Acronym n,oct-dip Name n-gon - octahedron duoprism Circumradius sqrt[1/2+1/(4 sin2(π/n))] Especially troct (n=3)   squoct (n=4)   poct (n=5)   hoct (n=6)   owoct (n=8)

Incidence matrix according to Dynkin symbol

```xno x3o4o   (n>2)

. . . . . | 6n |  2   4 | 1   8  4 |  4  8 1 | 4 2
----------+----+--------+----------+---------+----
x . . . . |  2 | 6n   * | 1   4  0 |  4  4 0 | 4 1
. . x . . |  2 |  * 12n | 0   2  2 |  1  4 1 | 2 2
----------+----+--------+----------+---------+----
xno . . . |  n |  n   0 | 6   *  * |  4  0 0 | 4 0
x . x . . |  4 |  2   2 | * 12n  * |  1  2 0 | 2 1
. . x3o . |  3 |  0   3 | *   * 8n |  0  2 1 | 1 2
----------+----+--------+----------+---------+----
xno x . . ♦ 2n | 2n   n | 2   n  0 | 12  * * | 2 0
x . x3o . ♦  6 |  3   6 | 0   3  2 |  * 8n * | 1 1
. . x3o4o ♦  6 |  0  12 | 0   0  8 |  *  * n | 0 2
----------+----+--------+----------+---------+----
xno x3o . ♦ 3n | 3n  3n | 3  3n  n |  3  n 0 | 8 *
x . x3o4o ♦ 12 |  6  24 | 0  12 16 |  0  8 2 | * n
```

```xno o3x3o   (n>2)

. . . . . | 6n |  2   4 | 1   8  2  2 |  4  4  4 1 | 2 2 2
----------+----+--------+-------------+------------+------
x . . . . |  2 | 6n   * | 1   4  0  0 |  4  2  2 0 | 2 2 1
. . . x . |  2 |  * 12n | 0   2  1  1 |  1  2  2 1 | 1 1 2
----------+----+--------+-------------+------------+------
xno . . . |  n |  n   0 | 6   *  *  * |  4  0  0 0 | 2 2 0
x . . x . |  4 |  2   2 | * 12n  *  * |  1  1  1 0 | 1 1 1
. . o3x . |  3 |  0   3 | *   * 4n  * |  0  2  0 1 | 1 0 2
. . . x3o |  3 |  0   3 | *   *  * 4n |  0  0  2 1 | 0 1 2
----------+----+--------+-------------+------------+------
xno . x . ♦ 2n | 2n   n | 2   n  0  0 | 12  *  * * | 1 1 0
x . o3x . ♦  6 |  3   6 | 0   3  2  0 |  * 4n  * * | 1 0 1
x . . x3o ♦  6 |  3   6 | 0   3  0  2 |  *  * 4n * | 0 1 1
. . o3x3o ♦  6 |  0  12 | 0   0  4  4 |  *  *  * n | 0 0 2
----------+----+--------+-------------+------------+------
xno o3x . ♦ 3n | 3n  3n | 3  3n  n  0 |  3  n  0 0 | 4 * *
xno . x3o ♦ 3n | 3n  3n | 3  3n  0  n |  3  0  n 0 | * 4 *
x . o3x3o ♦ 12 |  6  24 | 0  12  8  8 |  0  4  4 2 | * * n
```

```xo3ox xxnoo&#x   (n>2)   → height = sqrt(2/3) = 0.816497
(3,n-dip || (dual 3),n-dip)

o.3o. o.no.    | 3n  * |  2  2  2  0  0 | 1  4 1  2  1  4 0  0 0 | 2 2 1  4  2 2 0 0 | 1 2 2 1 0
