Acronym otet Name octagon-tetrahedron duoprism Circumradius sqrt[(11+4 sqrt(2))/8] = 1.442951 Confer n,tet-dip

Incidence matrix according to Dynkin symbol

```x8o x3o3o

. . . . . | 32 |  2  3 | 1  6  3 | 3  6 1 | 3 2
----------+----+-------+---------+--------+----
x . . . . |  2 | 32  * | 1  3  0 | 3  3 0 | 3 1
. . x . . |  2 |  * 48 | 0  2  2 | 1  4 1 | 2 2
----------+----+-------+---------+--------+----
x8o . . . |  8 |  8  0 | 4  *  * | 3  0 0 | 3 0
x . x . . |  4 |  2  2 | * 48  * | 1  2 0 | 2 1
. . x3o . |  3 |  0  3 | *  * 32 | 0  2 1 | 1 2
----------+----+-------+---------+--------+----
x8o x . . ♦ 16 | 16  8 | 2  8  0 | 6  * * | 2 0
x . x3o . ♦  6 |  3  6 | 0  3  2 | * 32 * | 1 1
. . x3o3o ♦  4 |  0  6 | 0  0  4 | *  * 8 | 0 2
----------+----+-------+---------+--------+----
x8o x3o . ♦ 24 | 24 24 | 3 24  8 | 3  8 0 | 4 *
x . x3o3o ♦  8 |  4 12 | 0  6  8 | 0  4 2 | * 8
```

```x4x x3o3o

. . . . . | 32 |  1  1  3 | 1  3  3  3 | 3  3  3 1 | 3 1 1
----------+----+----------+------------+-----------+------
x . . . . |  2 | 16  *  * | 1  3  0  0 | 3  3  0 0 | 3 1 0
. x . . . |  2 |  * 16  * | 1  0  3  0 | 3  0  3 0 | 3 0 1
. . x . . |  2 |  *  * 48 | 0  1  1  2 | 1  2  2 1 | 2 1 1
----------+----+----------+------------+-----------+------
x4x . . . |  8 |  4  4  0 | 4  *  *  * | 3  0  0 0 | 3 0 0
x . x . . |  4 |  2  0  2 | * 24  *  * | 1  2  0 0 | 2 1 0
. x x . . |  4 |  0  2  2 | *  * 24  * | 1  0  2 0 | 2 0 1
. . x3o . |  3 |  0  0  3 | *  *  * 32 | 0  1  1 1 | 1 1 1
----------+----+----------+------------+-----------+------
x4x x . . ♦ 16 |  8  8  8 | 2  4  4  0 | 6  *  * * | 2 0 0
x . x3o . ♦  6 |  3  0  6 | 0  3  0  2 | * 16  * * | 1 1 0
. x x3o . ♦  6 |  0  3  6 | 0  0  3  2 | *  * 16 * | 1 0 1
. . x3o3o ♦  4 |  0  0  6 | 0  0  0  4 | *  *  * 8 | 0 1 1
----------+----+----------+------------+-----------+------
x4x x3o . ♦ 24 | 12 12 24 | 3 12 12  8 | 3  4  4 0 | 4 * *
x . x3o3o ♦  8 |  4  0 12 | 0  6  0  8 | 0  4  0 2 | * 4 *
. x x3o3o ♦  8 |  0  4 12 | 0  0  6  8 | 0  0  4 2 | * * 4
```

```ox3oo xx8oo&#x   → height = sqrt(2/3) = 0.816497
({8} || todip)

o.3o. o.8o.    | 8  * | 2  3  0  0 | 1  3  6 0  0 0 | 1  6 3 0 0 | 2 3 0
.o3.o .o8.o    | * 24 | 0  1  2  2 | 0  2  2 1  4 1 | 1  4 1 2 2 | 2 2 1
---------------+------+------------+----------------+------------+------
.. .. x. ..    | 2  0 | 8  *  *  * | 1  0  3 0  0 0 | 0  3 3 0 0 | 1 3 0
oo3oo oo8oo&#x | 1  1 | * 24  *  * | 0  2  2 0  0 0 | 1  4 1 0 0 | 2 2 0
.x .. .. ..    | 0  2 | *  * 24  * | 0  1  0 1  2 0 | 1  2 0 2 1 | 2 1 1
.. .. .x ..    | 0  2 | *  *  * 24 | 0  0  1 0  2 1 | 0  2 1 1 2 | 1 2 1
---------------+------+------------+----------------+------------+------
.. .. x.8o.    | 8  0 | 8  0  0  0 | 1  *  * *  * * | 0  0 3 0 0 | 0 3 0
ox .. .. ..&#x | 1  2 | 0  2  1  0 | * 24  * *  * * | 1  2 0 0 0 | 2 1 0
.. .. xx ..&#x | 2  2 | 1  2  0  1 | *  * 24 *  * * | 0  2 1 0 0 | 1 2 0
.x3.o .. ..    | 0  3 | 0  0  3  0 | *  *  * 8  * * | 1  0 0 2 0 | 2 0 1
.x .. .x ..    | 0  4 | 0  0  2  2 | *  *  * * 24 * | 0  1 0 1 1 | 1 1 1
