﻿ hexippy
 Acronym hexippy Name hexip pyramid,vertex pyramid of rag Circumradius 1 Lace cityin approx. ASCII-art ``` o where: o = o3o3o4o (point) h h h = x3o3o4o (hex) ``` Confer uniform relative: rag   general polytopal classes: segmentopeta

Incidence matrix according to Dynkin symbol

```ox3oo3oo4oo ox&#x   → height = 1/2
(pt || hexip)

o.3o.3o.4o. o.    | 1  * ♦ 16  0 0 | 48 8  0  0 | 64 24  0  0 | 32 32 0  0 | 2 16 0
.o3.o3.o4.o .o    | * 16 |  1  6 1 |  6 3 12  6 | 12  6  8 12 |  8 12 1  8 | 1  8 1
------------------+------+---------+------------+-------------+------------+-------
oo3oo3oo4oo oo&#x | 1  1 | 16  * * |  6 1  0  0 | 12  6  0  0 |  8 12 0  0 | 1  8 0
.x .. .. .. ..    | 0  2 |  * 48 * |  1 0  4  1 |  4  1  4  4 |  4  4 1  4 | 1  4 1
.. .. .. .. .x    | 0  2 |  *  * 8 |  0 1  0  6 |  0  6  0 12 |  0 12 0  8 | 0  8 1
------------------+------+---------+------------+-------------+------------+-------
ox .. .. .. ..&#x | 1  2 |  2  1 0 | 48 *  *  * |  4  1  0  0 |  4  4 0  0 | 1  4 0
.. .. .. .. ox&#x | 1  2 |  2  0 1 |  * 8  *  * ♦  0  6  0  0 |  0 12 0  0 | 0  8 0
.x3.o .. .. ..    | 0  3 |  0  3 0 |  * * 64  * |  1  0  2  1 |  2  1 1  2 | 1  2 1
.x .. .. .. .x    | 0  4 |  0  2 2 |  * *  * 24 |  0  1  0  4 |  0  4 0  4 | 0  4 1
------------------+------+---------+------------+-------------+------------+-------
ox3oo .. .. ..&#x ♦ 1  3 |  3  3 0 |  3 0  1  0 | 64  *  *  * |  2  1 0  0 | 1  2 0
ox .. .. .. ox&#x ♦ 1  4 |  4  2 2 |  2 2  0  1 |  * 24  *  * |  0  4 0  0 | 0  4 0
.x3.o3.o .. ..    ♦ 0  4 |  0  6 0 |  0 0  4  0 |  *  * 32  * |  1  0 1  1 | 1  1 1
.x3.o .. .. .x    ♦ 0  6 |  0  6 3 |  0 0  2  3 |  *  *  * 32 |  0  1 0  2 | 0  2 1
------------------+------+---------+------------+-------------+------------+-------
ox3oo3oo .. ..&#x ♦ 1  4 |  4  6 0 |  6 0  4  0 |  4  0  1  0 | 32  * *  * | 1  1 0
ox3oo .. .. ox&#x ♦ 1  6 |  6  6 3 |  6 3  2  3 |  2  3  0  1 |  * 32 *  * | 0  2 0
.x3.o3.o4.o ..    ♦ 0  8 |  0 24 0 |  0 0 32  0 |  0  0 16  0 |  *  * 2  * | 1  0 1
.x3.o3.o .. .x    ♦ 0  8 |  0 12 4 |  0 0  8  6 |  0  0  2  4 |  *  * * 16 | 0  1 1
------------------+------+---------+------------+-------------+------------+-------
ox3oo3oo4oo ..&#x ♦ 1  8 |  8 24 0 | 24 0 32  0 | 32  0 16  0 | 16  0 1  0 | 2  * *
