﻿ copatope
 Acronym copatope Name cope atop tope,coatoe prism,cope-first monostratic cap of ricope Circumradius sqrt(13)/2 = 1.802776 Lace cityin approx. ASCII-art ``` o3x x x3x x x3o x -- x3o3x x (cope) x3x x u3x x x3u x x3x x -- x3x3x x (tope) ``` ``` x4o x o4q x x4o x -- x3o3x x (cope) x4o x u4o x x4q x u4o x x4o x -- x3x3x x (tope) ``` Confer uniform relative: ricope   general polytopal classes: segmentotera   lace simplices

Incidence matrix according to Dynkin symbol

```xx xx3ox3xx&#x   → height = 1/sqrt(2) = 0.707107
(cope || tope

o. o.3o.3o.    | 24  * |  1  2  2  2  0  0  0  0 |  2  2 1  2 1  2  2  1  2  0  0  0 0  0 0 | 1 2 1 1  2  1  2 1  2 1 0 0 0 0 | 1 1 2 1 1 0
.o .o3.o3.o    |  * 48 |  0  0  0  1  1  1  1  1 |  0  0 0  0 0  1  1  1  1  1  1  1 1  1 1 | 0 0 0 0  1  1  1 1  1 1 1 1 1 1 | 0 1 1 1 1 1
---------------+-------+-------------------------+------------------------------------------+---------------------------------+------------
x. .. .. ..    |  2  0 | 12  *  *  *  *  *  *  * |  2  2 0  0 0  2  0  0  0  0  0  0 0  0 0 | 1 2 1 0  2  1  2 0  0 0 0 0 0 0 | 1 1 2 1 0 0
.. x. .. ..    |  2  0 |  * 24  *  *  *  *  *  * |  1  0 1  1 0  0  1  0  0  0  0  0 0  0 0 | 1 1 0 1  1  0  0 1  1 0 0 0 0 0 | 1 1 1 0 1 0
.. .. .. x.    |  2  0 |  *  * 24  *  *  *  *  * |  0  1 0  1 1  0  0  0  1  0  0  0 0  0 0 | 0 1 1 1  0  0  1 0  1 1 0 0 0 0 | 1 0 1 1 1 0
oo oo3oo3oo&#x |  1  1 |  *  *  * 48  *  *  *  * |  0  0 0  0 0  1  1  1  1  0  0  0 0  0 0 | 0 0 0 0  1  1  1 1  1 1 0 0 0 0 | 0 1 1 1 1 0
.x .. .. ..    |  0  2 |  *  *  *  * 24  *  *  * |  0  0 0  0 0  1  0  0  0  1  1  1 0  0 0 | 0 0 0 0  1  1  1 0  0 0 1 1 1 0 | 0 1 1 1 0 1
.. .x .. ..    |  0  2 |  *  *  *  *  * 24  *  * |  0  0 0  0 0  0  1  0  0  1  0  0 1  1 0 | 0 0 0 0  1  0  0 1  1 0 1 1 0 1 | 0 1 1 0 1 1
.. .. .x ..    |  0  2 |  *  *  *  *  *  * 24  * |  0  0 0  0 0  0  0  1  0  0  1  0 1  0 1 | 0 0 0 0  0  1  0 1  0 1 1 0 1 1 | 0 1 0 1 1 1
.. .. .. .x    |  0  2 |  *  *  *  *  *  *  * 24 |  0  0 0  0 0  0  0  0  1  0  0  1 0  1 1 | 0 0 0 0  0  0  1 0  1 1 0 1 1 1 | 0 0 1 1 1 1
---------------+-------+-------------------------+------------------------------------------+---------------------------------+------------
x. x. .. ..    |  4  0 |  2  2  0  0  0  0  0  0 | 12  * *  * *  *  *  *  *  *  *  * *  * * | 1 1 0 0  1  0  0 0  0 0 0 0 0 0 | 1 1 1 0 0 0
x. .. .. x.    |  4  0 |  2  0  2  0  0  0  0  0 |  * 12 *  * *  *  *  *  *  *  *  * *  * * | 0 1 1 0  0  0  1 0  0 0 0 0 0 0 | 1 0 1 1 0 0
