﻿ copatoe
 Acronym copatoe (alt.: coco totric) Name cope atop toe,(co,co,toe)-trigonic Circumradius sqrt(7/2) = 1.870829 Lace cityin approx. ASCII-art ``` o3x4o o3x4o x3x4o ``` Confer uniform relative: spat   related segmentotera: ritarico   general polytopal classes: segmentotera   lace simplices

This polyteron occurs as a wedge of spat. In fact it is a segment of ritarico, which in turn is a segment of spat.

Incidence matrix according to Dynkin symbol

```ox xx3xo3xx&#x   → height = 1/2
(toe || cope)

o. o.3o.3o.    | 24  * |  1  1  1  2  0  0  0 | 1 1 1  1  2  2  2  0  0 0  0 0 | 1  1  1  1 2  2 2 0 0 0 0 | 1 1 1 2 0
.o .o3.o3.o    |  * 24 |  0  0  0  2  1  2  2 | 0 0 0  2  2  1  2  2  2 1  2 1 | 0  2  1  2 1  2 1 1 2 1 1 | 1 2 1 1 1
---------------+-------+----------------------+--------------------------------+---------------------------+----------
.. x. .. ..    |  2  0 | 12  *  *  *  *  *  * | 1 1 0  0  2  0  0  0  0 0  0 0 | 1  1  0  0 2  2 0 0 0 0 0 | 1 1 0 2 0
.. .. x. ..    |  2  0 |  * 12  *  *  *  *  * | 1 0 1  0  0  2  0  0  0 0  0 0 | 1  0  1  0 2  0 2 0 0 0 0 | 1 0 1 2 0
.. .. .. x.    |  2  0 |  *  * 12  *  *  *  * | 0 1 1  0  0  0  2  0  0 0  0 0 | 1  0  0  1 0  2 2 0 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 | 0  1  1  1 1  1 1 0 0 0 0 | 1 1 1 1 0
.x .. .. ..    |  0  2 |  *  *  *  * 12  *  * | 0 0 0  2  0  0  0  2  2 0  0 0 | 0  2  1  2 0  0 0 1 2 1 0 | 1 2 1 0 1
.. .x .. ..    |  0  2 |  *  *  *  *  * 24  * | 0 0 0  0  1  0  0  1  0 1  1 0 | 0  1  0  0 1  1 0 1 1 0 1 | 1 1 0 1 1
.. .. .. .x    |  0  2 |  *  *  *  *  *  * 24 | 0 0 0  0  0  0  1  0  1 0  1 1 | 0  0  0  1 0  1 1 0 1 1 1 | 0 1 1 1 1
---------------+-------+----------------------+--------------------------------+---------------------------+----------
.. x.3x. ..    |  6  0 |  3  3  0  0  0  0  0 | 4 * *  *  *  *  *  *  * *  * * | 1  0  0  0 2  0 0 0 0 0 0 | 1 0 0 2 0
.. x. .. x.    |  4  0 |  2  0  2  0  0  0  0 | * 6 *  *  *  *  *  *  * *  * * | 1  0  0  0 0  2 0 0 0 0 0 | 0 1 0 2 0
.. .. x.3x.    |  6  0 |  0  3  3  0  0  0  0 | * * 4  *  *  *  *  *  * *  * * | 1  0  0  0 0  0 2 0 0 0 0 | 0 0 1 2 0
ox .. .. ..&#x |  1  2 |  0  0  0  2  1  0  0 | * * * 24  *  *  *  *  * *  * * | 0  1  1  1 0  0 0 0 0 0 0 | 1 1 1 0 0