ox3oo3oo .. ox&#x ♦ 1  8 |  8 12 4 | 12 4  8  6 |  8  6  2  4 |  2  4 0  1 | * 16 *
.x3.o3.o4.o .x    ♦ 0 16 |  0 48 8 |  0 0 64 24 |  0  0 32 32 |  0  0 2 16 | *  * 1
```

```xoo3ooo3oox xox&#x   → height(1,2) = height(2,3) = sqrt(3/8) = 0.612372
height(1,3) = 1/sqrt(2) = 0.707107

o..3o..3o.. o..    | 8 * * |  3 1 1  3 0  0 0 | 3 3  3 1  6  3  3  3  0 0 0 0 | 1 3 3 3 3  3  6 1  3  6  3  3 0 0 0 0 | 1 1 3 1 3 3 1 3  3  6 1  3 0 0 0 | 1 1 1 3 3 1 0
.o.3.o.3.o. .o.    | * 1 * ♦  0 0 8  0 8  0 0 | 0 0 12 4  0  0  0 24 12 4 0 0 | 0 0 8 6 0  0  0 0  0 24 24 12 8 6 0 0 | 0 2 4 0 0 0 0 8 12 12 8 12 2 4 0 | 1 0 2 4 6 4 1
..o3..o3..o ..o    | * * 8 |  0 0 0  3 1  3 1 | 0 0  0 0  3  6  3  3  3 1 3 3 | 0 0 0 0 1  3  3 3  6  3  6  3 3 3 1 3 | 0 0 0 1 1 3 3 1  3  3 3  6 1 3 1 | 0 1 1 1 3 3 1
-------------------+-------+------------------+-------------------------------+---------------------------------------+----------------------------------+--------------
x.. ... ... ...    | 2 0 0 | 12 * *  * *  * * | 2 1  1 0  2  0  0  0  0 0 0 0 | 1 2 2 1 2  1  2 0  0  2  0  0 0 0 0 0 | 1 1 2 1 2 1 0 2  1  2 0  0 0 0 0 | 1 1 1 2 1 0 0
... ... ... x..    | 2 0 0 |  * 4 *  * *  * * | 0 3  0 1  0  0  3  0  0 0 0 0 | 0 3 0 3 0  0  6 0  3  0  0  3 0 0 0 0 | 1 0 3 0 3 3 1 0  0  6 0  3 0 0 0 | 1 1 0 3 3 1 0
oo.3oo.3oo. oo.&#x | 1 1 0 |  * * 8  * *  * * | 0 0  3 1  0  0  0  3  0 0 0 0 | 0 0 3 3 0  0  0 0  0  6  3  3 0 0 0 0 | 0 1 3 0 0 0 0 3  3  6 1  3 0 0 0 | 1 0 1 3 3 1 0
o.o3o.o3o.o o.o&#x | 1 0 1 |  * * * 24 *  * * | 0 0  0 0  2  2  1  1  0 0 0 0 | 0 0 0 0 1  2  2 1  2  2  2  1 0 0 0 0 | 0 0 0 1 1 2 1 1  2  2 1  2 0 0 0 | 0 1 1 1 2 1 0
.oo3.oo3.oo .oo&#x | 0 1 1 |  * * *  * 8  * * | 0 0  0 0  0  0  0  3  3 1 0 0 | 0 0 0 0 0  0  0 0  0  3  6  3 3 3 0 0 | 0 0 0 0 0 0 0 1  3  3 3  6 1 3 0 | 0 0 1 1 3 3 1
... ... ..x ...    | 0 0 2 |  * * *  * * 12 * | 0 0  0 0  0  2  0  0  1 0 2 1 | 0 0 0 0 0  1  0 2  2  0  2  0 2 1 1 2 | 0 0 0 1 0 1 2 0  1  0 2  2 1 2 1 | 0 1 1 0 1 2 1
... ... ... ..x    | 0 0 2 |  * * *  * *  * 4 | 0 0  0 0  0  0  3  0  0 1 0 3 | 0 0 0 0 0  0  3 0  6  0  0  3 0 3 0 3 | 0 0 0 0 1 3 3 0  0  3 0  6 0 3 1 | 0 1 0 1 3 3 1
-------------------+-------+------------------+-------------------------------+---------------------------------------+----------------------------------+--------------
