﻿ coatuttip
 Acronym coatuttip Name co atop tuttip,co-first cap of sarx Circumradius sqrt(5/3) = 1.290994 Lace cityin approx. ASCII-art ``` x3o3x x3x3o x3x3o ``` Confer uniform relative: sarx   general polytopal classes: segmentotera   lace simplices

Incidence matrix according to Dynkin symbol

```ox xo3ox3xx&#x   → height = sqrt(3/8) = 0.612372
(co || tuttip)

o. o.3o.3o.    | 12  * |  2  2  4  0  0  0 | 1 2 1  2  4  2  4  0 0 0 0 | 1  2  1  2 2  4 2 0 0 0 | 1 2 1 2 0
.o .o3.o3.o    |  * 24 |  0  0  2  1  2  1 | 0 0 0  2  1  2  2  2 1 1 2 | 0  1  2  2 1  1 2 1 2 1 | 1 1 2 1 1
---------------+-------+-------------------+----------------------------+-------------------------+----------
.. x. .. ..    |  2  0 | 12  *  *  *  *  * | 1 1 0  0  2  0  0  0 0 0 0 | 1  1  0  0 2  2 0 0 0 0 | 1 1 0 2 0
.. .. .. x.    |  2  0 |  * 12  *  *  *  * | 0 1 1  0  0  0  2  0 0 0 0 | 1  0  0  1 0  2 2 0 0 0 | 0 1 1 2 0
oo oo3oo3oo&#x |  1  1 |  *  * 48  *  *  * | 0 0 0  1  1  1  1  0 0 0 0 | 0  1  1  1 1  1 1 0 0 0 | 1 1 1 1 0
.x .. .. ..    |  0  2 |  *  *  * 12  *  * | 0 0 0  2  0  0  0  2 1 0 0 | 0  1  2  2 0  0 0 1 2 0 | 1 1 2 0 1
.. .. .x ..    |  0  2 |  *  *  *  * 24  * | 0 0 0  0  0  1  0  1 0 1 1 | 0  0  1  0 1  0 1 1 1 1 | 1 0 1 1 1
.. .. .. .x    |  0  2 |  *  *  *  *  * 12 | 0 0 0  0  0  0  2  0 1 0 2 | 0  0  0  2 0  1 2 0 2 1 | 0 1 2 1 1
---------------+-------+-------------------+----------------------------+-------------------------+----------
.. x.3o. ..    |  3  0 |  3  0  0  0  0  0 | 4 * *  *  *  *  *  * * * * | 1  0  0  0 2  0 0 0 0 0 | 1 0 0 2 0
.. x. .. x.    |  4  0 |  2  2  0  0  0  0 | * 6 *  *  *  *  *  * * * * | 1  0  0  0 0  2 0 0 0 0 | 0 1 0 2 0
.. .. o.3x.    |  3  0 |  0  3  0  0  0  0 | * * 4  *  *  *  *  * * * * | 1  0  0  0 0  0 2 0 0 0 | 0 0 1 2 0
ox .. .. ..&#x |  1  2 |  0  0  2  1  0  0 | * * * 24  *  *  *  * * * * | 0  1  1  1 0  0 0 0 0 0 | 1 1 1 0 0
.. xo .. ..&#x |  2  1 |  1  0  2  0  0  0 | * * *  * 24  *  *  * * * * | 0  1  0  0 1  1 0 0 0 0 | 1 1 0 1 0
.. .. ox ..&#x |  1  2 |  0  0  2  0  1  0 | * * *  *  * 24  *  * * * * | 0  0  1  0 1  0 1 0 0 0 | 1 0 1 1 0
.. .. .. xx&#x |  2  2 |  0  1  2  0  0  1 | * * *  *  *  * 24  * * * * | 0  0  0  1 0  1 1 0 0 0 | 0 1 1 1 0
.x .. .x ..    |  0  4 |  0  0  0  2  2  0 | * * *  *  *  *  * 12 * * * | 0  0  1  0 0  0 0 1 1 0 | 1 0 1 0 1
.x .. .. .x    |  0  4 |  0  0  0  2  0  2 | * * *  *  *  *  *  * 6 * * | 0  0  0  2 0  0 0 0 2 0 | 0 1 2 0 1
.. .o3.x ..    |  0  3 |  0  0  0  0  3  0 | * * *  *  *  *  *  * * 8 * | 0  0  0  0 1  0 0 1 0 1 | 1 0 0 1 1
.. .. .x3.x    |  0  6 |  0  0  0  0  3  3 | * * *  *  *  *  *  * * * 8 | 0  0  0  0 0  0 1 0 1 1 | 0 0 1 1 1
---------------+-------+-------------------+----------------------------+-------------------------+----------
.. x.3o.3x.    ♦ 12  0 | 12 12  0  0  0  0 | 4 6 4  0  0  0  0  0 0 0 0 | 1  *  *  * *  * * * * * | 0 0 0 2 0
ox xo .. ..&#x ♦  2  2 |  1  0  4  1  0  0 | 0 0 0  2  2  0  0  0 0 0 0 | * 12  *  * *  * * * * * | 1 1 0 0 0
ox .. ox ..&#x ♦  1  4 |  0  0  4  2  2  0 | 0 0 0  2  0  2  0  1 0 0 0 | *  * 12  * *  * * * * * | 1 0 1 0 0
ox .. .. xx&#x ♦  2  4 |  0  1  4  2  0  2 | 0 0 0  2  0  0  2  0 1 0 0 | *  *  * 12 *  * * * * * | 0 1 1 0 0