.. x.3o. ..    |  3  0 |  0  3  0  0  0  0  0  0 |  *  * 8  * *  *  *  *  *  *  *  * *  * * | 1 0 0 1  0  0  0 1  0 0 0 0 0 0 | 1 1 0 0 1 0
.. x. .. x.    |  4  0 |  0  2  2  0  0  0  0  0 |  *  * * 12 *  *  *  *  *  *  *  * *  * * | 0 1 0 1  0  0  0 0  1 0 0 0 0 0 | 1 0 1 0 1 0
.. .. o.3x.    |  3  0 |  0  0  3  0  0  0  0  0 |  *  * *  * 8  *  *  *  *  *  *  * *  * * | 0 0 1 1  0  0  0 0  0 1 0 0 0 0 | 1 0 0 1 1 0
xx .. .. ..&#x |  2  2 |  1  0  0  2  1  0  0  0 |  *  * *  * * 24  *  *  *  *  *  * *  * * | 0 0 0 0  1  1  1 0  0 0 0 0 0 0 | 0 1 1 1 0 0
.. xx .. ..&#x |  2  2 |  0  1  0  2  0  1  0  0 |  *  * *  * *  * 24  *  *  *  *  * *  * * | 0 0 0 0  1  0  0 1  1 0 0 0 0 0 | 0 1 1 0 1 0
.. .. ox ..&#x |  1  2 |  0  0  0  2  0  0  1  0 |  *  * *  * *  *  * 24  *  *  *  * *  * * | 0 0 0 0  0  1  0 1  0 1 0 0 0 0 | 0 1 0 1 1 0
.. .. .. xx&#x |  2  2 |  0  0  1  2  0  0  0  1 |  *  * *  * *  *  *  * 24  *  *  * *  * * | 0 0 0 0  0  0  1 0  1 1 0 0 0 0 | 0 0 1 1 1 0
.x .x .. ..    |  0  4 |  0  0  0  0  2  2  0  0 |  *  * *  * *  *  *  *  * 12  *  * *  * * | 0 0 0 0  1  0  0 0  0 0 1 1 0 0 | 0 1 1 0 0 1
.x .. .x ..    |  0  4 |  0  0  0  0  2  0  2  0 |  *  * *  * *  *  *  *  *  * 12  * *  * * | 0 0 0 0  0  1  0 0  0 0 1 0 1 0 | 0 1 0 1 0 1
.x .. .. .x    |  0  4 |  0  0  0  0  2  0  0  2 |  *  * *  * *  *  *  *  *  *  * 12 *  * * | 0 0 0 0  0  0  1 0  0 0 0 1 1 0 | 0 0 1 1 0 1
.. .x3.x ..    |  0  6 |  0  0  0  0  0  3  3  0 |  *  * *  * *  *  *  *  *  *  *  * 8  * * | 0 0 0 0  0  0  0 1  0 0 1 0 0 1 | 0 1 0 0 1 1
.. .x .. .x    |  0  4 |  0  0  0  0  0  2  0  2 |  *  * *  * *  *  *  *  *  *  *  * * 12 * | 0 0 0 0  0  0  0 0  1 0 0 1 0 1 | 0 0 1 0 1 1
.. .. .x3.x    |  0  6 |  0  0  0  0  0  0  3  3 |  *  * *  * *  *  *  *  *  *  *  * *  * 8 | 0 0 0 0  0  0  0 0  0 1 0 0 1 1 | 0 0 0 1 1 1
---------------+-------+-------------------------+------------------------------------------+---------------------------------+------------
x. x.3o. ..    ♦  6  0 |  3  6  0  0  0  0  0  0 |  3  0 2  0 0  0  0  0  0  0  0  0 0  0 0 | 4 * * *  *  *  * *  * * * * * * | 1 1 0 0 0 0
x. x. .. x.    ♦  8  0 |  4  4  4  0  0  0  0  0 |  2  2 0  2 0  0  0  0  0  0  0  0 0  0 0 | * 6 * *  *  *  * *  * * * * * * | 1 0 1 0 0 0
x. .. o.3x.    ♦  6  0 |  3  0  6  0  0  0  0  0 |  0  3 0  0 2  0  0  0  0  0  0  0 0  0 0 | * * 4 *  *  *  * *  * * * * * * | 1 0 0 1 0 0
.. x.3o.3x.    ♦ 12  0 |  0 12 12  0  0  0  0  0 |  0  0 4  6 4  0  0  0  0  0  0  0 0  0 0 | * * * 2  *  *  * *  * * * * * * | 1 0 0 0 1 0