x..3o.. ... ...    | 3 0 0 |  3 0 0  0 0  0 0 | 8 *  * *  *  *  *  *  * * * * | 1 1 1 0 1  0  0 0  0  0  0  0 0 0 0 0 | 1 1 1 1 1 0 0 1  0  0 0  0 0 0 0 | 1 1 1 1 0 0 0
x.. ... ... x..    | 4 0 0 |  2 2 0  0 0  0 0 | * 6  * *  *  *  *  *  * * * * | 0 2 0 1 0  0  2 0  0  0  0  0 0 0 0 0 | 1 0 2 0 2 1 0 0  0  2 0  0 0 0 0 | 1 1 0 2 1 0 0
xo. ... ... ...&#x | 2 1 0 |  1 0 2  0 0  0 0 | * * 12 *  *  *  *  *  * * * * | 0 0 2 1 0  0  0 0  0  2  0  0 0 0 0 0 | 0 1 2 0 0 0 0 2  1  2 0  0 0 0 0 | 1 0 1 2 1 0 0
... ... ... xo.&#x | 2 1 0 |  0 1 2  0 0  0 0 | * *  * 4  *  *  *  *  * * * * ♦ 0 0 0 3 0  0  0 0  0  0  0  3 0 0 0 0 | 0 0 3 0 0 0 0 0  0  6 0  3 0 0 0 | 1 0 0 3 3 1 0
x.o ... ... ...&#x | 2 0 1 |  1 0 0  2 0  0 0 | * *  * * 24  *  *  *  * * * * | 0 0 0 0 1  1  1 0  0  1  0  0 0 0 0 0 | 0 0 0 1 1 1 0 1  1  1 0  0 0 0 0 | 0 1 1 1 1 0 0
... ... o.x ...&#x | 1 0 2 |  0 0 0  2 0  1 0 | * *  * *  * 24  *  *  * * * * | 0 0 0 0 0  1  0 1  1  0  1  0 0 0 0 0 | 0 0 0 1 0 1 1 0  1  0 1  1 0 0 0 | 0 1 1 0 1 1 0
... ... ... x.x&#x | 2 0 2 |  0 1 0  2 0  0 1 | * *  * *  *  * 12  *  * * * * | 0 0 0 0 0  0  2 0  2  0  0  1 0 0 0 0 | 0 0 0 0 1 2 1 0  0  2 0  2 0 0 0 | 0 1 0 1 2 1 0
ooo3ooo3ooo ooo&#x | 1 1 1 |  0 0 1  1 1  0 0 | * *  * *  *  *  * 24  * * * * | 0 0 0 0 0  0  0 0  0  2  2  1 0 0 0 0 | 0 0 0 0 0 0 0 1  2  2 1  2 0 0 0 | 0 0 1 1 2 1 0
... ... .ox ...&#x | 0 1 2 |  0 0 0  0 2  1 0 | * *  * *  *  *  *  * 12 * * * | 0 0 0 0 0  0  0 0  0  0  2  0 2 1 0 0 | 0 0 0 0 0 0 0 0  1  0 2  2 1 2 0 | 0 0 1 0 1 2 1
... ... ... .ox&#x | 0 1 2 |  0 0 0  0 2  0 1 | * *  * *  *  *  *  *  * 4 * * ♦ 0 0 0 0 0  0  0 0  0  0  0  3 0 3 0 0 | 0 0 0 0 0 0 0 0  0  3 0  6 0 3 0 | 0 0 0 1 3 3 1
... ..o3..x ...    | 0 0 3 |  0 0 0  0 0  3 0 | * *  * *  *  *  *  *  * * 8 * | 0 0 0 0 0  0  0 1  0  0  0  0 1 0 1 1 | 0 0 0 1 0 0 1 0  0  0 1  0 1 1 1 | 0 1 1 0 0 1 1
... ... ..x ..x    | 0 0 4 |  0 0 0  0 0  2 2 | * *  * *  *  *  *  *  * * * 6 | 0 0 0 0 0  0  0 0  2  0  0  0 0 2 0 2 | 0 0 0 0 0 1 2 0  0  0 0  2 0 2 1 | 0 1 0 0 1 2 1
-------------------+-------+------------------+-------------------------------+---------------------------------------+----------------------------------+--------------