.. xo3ox ..&#x ♦  3  3 |  3  0  6  0  3  0 | 1 0 0  0  3  3  0  0 0 1 0 | *  *  *  * 8  * * * * * | 1 0 0 1 0
.. xo .. xx&#x ♦  4  2 |  2  2  4  0  0  1 | 0 1 0  0  2  0  2  0 0 0 0 | *  *  *  * * 12 * * * * | 0 1 0 1 0
.. .. ox3xx&#x ♦  3  6 |  0  3  6  0  3  3 | 0 0 1  0  0  3  3  0 0 0 1 | *  *  *  * *  * 8 * * * | 0 0 1 1 0
.x .o3.x ..    ♦  0  6 |  0  0  0  3  6  0 | 0 0 0  0  0  0  0  3 0 2 0 | *  *  *  * *  * * 4 * * | 1 0 0 0 1
.x .. .x3.x    ♦  0 12 |  0  0  0  6  6  6 | 0 0 0  0  0  0  0  3 3 0 2 | *  *  *  * *  * * * 4 * | 0 0 1 0 1
.. .o3.x3.x    ♦  0 12 |  0  0  0  0 12  6 | 0 0 0  0  0  0  0  0 0 4 4 | *  *  *  * *  * * * * 2 | 0 0 0 1 1
---------------+-------+-------------------+----------------------------+-------------------------+----------
ox xo3ox ..&#x ♦  3  6 |  3  0 12  3  6  0 | 1 0 0  6  6  6  0  3 0 2 0 | 0  3  3  0 2  0 0 1 0 0 | 4 * * * *
ox xo .. xx&#x ♦  4  4 |  2  2  8  2  0  2 | 0 1 0  4  4  0  4  0 1 0 0 | 0  2  0  2 0  2 0 0 0 0 | * 6 * * *
ox .. ox3xx&#x ♦  3 12 |  0  3 12  6  6  6 | 0 0 1  6  0  6  6  3 3 0 2 | 0  0  3  3 0  0 2 0 1 0 | * * 4 * *
.. xo3ox3xx&#x ♦ 12 12 | 12 12 24  0 12  6 | 4 6 4  0 12 12 12  0 0 4 4 | 1  0  0  0 4  6 4 0 0 1 | * * * 2 *
.x .o3.x3.x    ♦  0 24 |  0  0  0 12 24 12 | 0 0 0  0  0  0  0 12 6 8 8 | 0  0  0  0 0  0 0 4 4 2 | * * * * 1
```

```oox3xxo3xxx&#x   → height height(1,2) = 1
height(1,3) = height(2,3) = sqrt(5/8) = 0.790569

o..3o..3o..    | 12  *  * |  2 1  1  2  0 0  0  0  0 | 1 2  2 1  2  1  2  2 0 0  0  0  0 0 0 0 | 1 1 2  1  2  2 1 1 2 0 0 0 0 0 | 1 1 1 2 1 0
.o.3.o.3.o.    |  * 12  * |  0 0  1  0  2 1  2  0  0 | 0 0  2 1  2  0  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  0  2  0 0  2  2  2 | 0 0  0 0  2  2  1  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 | 12 *  *  *  * *  *  *  * | 1 1  1 0  0  0  1  0 0 0  0  0  0 0 0 0 | 1 1 1  0  1  0 1 0 1 0 0 0 0 0 | 1 1 0 1 1 0
... ... x..    |  2  0  0 |  * 6  *  *  * *  *  *  * | 0 2  0 1  0  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 0  2 1  2  0  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 |  * *  * 24  * *  *  *  * | 0 0  0 0  1  1  1  1 0 0  0  0  0 0 0 0 | 0 0 0  1  1  1 1 1 1 0 0 0 0 0 | 0 1 1 1 1 0
... .x. ...    |  0  2  0 |  * *  *  * 12 *  *  *  * | 0 0  1 0  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  0 1  0  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 0  1  0  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  0  1  0  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  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  0 | 4 *  * *  *  *  *  * * *  *  *  * * * * | 1 1 0  0  0  0 1 0 0 0 0 0 0 0 | 1 1 0 0 1 0
... x..3x..    |  6  0  0 |  3 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
... xx. ...&#x |  2  2  0 |  1 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 |  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 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  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.o ...&#x |  2  0  1 |  1 0  0  2  0 0  0  0  0 | * *  * *  *  * 12  * * *  *  *  * * * * | 0 0 0  0  1  0 1 0 1 0 0 0 0 0 | 0 1 0 1 1 0
