Acronym shiddip, K-4.54 Name square - hexagon duoprism Circumradius sqrt(3/2) = 1.224745 General of army (is itself convex) Colonel of regiment (is itself locally convex) Confer general duoprisms: n,m-dip   2n,m-dip   2n,2m-dip   4,n-dip   4,2n-dip   6,n-dip Externallinks

Incidence matrix according to Dynkin symbol

```x4o x6o

. . . . | 24 |  2  2 | 1  4 1 | 2 2
--------+----+-------+--------+----
x . . . |  2 | 24  * | 1  2 0 | 2 1
. . x . |  2 |  * 24 | 0  2 1 | 1 2
--------+----+-------+--------+----
x4o . . |  4 |  4  0 | 6  * * | 2 0
x . x . |  4 |  2  2 | * 24 * | 1 1
. . x6o |  6 |  0  6 | *  * 4 | 0 2
--------+----+-------+--------+----
x4o x . ♦  8 |  8  4 | 2  4 0 | 6 *
x . x6o ♦ 12 |  6 12 | 0  6 2 | * 4
```

```x4o x6/5o

. . .   . | 24 |  2  2 | 1  4 1 | 2 2
----------+----+-------+--------+----
x . .   . |  2 | 24  * | 1  2 0 | 2 1
. . x   . |  2 |  * 24 | 0  2 1 | 1 2
----------+----+-------+--------+----
x4o .   . |  4 |  4  0 | 6  * * | 2 0
x . x   . |  4 |  2  2 | * 24 * | 1 1
. . x6/5o |  6 |  0  6 | *  * 4 | 0 2
----------+----+-------+--------+----
x4o x   . ♦  8 |  8  4 | 2  4 0 | 6 *
x . x6/5o ♦ 12 |  6 12 | 0  6 2 | * 4
```

```x4/3o x6o

.   . . . | 24 |  2  2 | 1  4 1 | 2 2
----------+----+-------+--------+----
x   . . . |  2 | 24  * | 1  2 0 | 2 1
.   . x . |  2 |  * 24 | 0  2 1 | 1 2
----------+----+-------+--------+----
x4/3o . . |  4 |  4  0 | 6  * * | 2 0
x   . x . |  4 |  2  2 | * 24 * | 1 1
.   . x6o |  6 |  0  6 | *  * 4 | 0 2
----------+----+-------+--------+----
x4/3o x . ♦  8 |  8  4 | 2  4 0 | 6 *
x   . x6o ♦ 12 |  6 12 | 0  6 2 | * 4
```

```x4/3o x6/5o

.   . .   . | 24 |  2  2 | 1  4 1 | 2 2
------------+----+-------+--------+----
x   . .   . |  2 | 24  * | 1  2 0 | 2 1
.   . x   . |  2 |  * 24 | 0  2 1 | 1 2
------------+----+-------+--------+----
x4/3o .   . |  4 |  4  0 | 6  * * | 2 0
x   . x   . |  4 |  2  2 | * 24 * | 1 1
.   . x6/5o |  6 |  0  6 | *  * 4 | 0 2
------------+----+-------+--------+----
x4/3o x   . ♦  8 |  8  4 | 2  4 0 | 6 *
x   . x6/5o ♦ 12 |  6 12 | 0  6 2 | * 4
```

```x4o x3x

. . . . | 24 |  2  1  1 | 1  2  2 1 | 1 1 2
--------+----+----------+-----------+------
x . . . |  2 | 24  *  * | 1  1  1 0 | 1 1 1
. . x . |  2 |  * 12  * | 0  2  0 1 | 1 0 2
. . . x |  2 |  *  * 12 | 0  0  2 1 | 0 1 2
--------+----+----------+-----------+------
