﻿ tetco tuttric
Acronym tetco tuttric
Name (tet,co,tut)-trigonic
Lace city
in approx. ASCII-art
```    x3o3o

x3x3o     x3o3x
```
Lace hyper city
in approx. ASCII-art
 ``` o3o o3x ``` (tet layer) ```o3x x3o o3u x3x x3x o3x ``` (coatut layer)
Confer
related segmentotera:
penasrip
general polytopal classes:
segmentotera   lace simplices

Incidence matrix according to Dynkin symbol

```oox3oxo3xxx&#x   → height(1,2) = 1/sqrt(2) = 0.707107
height(1,3) = height(2,3) = sqrt(5/8) = 0.790569
height(1,23) = sqrt(2/5) = 0.632456 (tet || coatut)

o..3o..3o..    | 4  *  * | 3  3  3  0 0  0  0  0 | 3  3 3  6  3  6 0 0  0  0  0 0 0 0 | 1 1 3  3  3  6 1 3 3 0 0 0 0 0 | 1 1 3 3 1 0
.o.3.o.3.o.    | * 12  * | 0  1  0  2 1  2  0  0 | 0  2 1  2  0  0 1 2  1  2  2 0 0 0 | 0 1 2  1  2  2 0 0 0 1 1 1 2 0 | 1 1 1 2 0 1
..o3..o3..o    | *  * 12 | 0  0  1  0 0  2  2  2 | 0  0 0  2  2  2 0 0  2  1  2 1 2 1 | 0 0 0  2  1  2 1 2 1 0 1 2 1 1 | 0 1 2 1 1 1
---------------+---------+-----------------------+------------------------------------+--------------------------------+------------
... ... x..    | 2  0  0 | 6  *  *  * *  *  *  * | 2  0 1  0  0  2 0 0  0  0  0 0 0 0 | 1 0 2  0  0  2 0 1 2 0 0 0 0 0 | 1 0 1 2 1 0
oo.3oo.3oo.&#x | 1  1  0 | * 12  *  * *  *  *  * | 0  2 1  2  0  0 0 0  0  0  0 0 0 0 | 0 1 2  1  2  2 0 0 0 0 0 0 0 0 | 1 1 1 2 0 0
o.o3o.o3o.o&#x | 1  0  1 | *  * 12  * *  *  *  * | 0  0 0  2  2  2 0 0  0  0  0 0 0 0 | 0 0 0  2  1  2 1 2 1 0 0 0 0 0 | 0 1 2 1 1 0
... .x. ...    | 0  2  0 | *  *  * 12 *  *  *  * | 0  1 0  0  0  0 1 1  0  1  0 0 0 0 | 0 1 1  0  1  0 0 0 0 1 1 0 1 0 | 1 1 0 1 0 1
... ... .x.    | 0  2  0 | *  *  *  * 6  *  *  * | 0  0 1  0  0  0 0 2  0  0  2 0 0 0 | 0 0 2  0  0  2 0 0 0 1 0 1 2 0 | 1 0 1 2 0 1
.oo3.oo3.oo&#x | 0  1  1 | *  *  *  * * 24  *  * | 0  0 0  1  0  0 0 0  1  1  1 0 0 0 | 0 0 0  1  1  1 0 0 0 0 1 1 1 0 | 0 1 1 1 0 1
..x ... ...    | 0  0  2 | *  *  *  * *  * 12  * | 0  0 0  0  1  0 0 0  1  0  0 1 1 0 | 0 0 0  1  0  0 1 1 0 0 1 1 0 1 | 0 1 1 0 1 1
... ... ..x    | 0  0  2 | *  *  *  * *  *  * 12 | 0  0 0  0  0  1 0 0  0  0  1 0 1 1 | 0 0 0  0  0  1 0 1 1 0 0 1 1 1 | 0 0 1 1 1 1
---------------+---------+-----------------------+------------------------------------+--------------------------------+------------
... o..3x..    | 3  0  0 | 3  0  0  0 0  0  0  0 | 4  * *  *  *  * * *  *  *  * * * * | 1 0 1  0  0  0 0 0 1 0 0 0 0 0 | 1 0 0 1 1 0