.. .. .x8.o    | 0  8 | 0  0  0  8 | *  *  * *  * 3 | 0  0 1 0 2 | 0 2 1
---------------+------+------------+----------------+------------+------
ox3oo .. ..&#x ♦ 1  3 | 0  3  3  0 | 0  3  0 1  0 0 | 8  * * * * | 2 0 0
ox .. xx ..&#x ♦ 2  4 | 1  4  2  2 | 0  2  2 0  1 0 | * 24 * * * | 1 1 0
.. .. xx8oo&#x ♦ 8  8 | 8  8  0  8 | 1  0  8 0  0 1 | *  * 3 * * | 0 2 0
.x3.o .x ..    ♦ 0  6 | 0  0  6  3 | 0  0  0 2  3 0 | *  * * 8 * | 1 0 1
.x .. .x8.o    ♦ 0 16 | 0  0  8 16 | 0  0  0 0  8 2 | *  * * * 3 | 0 1 1
---------------+------+------------+----------------+------------+------
ox3oo xx ..    ♦ 2  6 | 1  6  6  3 | 0  6  3 2  3 0 | 2  3 0 1 0 | 8 * *
ox .. xx8oo&#x ♦ 8 16 | 8 16  8 16 | 1  8 16 0  8 2 | 0  8 2 0 1 | * 3 *
.x3.o .x8.o    ♦ 0 24 | 0  0 24 24 | 0  0  0 8 24 3 | 0  0 0 8 3 | * * 1
```

```ox xo xx8oo&#x   → height = 1/sqrt(2) = 0.707107
(op || lacing-ortho op)

o. o. o.no.    | 16  * | 1  2  2 0  0 | 2 1  1  2  4 0 0 | 1 1  2  4 2 0 | 2 1 2
.o .o .on.o    |  * 16 | 0  0  2 1  2 | 0 0  2  1  4 2 1 | 0 1  4  2 2 1 | 2 2 1
---------------+-------+--------------+------------------+---------------+------
.. x. .. ..    |  2  0 | 8  *  * *  * | 2 0  0  2  0 0 0 | 1 1  0  2 0 0 | 2 0 2
.. .. x. ..    |  2  0 | * 16  * *  * | 1 1  0  0  2 0 0 | 1 0  1  2 2 0 | 1 1 2
oo oo oonoo&#x |  1  1 | *  * 32 *  * | 0 0  1  1  2 0 0 | 0 1  2  2 1 0 | 2 1 1
.x .. .. ..    |  0  2 | *  *  * 8  * | 0 0  2  0  0 2 0 | 0 1  4  0 0 1 | 2 2 0
.. .. .x ..    |  0  2 | *  *  * * 16 | 0 0  0  0  2 1 1 | 0 0  2  1 2 1 | 1 2 1
---------------+-------+--------------+------------------+---------------+------
.. x. x. ..    |  4  0 | 2  2  0 0  0 | 8 *  *  *  * * * | 1 0  0  2 0 0 | 1 0 2
.. .. x.no.    |  8  0 | 0  8  0 0  0 | * 2  *  *  * * * | 1 0  0  0 2 0 | 0 1 2
ox .. .. ..&#x |  1  2 | 0  0  2 1  0 | * * 16  *  * * * | 0 1  2  0 0 0 | 2 1 0
.. xo .. ..&#x |  2  1 | 1  0  2 0  0 | * *  * 16  * * * | 0 1  0  2 0 0 | 2 0 1
.. .. xx ..&#x |  2  2 | 0  1  2 0  1 | * *  *  * 32 * * | 0 0  1  1 1 0 | 1 1 1
.x .. .x ..    |  0  4 | 0  0  0 2  2 | * *  *  *  * 8 * | 0 0  2  0 0 1 | 1 2 0
.. .. .xn.o    |  0  8 | 0  0  0 0  8 | * *  *  *  * * 2 | 0 0  0  0 2 1 | 0 2 1
---------------+-------+--------------+------------------+---------------+------
.. x. x.no.    ♦ 16  0 | 8 16  0 0  0 | 8 2  0  0  0 0 0 | 1 *  *  * * * | 0 0 2
ox xo .. ..&#x ♦  2  2 | 1  0  4 1  0 | 0 0  2  2  0 0 0 | * 8  *  * * * | 2 0 0
ox .. xx ..&#x ♦  2  4 | 0  1  4 2  2 | 0 0  2  0  2 1 0 | * * 16  * * * | 1 1 0
.. xo xx ..&#x ♦  4  2 | 2  2  4 0  1 | 1 0  0  2  2 0 0 | * *  * 16 * * | 1 0 1
.. .. xxnoo&#x ♦  8  8 | 0  8  8 0  8 | 0 1  0  0  8 0 1 | * *  *  * 4 * | 0 1 1
.x .. .xn.o    ♦  0 16 | 0  0  0 8 16 | 0 0  0  0  0 8 2 | * *  *  * * 1 | 0 2 0
---------------+-------+--------------+------------------+---------------+------
ox xo xx ..&#x ♦  4  4 | 2  2  8 2  2 | 1 0  4  4  4 1 0 | 0 2  2  2 0 0 | 8 * *
ox .. xxnoo&#x ♦  8 16 | 0  8 16 8 16 | 0 1  8  0 16 8 2 | 0 0  8  0 2 1 | * 2 *
.. xo xxnoo&#x ♦ 16  8 | 8 16 16 0  8 | 8 2  0  8 16 0 1 | 1 0  0  8 2 0 | * * 2
```