.. xx .. ..&#x |  2  2 |  1  0  0  2  0  1  0 | * * *  * 24  *  *  *  * *  * * | 0  1  0  0 1  1 0 0 0 0 0 | 1 1 0 1 0
.. .. xo ..&#x |  2  1 |  0  1  0  2  0  0  0 | * * *  *  * 24  *  *  * *  * * | 0  0  1  0 1  0 1 0 0 0 0 | 1 0 1 1 0
.. .. .. xx&#x |  2  2 |  0  0  1  2  0  0  1 | * * *  *  *  * 24  *  * *  * * | 0  0  0  1 0  1 1 0 0 0 0 | 0 1 1 1 0
.x .x .. ..    |  0  4 |  0  0  0  0  2  2  0 | * * *  *  *  *  * 12  * *  * * | 0  1  0  0 0  0 0 1 1 0 0 | 1 1 0 0 1
.x .. .. .x    |  0  4 |  0  0  0  0  2  0  2 | * * *  *  *  *  *  * 12 *  * * | 0  0  0  1 0  0 0 0 1 1 0 | 0 1 1 0 1
.. .x3.o ..    |  0  3 |  0  0  0  0  0  3  0 | * * *  *  *  *  *  *  * 8  * * | 0  0  0  0 1  0 0 1 0 0 1 | 1 0 0 1 1
.. .x .. .x    |  0  4 |  0  0  0  0  0  2  2 | * * *  *  *  *  *  *  * * 12 * | 0  0  0  0 0  1 0 0 1 0 1 | 0 1 0 1 1
.. .. .o3.x    |  0  3 |  0  0  0  0  0  0  3 | * * *  *  *  *  *  *  * *  * 8 | 0  0  0  0 0  0 1 0 0 1 1 | 0 0 1 1 1
---------------+-------+----------------------+--------------------------------+---------------------------+----------
.. x.3x.3x.    ♦ 24  0 | 12 12 12  0  0  0  0 | 4 6 4  0  0  0  0  0  0 0  0 0 | 1  *  *  * *  * * * * * * | 0 0 0 2 0
ox xx .. ..&#x ♦  2  4 |  1  0  0  4  2  2  0 | 0 0 0  2  2  0  0  1  0 0  0 0 | * 12  *  * *  * * * * * * | 1 1 0 0 0
ox .. xo ..&#x ♦  2  2 |  0  1  0  4  1  0  0 | 0 0 0  2  0  2  0  0  0 0  0 0 | *  * 12  * *  * * * * * * | 1 0 1 0 0
ox .. .. xx&#x ♦  2  4 |  0  0  1  4  2  0  2 | 0 0 0  2  0  0  2  0  1 0  0 0 | *  *  * 12 *  * * * * * * | 0 1 1 0 0
.. xx3xo ..&#x ♦  6  3 |  3  3  0  6  0  3  0 | 1 0 0  0  3  3  0  0  0 1  0 0 | *  *  *  * 8  * * * * * * | 1 0 0 1 0
.. xx .. xx&#x ♦  4  4 |  2  0  2  4  0  2  2 | 0 1 0  0  2  0  2  0  0 0  1 0 | *  *  *  * * 12 * * * * * | 0 1 0 1 0
.. .. xo3xx&#x ♦  6  3 |  0  3  3  6  0  0  3 | 0 0 1  0  0  3  3  0  0 0  0 1 | *  *  *  * *  * 8 * * * * | 0 0 1 1 0
.x .x3.o ..    ♦  0  6 |  0  0  0  0  3  6  0 | 0 0 0  0  0  0  0  3  0 2  0 0 | *  *  *  * *  * * 4 * * * | 1 0 0 0 1
.x .x .. .x    ♦  0  8 |  0  0  0  0  4  4  4 | 0 0 0  0  0  0  0  2  2 0  2 0 | *  *  *  * *  * * * 6 * * | 0 1 0 0 1
.x .. .o3.x    ♦  0  6 |  0  0  0  0  3  0  6 | 0 0 0  0  0  0  0  0  3 0  0 2 | *  *  *  * *  * * * * 4 * | 0 0 1 0 1