... ox. ...&#x | 1  2  0 | 0  2  0  1 0  0  0  0 | * 12 *  *  *  * * *  *  *  * * * * | 0 1 1  0  1  0 0 0 0 0 0 0 0 0 | 1 1 0 1 0 0
... ... xx.&#x | 2  2  0 | 1  2  0  0 1  0  0  0 | *  * 6  *  *  * * *  *  *  * * * * | 0 0 2  0  0  2 0 0 0 0 0 0 0 0 | 1 0 1 2 0 0
ooo3ooo3ooo&#x | 1  1  1 | 0  1  1  0 0  1  0  0 | *  * * 24  *  * * *  *  *  * * * * | 0 0 0  1  1  1 0 0 0 0 0 0 0 0 | 0 1 1 1 0 0
o.x ... ...&#x | 1  0  2 | 0  0  2  0 0  0  1  0 | *  * *  * 12  * * *  *  *  * * * * | 0 0 0  1  0  0 1 1 0 0 0 0 0 0 | 0 1 1 0 1 0
... ... x.x&#x | 2  0  2 | 1  0  2  0 0  0  0  1 | *  * *  *  * 12 * *  *  *  * * * * | 0 0 0  0  0  1 0 1 1 0 0 0 0 0 | 0 0 1 1 1 0
.o.3.x. ...    | 0  3  0 | 0  0  0  3 0  0  0  0 | *  * *  *  *  * 4 *  *  *  * * * * | 0 1 0  0  0  0 0 0 0 1 1 0 0 0 | 1 1 0 0 0 1
... .x.3.x.    | 0  6  0 | 0  0  0  3 3  0  0  0 | *  * *  *  *  * * 4  *  *  * * * * | 0 0 1  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  2  1  0 | *  * *  *  *  * * * 12  *  * * * * | 0 0 0  1  0  0 0 0 0 0 1 1 0 0 | 0 1 1 0 0 1
... .xo ...&#x | 0  2  1 | 0  0  0  1 0  2  0  0 | *  * *  *  *  * * *  * 12  * * * * | 0 0 0  0  1  0 0 0 0 0 1 0 1 0 | 0 1 0 1 0 1
... ... .xx&#x | 0  2  2 | 0  0  0  0 1  2  0  1 | *  * *  *  *  * * *  *  * 12 * * * | 0 0 0  0  0  1 0 0 0 0 0 1 1 0 | 0 0 1 1 0 1
..x3..o ...    | 0  0  3 | 0  0  0  0 0  0  3  0 | *  * *  *  *  * * *  *  *  * 4 * * | 0 0 0  0  0  0 1 0 0 0 1 0 0 1 | 0 1 0 0 1 1
..x ... ..x    | 0  0  4 | 0  0  0  0 0  0  2  2 | *  * *  *  *  * * *  *  *  * * 6 * | 0 0 0  0  0  0 0 1 0 0 0 1 0 1 | 0 0 1 0 1 1
... ..o3..x    | 0  0  3 | 0  0  0  0 0  0  0  3 | *  * *  *  *  * * *  *  *  * * * 4 | 0 0 0  0  0  0 0 0 1 0 0 0 1 1 | 0 0 0 1 1 1
---------------+---------+-----------------------+------------------------------------+--------------------------------+------------
o..3o..3x..    ♦ 4  0  0 | 6  0  0  0 0  0  0  0 | 4  0 0  0  0  0 0 0  0  0  0 0 0 0 | 1 * *  *  *  * * * * * * * * * | 1 0 0 0 1 0
oo.3ox. ...&#x ♦ 1  3  0 | 0  3  0  3 0  0  0  0 | 0  3 0  0  0  0 1 0  0  0  0 0 0 0 | * 4 *  *  *  * * * * * * * * * | 1 1 0 0 0 0
... ox.3xx.&#x ♦ 3  6  0 | 3  6  0  3 3  0  0  0 | 1  3 3  0  0  0 0 1  0  0  0 0 0 0 | * * 4  *  *  * * * * * * * * * | 1 0 0 1 0 0