x4o . . |  4 |  4  0  0 | 6  *  * * | 1 1 0
x . x . |  4 |  2  2  0 | * 12  * * | 1 0 1
x . . x |  4 |  2  0  2 | *  * 12 * | 0 1 1
. . x3x |  6 |  0  3  3 | *  *  * 4 | 0 0 2
--------+----+----------+-----------+------
x4o x . ♦  8 |  8  4  0 | 2  4  0 0 | 3 * *
x4o . x ♦  8 |  8  0  4 | 2  0  4 0 | * 3 *
x . x3x ♦ 12 |  6  6  6 | 0  3  3 2 | * * 4
```

```x4/3o x3x

.   . . . | 24 |  2  1  1 | 1  2  2 1 | 1 1 2
----------+----+----------+-----------+------
x   . . . |  2 | 24  *  * | 1  1  1 0 | 1 1 1
.   . x . |  2 |  * 12  * | 0  2  0 1 | 1 0 2
.   . . x |  2 |  *  * 12 | 0  0  2 1 | 0 1 2
----------+----+----------+-----------+------
x4/3o . . |  4 |  4  0  0 | 6  *  * * | 1 1 0
x   . x . |  4 |  2  2  0 | * 12  * * | 1 0 1
x   . . x |  4 |  2  0  2 | *  * 12 * | 0 1 1
.   . x3x |  6 |  0  3  3 | *  *  * 4 | 0 0 2
----------+----+----------+-----------+------
x4/3o x . ♦  8 |  8  4  0 | 2  4  0 0 | 3 * *
x4/3o . x ♦  8 |  8  0  4 | 2  0  4 0 | * 3 *
x   . x3x ♦ 12 |  6  6  6 | 0  3  3 2 | * * 4
```

```x x x6o

. . . . | 24 |  1  1  2 | 1  2  2 1 | 2 1 1
--------+----+----------+-----------+------
x . . . |  2 | 12  *  * | 1  2  0 0 | 2 1 0
. x . . |  2 |  * 12  * | 1  0  2 0 | 2 0 1
. . x . |  2 |  *  * 24 | 0  1  1 1 | 1 1 1
--------+----+----------+-----------+------
x x . . |  4 |  2  2  0 | 6  *  * * | 2 0 0
x . x . |  4 |  2  0  2 | * 12  * * | 1 1 0
. x x . |  4 |  0  2  2 | *  * 12 * | 1 0 1
. . x6o |  6 |  0  0  6 | *  *  * 4 | 0 1 1
--------+----+----------+-----------+------
x x x . ♦  8 |  4  4  4 | 2  2  2 0 | 6 * *
x . x6o ♦ 12 |  6  0 12 | 0  6  0 2 | * 2 *
. x x6o ♦ 12 |  0  6 12 | 0  0  6 2 | * * 2
```

```x x x6/5o

. . .   . | 24 |  1  1  2 | 1  2  2 1 | 2 1 1
----------+----+----------+-----------+------
x . .   . |  2 | 12  *  * | 1  2  0 0 | 2 1 0
. x .   . |  2 |  * 12  * | 1  0  2 0 | 2 0 1
. . x   . |  2 |  *  * 24 | 0  1  1 1 | 1 1 1
----------+----+----------+-----------+------
x x .   . |  4 |  2  2  0 | 6  *  * * | 2 0 0
x . x   . |  4 |  2  0  2 | * 12  * * | 1 1 0
. x x   . |  4 |  0  2  2 | *  * 12 * | 1 0 1
. . x6/5o |  6 |  0  0  6 | *  *  * 4 | 0 1 1
----------+----+----------+-----------+------
x x x   . ♦  8 |  4  4  4 | 2  2  2 0 | 6 * *
x . x6/5o ♦ 12 |  6  0 12 | 0  6  0 2 | * 2 *
. x x6/5o ♦ 12 |  0  6 12 | 0  0  6 2 | * * 2