.. .x3.o3.x    ♦  0 12 |  0  0  0  0  0 12 12 | 0 0 0  0  0  0  0  0  0 4  6 4 | *  *  *  * *  * * * * * 2 | 0 0 0 1 1
---------------+-------+----------------------+--------------------------------+---------------------------+----------
ox xx3xo ..&#x ♦  6  6 |  3  3  0 12  3  6  0 | 1 0 0  6  6  6  0  3  0 2  0 0 | 0  3  3  0 2  0 0 1 0 0 0 | 4 * * * *
ox xx .. xx&#x ♦  4  8 |  2  0  2  8  4  4  4 | 0 1 0  4  4  0  4  2  2 0  2 0 | 0  2  0  2 0  2 0 0 1 0 0 | * 6 * * *
ox .. xo3xx&#x ♦  6  6 |  0  3  3 12  3  0  6 | 0 0 1  6  0  6  6  0  3 0  0 2 | 0  0  3  3 0  0 2 0 0 1 0 | * * 4 * *
.. xx3xo3xx&#x ♦ 24 12 | 12 12 12 24  0 12 12 | 4 6 4  0 12 12 12  0  0 4  6 4 | 1  0  0  0 4  6 4 0 0 0 1 | * * * 2 *
.x .x3.o3.x    ♦  0 24 |  0  0  0  0 12 24 24 | 0 0 0  0  0  0  0 12 12 8 12 8 | 0  0  0  0 0  0 0 4 6 4 2 | * * * * 1
```

```xxx3oox3xxx&#x   → height(1,2) = 1
height(1,3) = height(2,3) = 1/sqrt(2) = 0.707107

o..3o..3o..    | 12  *  * |  2  2  1  2  0  0  0  0  0  0 | 1 2 1  2  2  2  2  1  2 0 0 0  0  0  0 0 0 0 | 1 1 2 1  2  1  2 1 2 1 0 0 0 0 0 | 1 1 2 1 1 0
.o.3.o.3.o.    |  * 12  * |  0  0  1  0  2  2  2  0  0  0 | 0 0 0  2  2  2  0  0  0 1 2 1  2  1  2 0 0 0 | 0 1 2 1  2  1  2 0 0 0 1 1 2 1 0 | 1 1 2 1 0 1
..o3..o3..o    |  *  * 24 |  0  0  0  1  0  0  1  1  1  1 | 0 0 0  0  0  1  1  1  1 0 0 0  1  1  1 1 1 1 | 0 0 0 0  1  1  1 1 1 1 0 1 1 1 1 | 0 1 1 1 1 1
---------------+----------+-------------------------------+----------------------------------------------+----------------------------------+------------
x.. ... ...    |  2  0  0 | 12  *  *  *  *  *  *  *  *  * | 1 1 0  1  0  0  1  0  0 0 0 0  0  0  0 0 0 0 | 1 1 1 0  1  0  0 1 1 0 0 0 0 0 0 | 1 1 1 0 1 0
... ... x..    |  2  0  0 |  * 12  *  *  *  *  *  *  *  * | 0 1 1  0  1  0  0  0  1 0 0 0  0  0  0 0 0 0 | 1 0 1 1  0  0  1 0 1 1 0 0 0 0 0 | 1 0 1 1 1 0
oo.3oo.3oo.&#x |  1  1  0 |  *  * 12  *  *  *  *  *  *  * | 0 0 0  2  2  2  0  0  0 0 0 0  0  0  0 0 0 0 | 0 1 2 1  2  1  2 0 0 0 0 0 0 0 0 | 1 1 2 1 0 0
o.o3o.o3o.o&#x |  1  0  1 |  *  *  * 24  *  *  *  *  *  * | 0 0 0  0  0  1  1  1  1 0 0 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 0  1  0  0  0  0  0 1 1 0  1  0  0 0 0 0 | 0 1 1 0  1  0  0 0 0 0 1 1 1 0 0 | 1 1 1 0 0 1