x..3o..3o.. ...    ♦ 4 0 0 |  6 0 0  0 0  0 0 | 4 0  0 0  0  0  0  0  0 0 0 0 | 2 * * * *  *  * *  *  *  *  * * * * * | 1 1 0 1 0 0 0 0  0  0 0  0 0 0 0 | 1 1 1 0 0 0 0
x..3o.. ... x..    ♦ 6 0 0 |  6 3 0  0 0  0 0 | 2 3  0 0  0  0  0  0  0 0 0 0 | * 4 * * *  *  * *  *  *  *  * * * * * | 1 0 1 0 1 0 0 0  0  0 0  0 0 0 0 | 1 1 0 1 0 0 0
xo.3oo. ... ...&#x ♦ 3 1 0 |  3 0 3  0 0  0 0 | 1 0  3 0  0  0  0  0  0 0 0 0 | * * 8 * *  *  * *  *  *  *  * * * * * | 0 1 1 0 0 0 0 1  0  0 0  0 0 0 0 | 1 0 1 1 0 0 0
xo. ... ... xo.&#x ♦ 4 1 0 |  2 2 4  0 0  0 0 | 0 1  2 2  0  0  0  0  0 0 0 0 | * * * 6 *  *  * *  *  *  *  * * * * * | 0 0 2 0 0 0 0 0  0  2 0  0 0 0 0 | 1 0 0 2 1 0 0
x.o3o.o ... ...&#x ♦ 3 0 1 |  3 0 0  3 0  0 0 | 1 0  0 0  3  0  0  0  0 0 0 0 | * * * * 8  *  * *  *  *  *  * * * * * | 0 0 0 1 1 0 0 1  0  0 0  0 0 0 0 | 0 1 1 1 0 0 0
x.o ... o.x ...&#x ♦ 2 0 2 |  1 0 0  4 0  1 0 | 0 0  0 0  2  2  0  0  0 0 0 0 | * * * * * 12  * *  *  *  *  * * * * * | 0 0 0 1 0 1 0 0  1  0 0  0 0 0 0 | 0 1 1 0 1 0 0
x.o ... ... x.x&#x ♦ 4 0 2 |  2 2 0  4 0  0 1 | 0 1  0 0  2  0  2  0  0 0 0 0 | * * * * *  * 12 *  *  *  *  * * * * * | 0 0 0 0 1 1 0 0  0  1 0  0 0 0 0 | 0 1 0 1 1 0 0
... o.o3o.x ...&#x ♦ 1 0 3 |  0 0 0  3 0  3 0 | 0 0  0 0  0  3  0  0  0 0 1 0 | * * * * *  *  * 8  *  *  *  * * * * * | 0 0 0 1 0 0 1 0  0  0 1  0 0 0 0 | 0 1 1 0 0 1 0
... ... o.x x.x&#x ♦ 2 0 4 |  0 1 0  4 0  2 2 | 0 0  0 0  0  2  2  0  0 0 0 1 | * * * * *  *  * * 12  *  *  * * * * * | 0 0 0 0 0 1 1 0  0  0 0  1 0 0 0 | 0 1 0 0 1 1 0
xoo ... ... ...&#x ♦ 2 1 1 |  1 0 2  2 1  0 0 | 0 0  1 0  1  0  0  2  0 0 0 0 | * * * * *  *  * *  * 24  *  * * * * * | 0 0 0 0 0 0 0 1  1  1 0  0 0 0 0 | 0 0 1 1 1 0 0
... ... oox ...&#x ♦ 1 1 2 |  0 0 1  2 2  1 0 | 0 0  0 0  0  1  0  2  1 0 0 0 | * * * * *  *  * *  *  * 24  * * * * * | 0 0 0 0 0 0 0 0  1  0 1  1 0 0 0 | 0 0 1 0 1 1 0
... ... ... xox&#x ♦ 2 1 2 |  0 1 2  2 2  0 1 | 0 0  0 1  0  0  1  2  0 1 0 0 | * * * * *  *  * *  *  *  * 12 * * * * | 0 0 0 0 0 0 0 0  0  2 0  2 0 0 0 | 0 0 0 1 2 1 0
... .oo3.ox ...&#x ♦ 0 1 3 |  0 0 0  0 3  3 0 | 0 0  0 0  0  0  0  0  3 0 1 0 | * * * * *  *  * *  *  *  *  * 8 * * * | 0 0 0 0 0 0 0 0  0  0 1  0 1 1 0 | 0 0 1 0 0 1 1
