﻿ hexipaico
 Acronym hexipaico Name hexip atop ico,diminished 1/4-lune of rag Circumradius 1 Lace cityin approx. ASCII-art ``` I where: I = o3x3o4o (ico) h h h = x3o3o4o (hex) ``` Confer uniform relative: rag   general polytopal classes: segmentopeta

Incidence matrix according to Dynkin symbol

```ox3xo3oo4oo ox&#x   → height = 1/2
(ico || hexip)

o.3o.3o.4o. o.    | 24  * |  8  4  0 0 |  4  8  2  16  2  0  0 |  4 2  8  1  16  8  0  0 | 1  8  4  4  8 0  0 | 2  4 2 0
.o3.o3.o4.o .o    |  * 16 |  0  6  6 1 |  0  0  6  12  6 12  6 |  0 0 12  6   8 12  8 12 | 0  8 12  1  8 1  8 | 1  8 2 1
------------------+-------+------------+-----------------------+-------------------------+--------------------+---------
.. x. .. .. ..    |  2  0 | 96  *  * * |  1  2  0   2  0  0  0 |  2 1  2  0   4  1  0  0 | 1  4  1  2  2 0  0 | 2  2 1 0
oo3oo3oo4oo oo&#x |  1  1 |  * 96  * * |  0  0  1   4  1  0  0 |  0 0  4  1   4  4  0  0 | 0  4  4  1  4 0  0 | 1  4 1 0
.x .. .. .. ..    |  0  2 |  *  * 48 * |  0  0  1   0  0  4  1 |  0 0  4  1   0  0  4  4 | 0  4  4  0  0 1  4 | 1  4 0 1
.. .. .. .. .x    |  0  2 |  *  *  * 8 |  0  0  0   0  6  0  6 |  0 0  0  6   0 12  0 12 | 0  0 12  0  8 0  8 | 0  8 1 1
------------------+-------+------------+-----------------------+-------------------------+--------------------+---------
o.3x. .. .. ..    |  3  0 |  3  0  0 0 | 32  *  *   *  *  *  * |  2 0  2  0   0  0  0  0 | 1  4  1  0  0 0  0 | 2  2 0 0
.. x.3o. .. ..    |  3  0 |  3  0  0 0 |  * 64  *   *  *  *  * |  1 1  0  0   2  0  0  0 | 1  2  0  2  1 0  0 | 2  1 1 0
ox .. .. .. ..&#x |  1  2 |  0  2  1 0 |  *  * 48   *  *  *  * |  0 0  4  1   0  0  0  0 | 0  4  4  0  0 0  0 | 1  4 0 0
.. xo .. .. ..&#x |  2  1 |  1  2  0 0 |  *  *  * 192  *  *  * |  0 0  1  0   2  1  0  0 | 0  2  1  1  2 0  0 | 1  2 1 0
.. .. .. .. ox&#x |  1  2 |  0  2  0 1 |  *  *  *   * 48  *  * |  0 0  0  1   0  4  0  0 | 0  0  4  0  4 0  0 | 0  4 1 0
.x3.o .. .. ..    |  0  3 |  0  0  3 0 |  *  *  *   *  * 64  * |  0 0  1  0   0  0  2  1 | 0  2  1  0  0 1  2 | 1  2 0 1
.x .. .. .. .x    |  0  4 |  0  0  2 2 |  *  *  *   *  *  * 24 |  0 0  0  1   0  0  0  4 | 0  0  4  0  0 0  4 | 0  4 0 1
------------------+-------+------------+-----------------------+-------------------------+--------------------+---------
o.3x.3o. .. ..    ♦  6  0 | 12  0  0 0 |  4  4  0   0  0  0  0 | 16 *  *  *   *  *  *  * | 1  2  0  0  0 0  0 | 2  1 0 0