... ... .x.    |  0  2  0 |  *  *  *  *  * 12  *  *  *  * | 0 0 0  0  1  0  0  0  0 0 1 1  0  0  1 0 0 0 | 0 0 1 1  0  0  1 0 0 0 1 0 1 1 0 | 1 0 1 1 0 1
.oo3.oo3.oo&#x |  0  1  1 |  *  *  *  *  *  * 24  *  *  * | 0 0 0  0  0  1  0  0  0 0 0 0  1  1  1 0 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  0  1  0  0 0 0 0  1  0  0 1 1 0 | 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  0  1  0 1 0 1 | 0 0 0 0  0  1  0 1 0 1 0 1 0 1 1 | 0 1 0 1 1 1
... ... ..x    |  0  0  2 |  *  *  *  *  *  *  *  *  * 12 | 0 0 0  0  0  0  0  0  1 0 0 0  0  0  1 0 1 1 | 0 0 0 0  0  0  1 0 1 1 0 0 1 1 1 | 0 0 1 1 1 1
---------------+----------+-------------------------------+----------------------------------------------+----------------------------------+------------
x..3o.. ...    |  3  0  0 |  3  0  0  0  0  0  0  0  0  0 | 4 * *  *  *  *  *  *  * * * *  *  *  * * * * | 1 1 0 0  0  0  0 1 0 0 0 0 0 0 0 | 1 1 0 0 1 0
x.. ... x..    |  4  0  0 |  2  2  0  0  0  0  0  0  0  0 | * 6 *  *  *  *  *  *  * * * *  *  *  * * * * | 1 0 1 0  0  0  0 0 1 0 0 0 0 0 0 | 1 0 1 0 1 0
... o..3x..    |  3  0  0 |  0  3  0  0  0  0  0  0  0  0 | * * 4  *  *  *  *  *  * * * *  *  *  * * * * | 1 0 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  0 | * * * 12  *  *  *  *  * * * *  *  *  * * * * | 0 1 1 0  1  0  0 0 0 0 0 0 0 0 0 | 1 1 1 0 0 0
... ... xx.&#x |  2  2  0 |  0  1  2  0  0  1  0  0  0  0 | * * *  * 12  *  *  *  * * * *  *  *  * * * * | 0 0 1 1  0  0  1 0 0 0 0 0 0 0 0 | 1 0 1 1 0 0
ooo3ooo3ooo&#x |  1  1  1 |  0  0  1  1  0  0  1  0  0  0 | * * *  *  * 24  *  *  * * * *  *  *  * * * * | 0 0 0 0  1  1  1 0 0 0 0 0 0 0 0 | 0 1 1 1 0 0
x.x ... ...&#x |  2  0  2 |  1  0  0  2  0  0  0  1  0  0 | * * *  *  *  * 12  *  * * * *  *  *  * * * * | 0 0 0 0  1  0  0 1 1 0 0 0 0 0 0 | 0 1 1 0 1 0
... o.x ...&#x |  1  0  2 |  0  0  0  2  0  0  0  0  1  0 | * * *  *  *  *  * 12  * * * *  *  *  * * * * | 0 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  0  1 | * * *  *  *  *  *  * 12 * * *  *  *  * * * * | 0 0 0 0  0  0  1 0 1 1 0 0 0 0 0 | 0 0 1 1 1 0
.x.3.o. ...    |  0  3  0 |  0  0  0  0  3  0  0  0  0  0 | * * *  *  *  *  *  *  * 4 * *  *  *  * * * * | 0 1 0 0  0  0  0 0 0 0 1 1 0 0 0 | 1 1 0 0 0 1
.x. ... .x.    |  0  4  0 |  0  0  0  0  2  2  0  0  0  0 | * * *  *  *  *  *  *  * * 6 *  *  *  * * * * | 0 0 1 0  0  0  0 0 0 0 1 0 1 0 0 | 1 0 1 0 0 1