```

```x x x3x

. . . . | 24 |  1  1  1  1 | 1 1 1 1 1 1 | 1 1 1 1
--------+----+-------------+-------------+--------
x . . . |  2 | 12  *  *  * | 1 1 1 0 0 0 | 1 1 1 0
. x . . |  2 |  * 12  *  * | 1 0 0 1 1 0 | 1 1 0 1
. . x . |  2 |  *  * 12  * | 0 1 0 1 0 1 | 1 0 1 1
. . . x |  2 |  *  *  * 12 | 0 0 1 0 1 1 | 0 1 1 1
--------+----+-------------+-------------+--------
x x . . |  4 |  2  2  0  0 | 6 * * * * * | 1 1 0 0
x . x . |  4 |  2  0  2  0 | * 6 * * * * | 1 0 1 0
x . . x |  4 |  2  0  0  2 | * * 6 * * * | 0 1 1 0
. x x . |  4 |  0  2  2  0 | * * * 6 * * | 1 0 0 1
. x . x |  4 |  0  2  0  2 | * * * * 6 * | 0 1 0 1
. . x3x |  6 |  0  0  3  3 | * * * * * 4 | 0 0 1 1
--------+----+-------------+-------------+--------
x x x . ♦  8 |  4  4  4  0 | 2 2 0 2 0 0 | 3 * * *
x x . x ♦  8 |  4  4  0  4 | 2 0 2 0 2 0 | * 3 * *
x . x3x ♦ 12 |  6  0  6  6 | 0 3 3 0 0 2 | * * 2 *
. x x3x ♦ 12 |  0  6  6  6 | 0 0 0 3 3 2 | * * * 2
```

```xx xx6oo&#x   → height = 1
(hip || hip)

o. o.6o.    | 12  * | 1  2  1 0  0 | 2 1 1  2 0 0 | 1 2 1 0
.o .o6.o    |  * 12 | 0  0  1 1  2 | 0 0 1  2 2 1 | 0 2 1 1
------------+-------+--------------+--------------+--------
x. .. ..    |  2  0 | 6  *  * *  * | 2 0 1  0 0 0 | 1 2 0 0
.. x. ..    |  2  0 | * 12  * *  * | 1 1 0  1 0 0 | 1 1 1 0
oo oo6oo&#x |  1  1 | *  * 12 *  * | 0 0 1  2 0 0 | 0 2 1 0
.x .. ..    |  0  2 | *  *  * 6  * | 0 0 1  0 2 0 | 0 2 0 1
.. .x ..    |  0  2 | *  *  * * 12 | 0 0 0  1 1 1 | 0 1 1 1
------------+-------+--------------+--------------+--------
x. x. ..    |  4  0 | 2  2  0 0  0 | 6 * *  * * * | 1 1 0 0
.. x.6o.    |  6  0 | 0  6  0 0  0 | * 2 *  * * * | 1 0 1 0
xx .. ..&#x |  2  2 | 1  0  2 1  0 | * * 6  * * * | 0 2 0 0
.. xx ..&#x |  2  2 | 0  1  2 0  1 | * * * 12 * * | 0 1 1 0
.x .x ..    |  0  4 | 0  0  0 2  2 | * * *  * 6 * | 0 1 0 1
.. .x6.o    |  0  6 | 0  0  0 0  6 | * * *  * * 2 | 0 0 1 1
------------+-------+--------------+--------------+--------
x. x.6o.    | 12  0 | 6 12  0 0  0 | 6 2 0  0 0 0 | 1 * * *
xx xx ..&#x |  4  4 | 2  2  4 2  2 | 1 0 2  2 1 0 | * 6 * *
.. xx6oo&#x |  6  6 | 0  6  6 0  6 | 0 1 0  6 0 1 | * * 2 *
.x .x6.o    |  0 12 | 0  0  0 6 12 | 0 0 0  0 6 2 | * * * 1
```

```xx xx3xx&#x   → height = 1
(hip || hip)

o. o.3o.    | 12  * | 1 1 1  1 0 0 0 | 1 1 1 1 1 1 0 0 0 | 1 1 1 1 0