... ... x.x&#x |  2  0  2 |  0 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  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  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 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  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  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  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  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  0  3 | * *  * *  *  *  *  * * *  *  *  * * * 4 | 0 0 0  0  0  0 0 0 1 0 0 0 1 1 | 0 0 0 1 1 1
---------------+----------+--------------------------+-----------------------------------------+--------------------------------+------------
o..3x..3x..    ♦ 12  0  0 | 12 6  0  0  0 0  0  0  0 | 4 4  0 0  0  0  0  0 0 0  0  0  0 0 0 0 | 1 * *  *  *  * * * * * * * * * | 1 0 0 0 1 0
oo.3xx. ...&#x ♦  3  3  0 |  3 0  3  0  3 0  0  0  0 | 1 0  3 0  0  0  0  0 1 0  0  0  0 0 0 0 | * 4 *  *  *  * * * * * * * * * | 1 1 0 0 0 0
... xx.3xx.&#x ♦  6  6  0 |  3 3  6  0  3 3  0  0  0 | 0 1  3 3  0  0  0  0 0 1  0  0  0 0 0 0 | * * 4  *  *  * * * * * * * * * | 1 0 0 1 0 0
oox ... ...&#x ♦  1  1  2 |  0 0  1  2  0 0  2  1  0 | 0 0  0 0  2  1  0  0 0 0  1  0  0 0 0 0 | * * * 12  *  * * * * * * * * * | 0 1 1 0 0 0
... xxo ...&#x ♦  2  2  1 |  1 0  2  2  1 0  2  0  0 | 0 0  1 0  2  0  1  0 0 0  0  1  0 0 0 0 | * * *  * 12  * * * * * * * * * | 0 1 0 1 0 0
... ... xxx&#x ♦  2  2  2 |  0 1  2  2  0 1  2  0  1 | 0 0  0 1  2  0  0  1 0 0  0  0  1 0 0 0 | * * *  *  * 12 * * * * * * * * | 0 0 1 1 0 0
o.x3x.o ...&#x ♦  3  0  3 |  3 0  0  6  0 0  0  3  0 | 1 0  0 0  0  3  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 |  0 1  0  4  0 0  0  2  2 | 0 0  0 0  0  2  0  2 0 0  0  0  0 0 1 0 | * * *  *  *  * * 6 * * * * * * | 0 0 1 0 1 0
... x.o3x.x&#x ♦  6  0  3 |  3 3  0  6  0 0  0  0  3 | 0 1  0 0  0  0  3  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  0 12 6  0  0  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  0  3 0  6  3  0 | 0 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  0 1  4  2  2 | 0 0  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  0  3 3  6  0  3 | 0 0  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  0 12 12 | 0 0  0 0  0  0  0  0 0 0  0  0  0 4 6 4 | * * *  *  *  * * * * * * * * 1 | 0 0 0 0 1 1
---------------+----------+--------------------------+-----------------------------------------+--------------------------------+------------
oo.3xx.3xx.&#x ♦ 12 12  0 | 12 6 12  0 12 6  0  0  0 | 4 4 12 6  0  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 * * * * *
oox3xxo ...&#x ♦  3  3  3 |  3 0  3  6  3 0  6  3  0 | 1 0  3 0  6  3  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 |  0 1  2  4  0 1  4  2  2 | 0 0  0 1  4  2  0  2 0 0  2  0  2 0 1 0 | 0 0 0  2  0  2 0 1 0 0 0 1 0 0 | * * 6 * * *
... xxo3xxx&#x ♦  6  6  3 |  3 3  6  6  3 3  6  0  3 | 0 1  3 3  6  0  3  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.x3x.o3x.x&#x ♦ 12  0 12 | 12 6  0 24  0 0  0 12 12 | 4 4  0 0  0 12 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  0 12 6 24 12 12 | 0 0  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
```