... .o.3.x.    |  0  3  0 |  0  0  0  0  0  3  0  0  0  0 | * * *  *  *  *  *  *  * * * 4  *  *  * * * * | 0 0 0 1  0  0  0 0 0 0 1 0 0 1 0 | 1 0 0 1 0 1
.xx ... ...&#x |  0  2  2 |  0  0  0  0  1  0  2  1  0  0 | * * *  *  *  *  *  *  * * * * 12  *  * * * * | 0 0 0 0  1  0  0 0 0 0 0 1 1 0 0 | 0 1 1 0 0 1
... .ox ...&#x |  0  1  2 |  0  0  0  0  0  0  2  0  1  0 | * * *  *  *  *  *  *  * * * *  * 12  * * * * | 0 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  0  1 | * * *  *  *  *  *  *  * * * *  *  * 12 * * * | 0 0 0 0  0  0  1 0 0 0 0 0 1 1 0 | 0 0 1 1 0 1
..x3..x ...    |  0  0  6 |  0  0  0  0  0  0  0  3  3  0 | * * *  *  *  *  *  *  * * * *  *  *  * 4 * * | 0 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  0  2 | * * *  *  *  *  *  *  * * * *  *  *  * * 6 * | 0 0 0 0  0  0  0 0 1 0 0 0 1 0 1 | 0 0 1 0 1 1
... ..x3..x    |  0  0  6 |  0  0  0  0  0  0  0  0  3  3 | * * *  *  *  *  *  *  * * * *  *  *  * * * 4 | 0 0 0 0  0  0  0 0 0 1 0 0 0 1 1 | 0 0 0 1 1 1
---------------+----------+-------------------------------+----------------------------------------------+----------------------------------+------------
x..3o..3x..    ♦ 12  0  0 | 12 12  0  0  0  0  0  0  0  0 | 4 6 4  0  0  0  0  0  0 0 0 0  0  0  0 0 0 0 | 1 * * *  *  *  * * * * * * * * * | 1 0 0 0 1 0
xx.3oo. ...&#x ♦  3  3  0 |  3  0  3  0  3  0  0  0  0  0 | 1 0 0  3  0  0  0  0  0 1 0 0  0  0  0 0 0 0 | * 4 * *  *  *  * * * * * * * * * | 1 1 0 0 0 0
xx. ... xx.&#x ♦  4  4  0 |  2  2  4  0  2  2  0  0  0  0 | 0 1 0  2  2  0  0  0  0 0 1 0  0  0  0 0 0 0 | * * 6 *  *  *  * * * * * * * * * | 1 0 1 0 0 0
... oo.3xx.&#x ♦  3  3  0 |  0  3  3  0  0  3  0  0  0  0 | 0 0 1  0  3  0  0  0  0 0 0 1  0  0  0 0 0 0 | * * * 4  *  *  * * * * * * * * * | 1 0 0 1 0 0
xxx ... ...&#x ♦  2  2  2 |  1  0  2  2  1  0  2  1  0  0 | 0 0 0  1  0  2  1  0  0 0 0 0  1  0  0 0 0 0 | * * * * 12  *  * * * * * * * * * | 0 1 1 0 0 0
... oox ...&#x ♦  1  1  2 |  0  0  1  2  0  0  2  0  1  0 | 0 0 0  0  0  2  0  1  0 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  0  1 | 0 0 0  0  1  2  0  0  1 0 0 0  0  0  1 0 0 0 | * * * *  *  * 12 * * * * * * * * | 0 0 1 1 0 0