.o .o3.o    |  * 12 | 0 0 0  1 1 1 1 | 0 0 0 1 1 1 1 1 1 | 0 1 1 1 1
------------+-------+----------------+-------------------+----------
x. .. ..    |  2  0 | 6 * *  * * * * | 1 1 0 1 0 0 0 0 0 | 1 1 1 0 0
.. x. ..    |  2  0 | * 6 *  * * * * | 1 0 1 0 1 0 0 0 0 | 1 1 0 1 0
.. .. x.    |  2  0 | * * 6  * * * * | 0 1 1 0 0 1 0 0 0 | 1 0 1 1 0
oo oo3oo&#x |  1  1 | * * * 12 * * * | 0 0 0 1 1 1 0 0 0 | 0 1 1 1 0
.x .. ..    |  0  2 | * * *  * 6 * * | 0 0 0 1 0 0 1 1 0 | 0 1 1 0 1
.. .x ..    |  0  2 | * * *  * * 6 * | 0 0 0 0 1 0 1 0 1 | 0 1 0 1 1
.. .. .x    |  0  2 | * * *  * * * 6 | 0 0 0 0 0 1 0 1 1 | 0 0 1 1 1
------------+-------+----------------+-------------------+----------
x. x. ..    |  4  0 | 2 2 0  0 0 0 0 | 3 * * * * * * * * | 1 1 0 0 0
x. .. x.    |  4  0 | 2 0 2  0 0 0 0 | * 3 * * * * * * * | 1 0 1 0 0
.. x.3x.    |  6  0 | 0 3 3  0 0 0 0 | * * 2 * * * * * * | 1 0 0 1 0
xx .. ..&#x |  2  2 | 1 0 0  2 1 0 0 | * * * 6 * * * * * | 0 1 1 0 0
.. xx ..&#x |  2  2 | 0 1 0  2 0 1 0 | * * * * 6 * * * * | 0 1 0 1 0
.. .. xx&#x |  2  2 | 0 0 1  2 0 0 1 | * * * * * 6 * * * | 0 0 1 1 0
.x .x ..    |  0  4 | 0 0 0  0 2 2 0 | * * * * * * 3 * * | 0 1 0 0 1
.x .. .x    |  0  4 | 0 0 0  0 2 0 2 | * * * * * * * 3 * | 0 0 1 0 1
.. .x3.x    |  0  6 | 0 0 0  0 0 3 3 | * * * * * * * * 2 | 0 0 0 1 1
------------+-------+----------------+-------------------+----------
x. x.3x.    ♦ 12  0 | 6 6 6  0 0 0 0 | 3 3 2 0 0 0 0 0 0 | 1 * * * *
xx xx ..&#x ♦  4  4 | 2 2 0  4 2 2 0 | 1 0 0 2 2 0 1 0 0 | * 3 * * *
xx .. xx&#x ♦  4  4 | 2 0 2  4 2 0 2 | 0 1 0 2 0 2 0 1 0 | * * 3 * *
.. xx3xx&#x ♦  6  6 | 0 3 3  6 0 3 3 | 0 0 1 0 3 3 0 0 1 | * * * 2 *
.x .x3.x    ♦  0 12 | 0 0 0  0 6 6 6 | 0 0 0 0 0 0 3 3 2 | * * * * 1
```

```xux xxx4ooo&#xt   → both heights = sqrt(3)/2 = 0.866025
(cube || pseudo (x,x,u)-cube || cube)

o.. o..4o..     | 8 * * | 1 2 1 0 0 0 0 | 2 1 2 1 0 0 0 0 | 1 1 2 0 0
.o. .o.4.o.     | * 8 * | 0 0 1 2 1 0 0 | 0 0 2 1 1 2 0 0 | 0 1 2 1 0
..o ..o4..o     | * * 8 | 0 0 0 0 1 1 2 | 0 0 0 1 0 2 2 1 | 0 0 2 1 1
----------------+-------+---------------+-----------------+----------
x.. ... ...     | 2 0 0 | 4 * * * * * * | 2 0 0 1 0 0 0 0 | 1 0 2 0 0
... x.. ...     | 2 0 0 | * 8 * * * * * | 1 1 1 0 0 0 0 0 | 1 1 1 0 0
oo. oo.4oo.&#x  | 1 1 0 | * * 8 * * * * | 0 0 2 1 0 0 0 0 | 0 1 2 0 0