.. x.3o.4o. ..    ♦  6  0 | 12  0  0 0 |  0  8  0   0  0  0  0 |  * 8  *  *   *  *  *  * | 1  0  0  2  0 0  0 | 2  0 1 0
ox3xo .. .. ..&#x ♦  3  3 |  3  6  3 0 |  1  0  3   3  0  1  0 |  * * 64  *   *  *  *  * | 0  2  1  0  0 0  0 | 1  2 0 0
ox .. .. .. ox&#x ♦  1  4 |  0  4  2 2 |  0  0  2   0  2  0  1 |  * *  * 24   *  *  *  * | 0  0  4  0  0 0  0 | 0  4 0 0
.. xo3oo .. ..&#x ♦  3  1 |  3  3  0 0 |  0  1  0   3  0  0  0 |  * *  *  * 128  *  *  * | 0  1  0  1  1 0  0 | 1  1 1 0
.. xo .. .. ox&#x ♦  2  2 |  1  4  0 1 |  0  0  0   2  2  0  0 |  * *  *  *   * 96  *  * | 0  0  1  0  2 0  0 | 0  2 1 0
.x3.o3.o .. ..    ♦  0  4 |  0  0  6 0 |  0  0  0   0  0  4  0 |  * *  *  *   *  * 32  * | 0  1  0  0  0 1  1 | 1  1 0 1
.x3.o .. .. .x    ♦  0  6 |  0  0  6 3 |  0  0  0   0  0  2  3 |  * *  *  *   *  *  * 32 | 0  0  1  0  0 0  2 | 0  2 0 1
------------------+-------+------------+-----------------------+-------------------------+--------------------+---------
o.3x.3o.4o. ..    ♦ 24  0 | 96  0  0 0 | 32 64  0   0  0  0  0 | 16 8  0  0   0  0  0  0 | 1  *  *  *  * *  * | 2  0 0 0
ox3xo3oo .. ..&#x ♦  6  4 | 12 12  6 0 |  4  4  6  12  0  4  0 |  1 0  4  0   4  0  1  0 | * 32  *  *  * *  * | 1  1 0 0
ox3xo .. .. ox&#x ♦  3  6 |  3 12  6 3 |  1  0  6   6  6  2  3 |  0 0  2  3   0  3  0  1 | *  * 32  *  * *  * | 0  2 0 0
.. xo3oo4oo ..&#x ♦  6  1 | 12  6  0 0 |  0  8  0  12  0  0  0 |  0 1  0  0   8  0  0  0 | *  *  * 16  * *  * | 1  0 1 0
.. xo3oo .. ox&#x ♦  3  2 |  3  6  0 1 |  0  1  0   6  3  0  0 |  0 0  0  0   2  3  0  0 | *  *  *  * 64 *  * | 0  1 1 0
.x3.o3.o4.o ..    ♦  0  8 |  0  0 24 0 |  0  0  0   0  0 32  0 |  0 0  0  0   0  0 16  0 | *  *  *  *  * 2  * | 1  0 0 1
.x3.o3.o .. .x    ♦  0  8 |  0  0 12 4 |  0  0  0   0  0  8  6 |  0 0  0  0   0  0  2  4 | *  *  *  *  * * 16 | 0  1 0 1
------------------+-------+------------+-----------------------+-------------------------+--------------------+---------
ox3xo3oo4oo ..&#x ♦ 24  8 | 96 48 24 0 | 32 64 24  96  0 32  0 | 16 8 32  0  64  0 16  0 | 1 16  0  8  0 1  0 | 2  * * *
ox3xo3oo .. ox&#x ♦  6  8 | 12 24 12 4 |  4  4 12  24 12  8  6 |  1 0  8  6   8 12  2  4 | 0  2  4  0  4 0  1 | * 16 * *
.. xo3oo4oo ox&#x ♦  6  2 | 12 12  0 1 |  0  8  0  24  6  0  0 |  0 1  0  0  16 12  0  0 | 0  0  0  2  8 0  0 | *  * 8 *
