ASCII-art ``` +-- xxo oxx&#xt (gybef) / x o o x -- x3o3o (tet) x x ou uo x x -- x3o3x (co) o x x u u x x o -- o3x3x (inv tut) o o x x o o -- o3x3o (oct) ``` ``` o3x o3o -- x3o3o (tet) o3x x3x x3o -- x3o3x (co) x3o u3o x3x -- o3x3x (inv tut) x3o o3x -- o3x3o (oct) ``` Dihedral angles at {3} between oct and trip (across rim):   arccos(-sqrt[27/32]) = 156.716268° at {3} between co and tet:   arccos(-7/8) = 151.044976° at {4} between gybef and trip:   arccos(-2/3) = 131.810315° at {3} between gybef and tet:   arccos(-sqrt(3/8)) = 127.761244° at {3} between gybef and oct:   arccos(-sqrt(3/8)) = 127.761244° at {3} between oct and trip (on srip part):   arccos(-sqrt(3/8)) = 127.761244° at {3} between tet and trip:   arccos(-sqrt(3/8)) = 127.761244° at {4} between co and trip:   arccos(-1/sqrt(6)) = 114.094843° at {4} between co and gybef:   arccos(-1/sqrt(6)) = 114.094843° at {3} between co and oct:   arccos(-1/4) = 104.477512° at {3} between co and co:   arccos(1/4) = 75.522488° Confer uniform relative: srip   related segmentochora: tetaco   related CRFs: oxx3oox3xxo&#xt

A multi-augmentation with further tetacoes surely is possible, but that one would no longer be CRF, as tet-3-co (of tetaco) + co-3-co (of srip) + tet-3-co (of tetaco) = 3x 75.522488° will be concave.

Incidence matrix according to Dynkin symbol

```xxoo3ooxx3oxxo&#xt   → all heights = sqrt(5/8) = 0.790569
(tet || co || inv tut || oct)

o...3o...3o...     | 4  *  * * ♦ 3  3  0  0  0  0 0  0  0 | 3  6  3 0 0  0  0  0 0  0 0 0 0 | 1 3 3 1 0 0 0 0
.o..3.o..3.o..     | * 12  * * | 0  1  2  2  2  0 0  0  0 | 0  2  2 1 1  2  1  0 0  0 0 0 0 | 0 1 2 1 1 1 0 0
..o.3..o.3..o.     | *  * 12 * ♦ 0  0  0  0  2  2 1  1  0 | 0  0  0 0 0  1  2  2 1  2 1 0 0 | 0 0 1 0 1 2 1 0
...o3...o3...o     | *  *  * 6 ♦ 0  0  0  0  0  0 0  2  4 | 0  0  0 0 0  0  0  0 0  4 1 2 2 | 0 0 0 0 0 2 2 1
-------------------+-----------+--------------------------+---------------------------------+----------------
x... .... ....     | 2  0  0 0 | 6  *  *  *  *  * *  *  * | 2  2  0 0 0  0  0  0 0  0 0 0 0 | 1 2 1 0 0 0 0 0
oo..3oo..3oo..&#x  | 1  1  0 0 | * 12  *  *  *  * *  *  * | 0  2  2 0 0  0  0  0 0  0 0 0 0 | 0 1 2 1 0 0 0 0
.x.. .... ....     | 0  2  0 0 | *  * 12  *  *  * *  *  * | 0  1  0 1 0  1  0  0 0  0 0 0 0 | 0 1 1 0 1 0 0 0
.... .... .x..     | 0  2  0 0 | *  *  * 12  *  * *  *  * | 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 | *  *  *  * 24  * *  *  * | 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 | *  *  *  *  * 12 *  *  * | 0  0  0 0 0  0  1  0 1  1 0 0 0 | 0 0 0 0 1 1 1 0
.... .... ..x.     | 0  0  2 0 | *  *  *  *  *  * 6  *  * | 0  0  0 0 0  0  0  2 0  0 1 0 0 | 0 0 1 0 0 2 0 0
..oo3..oo3..oo&#x  | 0  0  1 1 | *  *  *  *  *  * * 12  * | 0  0  0 0 0  0  0  0 0  2 1 0 0 | 0 0 0 0 0 2 1 0