... ... .ox .ox&#x ♦ 0 1 4 |  0 0 0  0 4  2 2 | 0 0  0 0  0  0  0  0  2 2 0 1 | * * * * *  *  * *  *  *  *  * * 6 * * | 0 0 0 0 0 0 0 0  0  0 0  2 0 2 0 | 0 0 0 0 1 2 1
..o3..o3..x ...    ♦ 0 0 4 |  0 0 0  0 0  6 0 | 0 0  0 0  0  0  0  0  0 0 4 0 | * * * * *  *  * *  *  *  *  * * * 2 * | 0 0 0 1 0 0 0 0  0  0 0  0 1 0 1 | 0 1 1 0 0 0 1
... ..o3..x ..x    ♦ 0 0 6 |  0 0 0  0 0  6 3 | 0 0  0 0  0  0  0  0  0 0 2 3 | * * * * *  *  * *  *  *  *  * * * * 4 | 0 0 0 0 0 0 1 0  0  0 0  0 0 1 1 | 0 1 0 0 0 1 1
-------------------+-------+------------------+-------------------------------+---------------------------------------+----------------------------------+--------------
x..3o..3o.. x..    ♦ 8 0 0 | 12 4 0  0 0  0 0 | 8 6  0 0  0  0  0  0  0 0 0 0 | 2 4 0 0 0  0  0 0  0  0  0  0 0 0 0 0 | 1 * * * * * * *  *  * *  * * * * | 1 1 0 0 0 0 0
xo.3oo.3oo. ...&#x ♦ 4 1 0 |  6 0 4  0 0  0 0 | 4 0  6 0  0  0  0  0  0 0 0 0 | 1 0 4 0 0  0  0 0  0  0  0  0 0 0 0 0 | * 2 * * * * * *  *  * *  * * * * | 1 0 1 0 0 0 0
xo.3oo. ... xo.&#x ♦ 6 1 0 |  6 3 6  0 0  0 0 | 2 3  6 3  0  0  0  0  0 0 0 0 | 0 1 2 3 0  0  0 0  0  0  0  0 0 0 0 0 | * * 4 * * * * *  *  * *  * * * * | 1 0 0 1 0 0 0
x.o3o.o3o.x ...&#x ♦ 4 0 4 |  6 0 0 12 0  6 0 | 4 0  0 0 12 12  0  0  0 0 4 0 | 1 0 0 0 4  6  0 4  0  0  0  0 0 0 1 0 | * * * 2 * * * *  *  * *  * * * * | 0 1 1 0 0 0 0
x.o3o.o ... x.x&#x ♦ 6 0 2 |  6 3 0  6 0  0 1 | 2 3  0 0  6  0  3  0  0 0 0 0 | 0 1 0 0 2  0  3 0  0  0  0  0 0 0 0 0 | * * * * 4 * * *  *  * *  * * * * | 0 1 0 1 0 0 0
x.o ... o.x x.x&#x ♦ 4 0 4 |  2 2 0  8 0  2 2 | 0 1  0 0  4  4  4  0  0 0 0 1 | 0 0 0 0 0  2  2 0  2  0  0  0 0 0 0 0 | * * * * * 6 * *  *  * *  * * * * | 0 1 0 0 1 0 0
... o.o3o.x x.x&#x ♦ 2 0 6 |  0 1 0  6 0  6 3 | 0 0  0 0  0  6  3  0  0 0 2 3 | 0 0 0 0 0  0  0 2  3  0  0  0 0 0 0 1 | * * * * * * 4 *  *  * *  * * * * | 0 1 0 0 0 1 0
xoo3ooo ... ...&#x ♦ 3 1 1 |  3 0 3  3 1  0 0 | 1 0  3 0  3  0  0  3  0 0 0 0 | 0 0 1 0 1  0  0 0  0  3  0  0 0 0 0 0 | * * * * * * * 8  *  * *  * * * * | 0 0 1 1 0 0 0
xoo ... oox ...&#x ♦ 2 1 2 |  1 0 2  4 2  1 0 | 0 0  1 0  2  2  0  4  1 0 0 0 | 0 0 0 0 0  1  0 0  0  2  2  0 0 0 0 0 | * * * * * * * * 12  * *  * * * * | 0 0 1 0 1 0 0
xoo ... ... xox&#x ♦ 4 1 2 |  2 2 4  4 2  0 1 | 0 1  2 2  2  0  2  4  0 1 0 0 | 0 0 0 1 0  0  1 0  0  2  0  2 0 0 0 0 | * * * * * * * *  * 12 *  * * * * | 0 0 0 1 1 0 0