.x3.o3.o4.o .x    ♦  0 16 |  0  0 48 8 |  0  0  0   0  0 64 24 |  0 0  0  0   0  0 32 32 | 0  0  0  0  0 2 16 | *  * * 1
```

```xox3oxo3ooo4ooo&#x   → height(1,2) = height(2,3) = 1/sqrt(2) = 0.707107
height(1,3) = 1

o..3o..3o..4o..    & | 16  * |  6  6 1  0 | 12  6  12  6  6  0  0 |  8 12   8 12  6 12  0 0 | 1  8  1  8 12  8 0 | 1 1  8 1
.o.3.o.3.o.4.o.      |  * 24 |  0  4 0  8 |  0  2  16  0  2  4  8 |  0  8  16  0  1  8  4 2 | 0  8  4  0  4  8 1 | 2 0  4 2
---------------------+-------+------------+-----------------------+-------------------------+--------------------+---------
x.. ... ... ...    & |  2  0 | 48  * *  * |  4  1   0  0  0  0  0 |  4  4   0  4  1  0  0 0 | 1  4  0  4  4  0 0 | 1 1  4 0
oo.3oo.3oo.4oo.&#x & |  1  1 |  * 96 *  * |  0  1   4  0  1  0  0 |  0  4   4  0  1  4  0 0 | 0  4  1  0  4  4 0 | 1 0  4 1
o.o3o.o3o.o4o.o&#x   |  2  0 |  *  * 8  * |  0  0   0  6  6  0  0 |  0  0   0 12  6 12  0 0 | 0  0  0  8 12  8 0 | 0 1  8 1
... .x. ... ...      |  0  2 |  *  * * 96 |  0  0   2  0  0  1  2 |  0  2   4  0  0  1  2 1 | 0  4  2  0  1  2 1 | 2 0  2 1
---------------------+-------+------------+-----------------------+-------------------------+--------------------+---------
x..3o.. ... ...    & |  3  0 |  3  0 0  0 | 64  *   *  *  *  *  * |  2  1   0  1  0  0  0 0 | 1  2  0  2  1  0 0 | 1 1  2 0
xo. ... ... ...&#x & |  2  1 |  1  2 0  0 |  * 48   *  *  *  *  * |  0  4   0  0  1  0  0 0 | 0  4  0  0  4  0 0 | 1 0  4 0
... ox. ... ...&#x & |  1  2 |  0  2 0  1 |  *  * 192  *  *  *  * |  0  1   2  0  0  1  0 0 | 0  2  1  0  1  2 0 | 1 0  2 1
x.x ... ... ...&#x   |  4  0 |  2  0 2  0 |  *  *   * 24  *  *  * |  0  0   0  4  1  0  0 0 | 0  0  0  4  4  0 0 | 0 1  4 0
ooo3ooo3ooo4ooo&#x   |  2  1 |  0  2 1  0 |  *  *   *  * 48  *  * |  0  0   0  0  1  4  0 0 | 0  0  0  0  4  4 0 | 0 0  4 1
.o.3.x. ... ...      |  0  3 |  0  0 0  3 |  *  *   *  *  * 32  * |  0  2   0  0  0  0  2 0 | 0  4  0  0  1  0 1 | 2 0  2 0
... .x.3.o. ...      |  0  3 |  0  0 0  3 |  *  *   *  *  *  * 64 |  0  0   2  0  0  0  1 1 | 0  2  2  0  0  1 1 | 2 0  1 1
---------------------+-------+------------+-----------------------+-------------------------+--------------------+---------
x..3o..3o.. ...    & ♦  4  0 |  6  0 0  0 |  4  0   0  0  0  0  0 | 32  *   *  *  *  *  * * | 1  1  0  1  0  0 0 | 1 1  1 0
xo.3ox. ... ...&#x & ♦  3  3 |  3  6 0  3 |  1  3   3  0  0  1  0 |  * 64   *  *  *  *  * * | 0  2  0  0  1  0 0 | 1 0  2 0