.... ...x ....     | 0  0  0 2 | *  *  *  *  *  * *  * 12 | 0  0  0 0 0  0  0  0 0  1 0 1 1 | 0 0 0 0 0 1 1 1
-------------------+-----------+--------------------------+---------------------------------+----------------
x...3o... ....     | 3  0  0 0 | 3  0  0  0  0  0 0  0  0 | 4  *  * * *  *  *  * *  * * * * | 1 1 0 0 0 0 0 0
xx.. .... ....&#x  | 2  2  0 0 | 1  2  1  0  0  0 0  0  0 | * 12  * * *  *  *  * *  * * * * | 0 1 1 0 0 0 0 0
.... .... ox..&#x  | 1  2  0 0 | 0  2  0  1  0  0 0  0  0 | *  * 12 * *  *  *  * *  * * * * | 0 0 1 1 0 0 0 0
.x..3.o.. ....     | 0  3  0 0 | 0  0  3  0  0  0 0  0  0 | *  *  * 4 *  *  *  * *  * * * * | 0 1 0 0 1 0 0 0
.... .o..3.x..     | 0  3  0 0 | 0  0  0  3  0  0 0  0  0 | *  *  * * 4  *  *  * *  * * * * | 0 0 0 1 0 1 0 0
.xo. .... ....&#x  | 0  2  1 0 | 0  0  1  0  2  0 0  0  0 | *  *  * * * 12  *  * *  * * * * | 0 0 1 0 1 0 0 0
.... .ox. ....&#x  | 0  1  2 0 | 0  0  0  0  2  1 0  0  0 | *  *  * * *  * 12  * *  * * * * | 0 0 0 0 1 1 0 0
.... .... .xx.&#x  | 0  2  2 0 | 0  0  0  1  2  0 1  0  0 | *  *  * * *  *  * 12 *  * * * * | 0 0 1 0 0 1 0 0
..o.3..x. ....     | 0  0  3 0 | 0  0  0  0  0  3 0  0  0 | *  *  * * *  *  *  * 4  * * * * | 0 0 0 0 1 0 1 0
.... ..xx ....&#x  | 0  0  2 2 | 0  0  0  0  0  1 0  2  1 | *  *  * * *  *  *  * * 12 * * * | 0 0 0 0 0 1 1 0
.... .... ..xo&#x  | 0  0  2 1 | 0  0  0  0  0  0 1  2  0 | *  *  * * *  *  *  * *  * 6 * * | 0 0 0 0 0 2 0 0
...o3...x ....     | 0  0  0 3 | 0  0  0  0  0  0 0  0  3 | *  *  * * *  *  *  * *  * * 4 * | 0 0 0 0 0 0 1 1
.... ...x3...o     | 0  0  0 3 | 0  0  0  0  0  0 0  0  3 | *  *  * * *  *  *  * *  * * * 4 | 0 0 0 0 0 1 0 1
-------------------+-----------+--------------------------+---------------------------------+----------------
x...3o...3o...     ♦ 4  0  0 0 | 6  0  0  0  0  0 0  0  0 | 4  0  0 0 0  0  0  0 0  0 0 0 0 | 1 * * * * * * *
xx..3oo.. ....&#x  ♦ 3  3  0 0 | 3  3  3  0  0  0 0  0  0 | 1  3  0 1 0  0  0  0 0  0 0 0 0 | * 4 * * * * * *
xxo. .... oxx.&#xt ♦ 2  4  2 0 | 1  4  2  2  4  0 1  0  0 | 0  2  2 0 0  2  0  2 0  0 0 0 0 | * * 6 * * * * *
.... oo..3ox..&#x  ♦ 1  3  0 0 | 0  3  0  3  0  0 0  0  0 | 0  0  3 0 1  0  0  0 0  0 0 0 0 | * * * 4 * * * *
.xo.3.ox. ....&#x  ♦ 0  3  3 0 | 0  0  3  0  6  3 0  0  0 | 0  0  0 1 0  3  3  0 1  0 0 0 0 | * * * * 4 * * *
.... .oxx3.xxo&#xt ♦ 0  3  6 3 | 0  0  0  3  6  3 3  6  3 | 0  0  0 0 1  0  3  3 0  3 3 0 1 | * * * * * 4 * *
..oo3..xx ....&#x  ♦ 0  0  3 3 | 0  0  0  0  0  3 0  3  3 | 0  0  0 0 0  0  0  0 1  3 0 1 0 | * * * * * * 4 *
...o3...x3...o     ♦ 0  0  0 6 | 0  0  0  0  0  0 0  0 12 | 0  0  0 0 0  0  0  0 0  0 0 4 4 | * * * * * * * 1
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