... .x. ...     | 0 2 0 | * * * 8 * * * | 0 0 1 0 1 1 0 0 | 0 1 1 1 0
.oo .oo4.oo&#x  | 0 1 1 | * * * * 8 * * | 0 0 0 1 0 2 0 0 | 0 0 2 1 0
..x ... ...     | 0 0 2 | * * * * * 4 * | 0 0 0 1 0 0 2 0 | 0 0 2 0 1
... ..x ...     | 0 0 2 | * * * * * * 8 | 0 0 0 0 0 1 1 1 | 0 0 1 1 1
----------------+-------+---------------+-----------------+----------
x.. x.. ...     | 4 0 0 | 2 2 0 0 0 0 0 | 4 * * * * * * * | 1 0 1 0 0
... x..4o..     | 4 0 0 | 0 4 0 0 0 0 0 | * 2 * * * * * * | 1 1 0 0 0
... xx. ...&#x  | 2 2 0 | 0 1 2 1 0 0 0 | * * 8 * * * * * | 0 1 1 0 0
xux ... ...&#xt | 2 2 2 | 1 0 2 0 2 1 0 | * * * 4 * * * * | 0 0 2 0 0
... .x.4.o.     | 0 4 0 | 0 0 0 4 0 0 0 | * * * * 2 * * * | 0 1 0 1 0
... .xx ...&#x  | 0 2 2 | 0 0 0 1 2 0 1 | * * * * * 8 * * | 0 0 1 1 0
..x ..x ...     | 0 0 4 | 0 0 0 0 0 2 2 | * * * * * * 4 * | 0 0 1 0 1
... ..x4..o     | 0 0 4 | 0 0 0 0 0 0 4 | * * * * * * * 2 | 0 0 0 1 1
----------------+-------+---------------+-----------------+----------
x.. x..4o..     ♦ 8 0 0 | 4 8 0 0 0 0 0 | 4 2 0 0 0 0 0 0 | 1 * * * *
... xx.4oo.&#x  ♦ 4 4 0 | 0 4 4 4 0 0 0 | 0 1 4 0 1 0 0 0 | * 2 * * *
xux xxx ...&#xt ♦ 4 4 4 | 2 2 4 2 4 2 2 | 1 0 2 2 0 2 1 0 | * * 4 * *
... .xx4.oo&#x  ♦ 0 4 4 | 0 0 0 4 4 0 4 | 0 0 0 0 1 4 0 1 | * * * 2 *
..x ..x4..o     ♦ 0 0 8 | 0 0 0 0 0 4 8 | 0 0 0 0 0 0 4 2 | * * * * 1

or
o.. o..4o..      & | 16 * | 1  2  1 0 | 2 1  2 1 0 | 1 1 2
.o. .o.4.o.        |  * 8 | 0  0  2 2 | 0 0  4 1 1 | 0 2 2
-------------------+------+-----------+------------+------
x.. ... ...      & |  2 0 | 8  *  * * | 2 0  0 1 0 | 1 0 2
... x.. ...      & |  2 0 | * 16  * * | 1 1  1 0 0 | 1 1 1
oo. oo.4oo.&#x   & |  1 1 | *  * 16 * | 0 0  2 1 0 | 0 1 2
... .x. ...        |  0 2 | *  *  * 8 | 0 0  2 0 1 | 0 2 1
-------------------+------+-----------+------------+------
x.. x.. ...      & |  4 0 | 2  2  0 0 | 8 *  * * * | 1 0 1
... x..4o..      & |  4 0 | 0  4  0 0 | * 4  * * * | 1 1 0
... xx. ...&#x   & |  2 2 | 0  1  2 1 | * * 16 * * | 0 1 1
xux ... ...&#xt    |  4 2 | 2  0  4 0 | * *  * 4 * | 0 0 2
... .x.4.o.        |  0 4 | 0  0  0 4 | * *  * * 2 | 0 2 0
-------------------+------+-----------+------------+------
x.. x..4o..      & ♦  8 0 | 4  8  0 0 | 4 2  0 0 0 | 2 * *
... xx.4oo.&#x   & ♦  4 4 | 0  4  4 4 | 0 1  4 0 1 | * 4 *
xux xxx ...&#xt    ♦  8 4 | 4  4  8 2 | 2 0  4 2 0 | * * 4
```