... ox.3oo. ...&#x & ♦  1  3 |  0  3 0  3 |  0  0   3  0  0  0  1 |  *  * 128  *  *  *  * * | 0  1  1  0  0  1 0 | 1 0  1 1
x.x3o.o ... ...&#x   ♦  6  0 |  6  0 3  0 |  2  0   0  3  0  0  0 |  *  *   * 32  *  *  * * | 0  0  0  2  1  0 0 | 0 1  2 0
xox ... ... ...&#x   ♦  4  1 |  2  4 2  0 |  0  2   0  1  2  0  0 |  *  *   *  * 24  *  * * | 0  0  0  0  4  0 0 | 0 0  4 0
... oxo ... ...&#x   ♦  2  2 |  0  4 1  1 |  0  0   2  0  2  0  0 |  *  *   *  *  * 96  * * | 0  0  0  0  1  2 0 | 0 0  2 1
.o.3.x.3.o. ...      ♦  0  6 |  0  0 0 12 |  0  0   0  0  0  4  4 |  *  *   *  *  *  * 16 * | 0  2  0  0  0  0 1 | 2 0  1 0
... .x.3.o.4.o.      ♦  0  6 |  0  0 0 12 |  0  0   0  0  0  0  8 |  *  *   *  *  *  *  * 8 | 0  0  2  0  0  0 1 | 2 0  0 1
---------------------+-------+------------+-----------------------+-------------------------+--------------------+---------
x..3o..3o..4o..    & ♦  8  0 | 24  0 0  0 | 32  0   0  0  0  0  0 | 16  0   0  0  0  0  0 0 | 2  *  *  *  *  * * | 1 1  0 0
xo.3ox.3oo. ...&#x & ♦  4  6 |  6 12 0 12 |  4  6  12  0  0  4  4 |  1  4   4  0  0  0  1 0 | * 32  *  *  *  * * | 1 0  1 0
... ox.3oo.4oo.&#x & ♦  1  6 |  0  6 0 12 |  0  0  12  0  0  0  8 |  0  0   8  0  0  0  0 1 | *  * 16  *  *  * * | 1 0  0 1
x.x3o.o3o.o ...&#x   ♦  8  0 | 12  0 4  0 |  8  0   0  6  0  0  0 |  2  0   0  4  0  0  0 0 | *  *  * 16  *  * * | 0 1  1 0
xox3oxo ... ...&#x   ♦  6  3 |  6 12 3  3 |  2  6   6  3  6  1  0 |  0  2   0  1  3  3  0 0 | *  *  *  * 32  * * | 0 0  2 0
... oxo3ooo ...&#x   ♦  2  3 |  0  6 1  3 |  0  0   6  0  3  0  1 |  0  0   2  0  0  3  0 0 | *  *  *  *  * 64 * | 0 0  1 1
.o.3.x.3.o.4.o.      ♦  0 24 |  0  0 0 96 |  0  0   0  0  0 32 64 |  0  0   0  0  0  0 16 8 | *  *  *  *  *  * 1 | 2 0  0 0
---------------------+-------+------------+-----------------------+-------------------------+--------------------+---------
xo.3ox.3oo.4oo.&#x & ♦  8 24 | 24 48 0 96 | 32 24  96  0  0 32 64 | 16 32  64  0  0  0 16 8 | 1 16  8  0  0  0 1 | 2 *  * *
x.x3o.o3o.o4o.o&#x   ♦ 16  0 | 48  0 8  0 | 64  0   0 24  0  0  0 | 32  0   0 32  0  0  0 0 | 2  0  0 16  0  0 0 | * 1  * *
xox3oxo3ooo ...&#x   ♦  8  6 | 12 24 4 12 |  8 12  24  6 12  4  4 |  2  8   8  4  6 12  1 0 | 0  2  0  1  4  4 0 | * * 16 *
... oxo3ooo4ooo&#x   ♦  2  6 |  0 12 1 12 |  0  0  24  0  6  0  8 |  0  0  16  0  0 12  0 1 | 0  0  2  0  0  8 0 | * *  * 8
```