oox ... ...&#x ♦ 1  1  2 | 0  1  2  0 0  2  1  0 | 0  0 0  2  1  0 0 0  1  0  0 0 0 0 | * * * 12  *  * * * * * * * * * | 0 1 1 0 0 0
... oxo ...&#x ♦ 1  2  1 | 0  2  1  1 0  2  0  0 | 0  1 0  2  0  0 0 0  0  1  0 0 0 0 | * * *  * 12  * * * * * * * * * | 0 1 0 1 0 0
... ... xxx&#x ♦ 2  2  2 | 1  2  2  0 1  2  0  1 | 0  0 1  2  0  1 0 0  0  0  1 0 0 0 | * * *  *  * 12 * * * * * * * * | 0 0 1 1 0 0
o.x3o.o ...&#x ♦ 1  0  3 | 0  0  3  0 0  0  3  0 | 0  0 0  0  3  0 0 0  0  0  0 1 0 0 | * * *  *  *  * 4 * * * * * * * | 0 1 0 0 1 0
o.x ... x.x&#x ♦ 2  0  4 | 1  0  4  0 0  0  2  2 | 0  0 0  0  2  2 0 0  0  0  0 0 1 0 | * * *  *  *  * * 6 * * * * * * | 0 0 1 0 1 0
... o.o3x.x&#x ♦ 3  0  3 | 3  0  3  0 0  0  0  3 | 1  0 0  0  0  3 0 0  0  0  0 0 0 1 | * * *  *  *  * * * 4 * * * * * | 0 0 0 1 1 0
.o.3.x.3.x.    ♦ 0 12  0 | 0  0  0 12 6  0  0  0 | 0  0 0  0  0  0 4 4  0  0  0 0 0 0 | * * *  *  *  * * * * 1 * * * * | 1 0 0 0 0 1
.ox3.xo ...&#x ♦ 0  3  3 | 0  0  0  3 0  6  3  0 | 0  0 0  0  0  0 1 0  3  3  0 1 0 0 | * * *  *  *  * * * * * 4 * * * | 0 1 0 0 0 1
.ox ... .xx&#x ♦ 0  2  4 | 0  0  0  0 1  4  2  2 | 0  0 0  0  0  0 0 0  2  0  2 0 1 0 | * * *  *  *  * * * * * * 6 * * | 0 0 1 0 0 1
... .xo3.xx&#x ♦ 0  6  3 | 0  0  0  3 3  6  0  3 | 0  0 0  0  0  0 0 1  0  3  3 0 0 1 | * * *  *  *  * * * * * * * 4 * | 0 0 0 1 0 1
..x3..o3..x    ♦ 0  0 12 | 0  0  0  0 0  0 12 12 | 0  0 0  0  0  0 0 0  0  0  0 4 6 4 | * * *  *  *  * * * * * * * * 1 | 0 0 0 0 1 1
---------------+---------+-----------------------+------------------------------------+--------------------------------+------------
oo.3ox.3xx.&#x ♦ 4 12  0 | 6 12  0 12 6  0  0  0 | 4 12 6  0  0  0 4 4  0  0  0 0 0 0 | 1 4 4  0  0  0 0 0 0 1 0 0 0 0 | 1 * * * * *
oox3oxo ...&#x ♦ 1  3  3 | 0  3  3  3 0  6  3  0 | 0  3 0  6  3  0 1 0  3  3  0 1 0 0 | 0 1 0  3  3  0 1 0 0 0 1 0 0 0 | * 4 * * * *
oox ... xxx&#x ♦ 2  2  4 | 1  2  4  0 1  4  2  2 | 0  0 1  4  2  2 0 0  2  0  2 0 1 0 | 0 0 0  2  0  2 0 1 0 0 0 1 0 0 | * * 6 * * *
... oxo3xxx&#x ♦ 3  6  3 | 3  6  3  3 3  6  0  3 | 1  3 3  6  0  3 0 1  0  3  3 0 0 1 | 0 0 1  0  3  3 0 0 1 0 0 0 1 0 | * * * 4 * *
o.x3o.o3x.x&#x ♦ 4  0 12 | 6  0 12  0 0  0 12 12 | 4  0 0  0 12 12 0 0  0  0  0 4 6 4 | 1 0 0  0  0  0 4 6 4 0 0 0 0 1 | * * * * 1 *
.ox3.xo3.xx&#x ♦ 0 12 12 | 0  0  0 12 6 24 12 12 | 0  0 0  0  0  0 4 4 12 12 12 4 6 4 | 0 0 0  0  0  0 0 0 0 1 4 6 4 1 | * * * * * 1
```