... ooo3oox ...&#x ♦ 1 1 3 |  0 0 1  3 3  3 0 | 0 0  0 0  0  3  0  3  3 0 1 0 | 0 0 0 0 0  0  0 1  0  0  3  0 1 0 0 0 | * * * * * * * *  *  * 8  * * * * | 0 0 1 0 0 1 0
... ... oox xox&#x ♦ 2 1 4 |  0 1 2  4 4  2 2 | 0 0  0 1  0  2  2  4  2 2 0 1 | 0 0 0 0 0  0  0 0  1  0  2  2 0 1 0 0 | * * * * * * * *  *  * * 12 * * * | 0 0 0 0 1 1 0
.oo3.oo3.ox ...&#x ♦ 0 1 4 |  0 0 0  0 4  6 0 | 0 0  0 0  0  0  0  0  6 0 4 0 | 0 0 0 0 0  0  0 0  0  0  0  0 4 0 1 0 | * * * * * * * *  *  * *  * 2 * * | 0 0 1 0 0 0 1
... .oo3.ox .ox&#x ♦ 0 1 6 |  0 0 0  0 6  6 3 | 0 0  0 0  0  0  0  0  6 3 2 3 | 0 0 0 0 0  0  0 0  0  0  0  0 2 3 0 1 | * * * * * * * *  *  * *  * * 4 * | 0 0 0 0 0 1 1
..o3..o3..x ..x    ♦ 0 0 8 |  0 0 0  0 0 12 4 | 0 0  0 0  0  0  0  0  0 0 8 6 | 0 0 0 0 0  0  0 0  0  0  0  0 0 0 2 4 | * * * * * * * *  *  * *  * * * 1 | 0 1 0 0 0 0 1
-------------------+-------+------------------+-------------------------------+---------------------------------------+----------------------------------+--------------
xo.3oo.3oo. xo.&#x ♦ 8 1 0 | 12 4 8  0 0  0 0 | 8 6 12 4  0  0  0  0  0 0 0 0 | 2 4 8 6 0  0  0 0  0  0  0  0 0 0 0 0 | 1 2 4 0 0 0 0 0  0  0 0  0 0 0 0 | 1 * * * * * *
x.o3o.o3o.x x.x&#x ♦ 8 0 8 | 12 4 0 24 0 12 4 | 8 6  0 0 24 24 12  0  0 0 8 6 | 2 4 0 0 8 12 12 8 12  0  0  0 0 0 2 4 | 1 0 0 2 4 6 4 0  0  0 0  0 0 0 1 | * 1 * * * * *
xoo3ooo3oox ...&#x ♦ 4 1 4 |  6 0 4 12 4  6 0 | 4 0  6 0 12 12  0 12  6 0 4 0 | 1 0 4 0 4  6  0 4  0 12 12  0 4 0 1 0 | 0 1 0 1 0 0 0 4  6  0 4  0 1 0 0 | * * 2 * * * *
xoo3ooo ... xox&#x ♦ 6 1 2 |  6 3 6  6 2  0 1 | 2 3  6 3  6  0  3  6  0 1 0 0 | 0 1 2 3 2  0  3 0  0  6  0  3 0 0 0 0 | 0 0 1 0 1 0 0 2  0  3 0  0 0 0 0 | * * * 4 * * *
xoo ... oox xox&#x ♦ 4 1 4 |  2 2 4  8 4  2 2 | 0 1  2 2  4  4  4  8  2 2 0 1 | 0 0 0 1 0  2  2 0  2  4  4  4 0 1 0 0 | 0 0 0 0 0 1 0 0  2  2 0  2 0 0 0 | * * * * 6 * *
... ooo3oox xox&#x ♦ 2 1 6 |  0 1 2  6 6  6 3 | 0 0  0 1  0  6  3  6  6 3 2 3 | 0 0 0 0 0  0  0 2  3  0  6  3 2 3 0 1 | 0 0 0 0 0 0 1 0  0  0 2  3 0 1 0 | * * * * * 4 *
.oo3.oo3.ox .ox&#x ♦ 0 1 8 |  0 0 0  0 8 12 4 | 0 0  0 0  0  0  0  0 12 4 8 6 | 0 0 0 0 0  0  0 0  0  0  0  0 8 6 2 4 | 0 0 0 0 0 0 0 0  0  0 0  0 2 4 1 | * * * * * * 1
```