x.x3o.x ...&#x ♦  3  0  6 |  3  0  0  6  0  0  0  3  3  0 | 1 0 0  0  0  0  3  3  0 0 0 0  0  0  0 1 0 0 | * * * *  *  *  * 4 * * * * * * * | 0 1 0 0 1 0
x.x ... x.x&#x ♦  4  0  4 |  2  2  0  4  0  0  0  2  0  2 | 0 1 0  0  0  0  2  0  2 0 0 0  0  0  0 0 1 0 | * * * *  *  *  * * 6 * * * * * * | 0 0 1 0 1 0
... o.x3x.x&#x ♦  3  0  6 |  0  3  0  6  0  0  0  0  3  3 | 0 0 1  0  0  0  0  3  3 0 0 0  0  0  0 0 0 1 | * * * *  *  *  * * * 4 * * * * * | 0 0 0 1 1 0
.x.3.o.3.x.    ♦  0 12  0 |  0  0  0  0 12 12  0  0  0  0 | 0 0 0  0  0  0  0  0  0 4 6 4  0  0  0 0 0 0 | * * * *  *  *  * * * * 1 * * * * | 1 0 0 0 0 1
.xx3.ox ...&#x ♦  0  3  6 |  0  0  0  0  3  0  6  3  3  0 | 0 0 0  0  0  0  0  0  0 1 0 0  3  3  0 1 0 0 | * * * *  *  *  * * * * * 4 * * * | 0 1 0 0 0 1
.xx ... .xx&#x ♦  0  4  4 |  0  0  0  0  2  2  4  2  0  2 | 0 0 0  0  0  0  0  0  0 0 1 0  2  0  2 0 1 0 | * * * *  *  *  * * * * * * 6 * * | 0 0 1 0 0 1
... .ox3.xx&#x ♦  0  3  6 |  0  0  0  0  0  3  6  0  3  3 | 0 0 0  0  0  0  0  0  0 0 0 1  0  3  3 0 0 1 | * * * *  *  *  * * * * * * * 4 * | 0 0 0 1 0 1
..x3..x3..x    ♦  0  0 24 |  0  0  0  0  0  0  0 12 12 12 | 0 0 0  0  0  0  0  0  0 0 0 0  0  0  0 4 6 4 | * * * *  *  *  * * * * * * * * 1 | 0 0 0 0 1 1
---------------+----------+-------------------------------+----------------------------------------------+----------------------------------+------------
xx.3oo.3xx.&#x ♦ 12 12  0 | 12 12 12  0 12 12  0  0  0  0 | 4 6 4 12 12  0  0  0  0 4 6 4  0  0  0 0 0 0 | 1 4 6 4  0  0  0 0 0 0 1 0 0 0 0 | 1 * * * * *
xxx3oox ...&#x ♦  3  3  6 |  3  0  3  6  3  0  6  3  3  0 | 1 0 0  3  0  6  3  3  0 1 0 0  3  3  0 1 0 0 | 0 1 0 0  3  3  0 1 0 0 0 1 0 0 0 | * 4 * * * *
xxx ... xxx&#x ♦  4  4  4 |  2  2  4  4  2  2  4  2  0  2 | 0 1 0  2  2  4  2  0  2 0 1 0  2  0  2 0 1 0 | 0 0 1 0  2  0  2 0 1 0 0 0 1 0 0 | * * 6 * * *
... oox3xxx&#x ♦  3  3  6 |  0  3  3  6  0  3  6  0  3  3 | 0 0 1  0  3  6  0  3  3 0 0 1  0  3  3 0 0 1 | 0 0 0 1  0  3  3 0 0 1 0 0 0 1 0 | * * * 4 * *
x.x3o.x3x.x&#x ♦ 12  0 24 | 12 12  0 24  0  0  0 12 12 12 | 4 6 4  0  0  0 12 12 12 0 0 0  0  0  0 4 6 4 | 1 0 0 0  0  0  0 4 6 4 0 0 0 0 1 | * * * * 1 *
.xx3.ox3.xx&#x ♦  0 12 24 |  0  0  0  0 12 12 24 12 12 12 | 0 0 0  0  0  0  0  0  0 4 6 4 12 12 12 4 6 4 | 0 0 0 0  0  0  0 0 0 0 1 4 6 4 1 | * * * * * 1
```