xx xx .. ..&#x ♦  4  4 |  2  2  0  4  2  2  0  0 |  1  0 0  0 0  2  2  0  0  1  0  0 0  0 0 | * * * * 12  *  * *  * * * * * * | 0 1 1 0 0 0
xx .. ox ..&#x ♦  2  4 |  1  0  0  4  2  0  2  0 |  0  0 0  0 0  2  0  2  0  0  1  0 0  0 0 | * * * *  * 12  * *  * * * * * * | 0 1 0 1 0 0
xx .. .. xx&#x ♦  4  4 |  2  0  2  4  2  0  0  2 |  0  1 0  0 0  2  0  0  2  0  0  1 0  0 0 | * * * *  *  * 12 *  * * * * * * | 0 0 1 1 0 0
.. xx3ox ..&#x ♦  3  6 |  0  3  0  6  0  3  3  0 |  0  0 1  0 0  0  3  3  0  0  0  0 1  0 0 | * * * *  *  *  * 8  * * * * * * | 0 1 0 0 1 0
.. xx .. xx&#x ♦  4  4 |  0  2  2  4  0  2  0  2 |  0  0 0  1 0  0  2  0  2  0  0  0 0  1 0 | * * * *  *  *  * * 12 * * * * * | 0 0 1 0 1 0
.. .. ox3xx&#x ♦  3  6 |  0  0  3  6  0  0  3  3 |  0  0 0  0 1  0  0  3  3  0  0  0 0  0 1 | * * * *  *  *  * *  * 8 * * * * | 0 0 0 1 1 0
.x .x3.x ..    ♦  0 12 |  0  0  0  0  6  6  6  0 |  0  0 0  0 0  0  0  0  0  3  3  0 2  0 0 | * * * *  *  *  * *  * * 4 * * * | 0 1 0 0 0 1
.x .x .. .x    ♦  0  8 |  0  0  0  0  4  4  0  4 |  0  0 0  0 0  0  0  0  0  2  0  2 0  2 0 | * * * *  *  *  * *  * * * 6 * * | 0 0 1 0 0 1
.x .. .x3.x    ♦  0 12 |  0  0  0  0  6  0  6  6 |  0  0 0  0 0  0  0  0  0  0  3  3 0  0 2 | * * * *  *  *  * *  * * * * 4 * | 0 0 0 1 0 1
.. .x3.x3.x    ♦  0 24 |  0  0  0  0  0 12 12 12 |  0  0 0  0 0  0  0  0  0  0  0  0 4  6 4 | * * * *  *  *  * *  * * * * * 2 | 0 0 0 0 1 1
---------------+-------+-------------------------+------------------------------------------+---------------------------------+------------
x. x.3o.3x.    ♦ 24  0 | 12 24 24  0  0  0  0  0 | 12 12 8 12 8  0  0  0  0  0  0  0 0  0 0 | 4 6 4 2  0  0  0 0  0 0 0 0 0 0 | 1 * * * * *
xx xx3ox ..&#x ♦  6 12 |  3  6  0 12  6  6  6  0 |  3  0 2  0 0  6  6  6  0  3  3  0 2  0 0 | 1 0 0 0  3  3  0 2  0 0 1 0 0 0 | * 4 * * * *
xx xx .. xx&#x ♦  8  8 |  4  4  4  8  4  4  0  4 |  2  2 0  2 0  4  4  0  4  2  0  2 0  2 0 | 0 1 0 0  2  0  2 0  2 0 0 1 0 0 | * * 6 * * *
xx .. ox3xx&#x ♦  6 12 |  3  0  6 12  6  0  6  6 |  0  3 0  0 2  6  0  6  6  0  3  3 0  0 2 | 0 0 1 0  0  3  3 0  0 2 0 0 1 0 | * * * 4 * *
.. xx3ox3xx&#x ♦ 12 24 |  0 12 12 24  0 12 12 12 |  0  0 4  6 4  0 12 12 12  0  0  0 4  6 4 | 0 0 0 1  0  0  0 4  6 4 0 0 0 1 | * * * * 2 *
.x .x3.x3.x    ♦  0 48 |  0  0  0  0 24 24 24 24 |  0  0 0  0 0  0  0  0  0 12 12 12 8 12 8 | 0 0 0 0  0  0  0 0  0 0 4 6 4 2 | * * * * * 1
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