.o3.o .on.o    |  * 3n |  0  0  2  2  2 | 0  0 0  1  2  4 1  4 1 | 0 0 1  2  4 2 2 2 | 0 2 1 2 1
---------------+-------+----------------+------------------------+-------------------+----------
x. .. .. ..    |  2  0 | 3n  *  *  *  * | 1  2 0  1  0  0 0  0 0 | 2 1 1  2  0 0 0 0 | 1 2 1 0 0
.. .. x. ..    |  2  0 |  * 3n  *  *  * | 0  2 1  0  0  2 0  0 0 | 1 2 0  2  1 2 0 0 | 1 2 2 1 0
oo3oo oonoo&#x |  1  1 |  *  * 6n  *  * | 0  0 0  1  1  2 0  0 0 | 0 0 1  2  2 1 0 0 | 0 1 1 1 0
.. .x .. ..    |  0  2 |  *  *  * 3n  * | 0  0 0  0  1  0 1  2 0 | 0 0 1  0  2 0 2 1 | 0 2 0 1 1
.. .. .x ..    |  0  2 |  *  *  *  * 3n | 0  0 0  0  0  2 0  2 1 | 0 0 0  1  2 2 1 2 | 0 2 1 2 1
---------------+-------+----------------+------------------------+-------------------+----------
x.3o. .. ..    |  3  0 |  3  0  0  0  0 | n  * *  *  *  * *  * * | 2 0 1  0  0 0 0 0 | 1 2 0 0 0
x. .. x. ..    |  4  0 |  2  2  0  0  0 | * 3n *  *  *  * *  * * | 1 1 0  1  0 0 0 0 | 1 1 1 0 0
.. .. x.no.    |  n  0 |  0  n  0  0  0 | *  * 3  *  *  * *  * * | 0 2 0  0  0 2 0 0 | 1 0 2 1 0
xo .. .. ..&#x |  2  1 |  1  0  2  0  0 | *  * * 3n  *  * *  * * | 0 0 1  2  0 0 0 0 | 0 2 1 0 0
.. ox .. ..&#x |  1  2 |  0  0  2  1  0 | *  * *  * 3n  * *  * * | 0 0 1  0  2 0 0 0 | 0 2 0 1 0
.. .. xx ..&#x |  2  2 |  0  1  2  0  1 | *  * *  *  * 6n *  * * | 0 0 0  1  1 1 0 0 | 0 1 1 1 0
.o3.x .. ..    |  0  3 |  0  0  0  3  0 | *  * *  *  *  * n  * * | 0 0 1  0  0 0 2 0 | 0 2 0 0 1
.. .x .x ..    |  0  4 |  0  0  0  2  2 | *  * *  *  *  * * 3n * | 0 0 0  0  1 0 1 1 | 0 1 0 1 1
.. .. .xn.o    |  0  n |  0  0  0  0  n | *  * *  *  *  * *  * 3 | 0 0 0  0  0 2 0 2 | 0 0 1 2 1
---------------+-------+----------------+------------------------+-------------------+----------
x.3o. x. ..    ♦  6  0 |  6  3  0  0  0 | 2  3 0  0  0  0 0  0 0 | n * *  *  * * * * | 1 1 0 0 0
x. .. x.no.    ♦ 2n  0 |  n 2n  0  0  0 | 0  n 2  0  0  0 0  0 0 | * 3 *  *  * * * * | 1 0 1 0 0
xo3ox .. ..&#x ♦  3  3 |  3  0  6  3  0 | 1  0 0  3  3  0 1  0 0 | * * n  *  * * * * | 0 2 0 0 0
xo .. xx ..&#x ♦  4  2 |  2  2  4  0  1 | 0  1 0  2  0  2 0  0 0 | * * * 3n  * * * * | 0 1 1 0 0
.. ox xx ..&#x ♦  2  4 |  0  1  4  2  2 | 0  0 0  0  2  2 0  1 0 | * * *  * 3n * * * | 0 1 0 1 0
.. .. xxnoo&#x ♦  n  n |  0  n  n  0  n | 0  0 1  0  0  n 0  0 1 | * * *  *  * 6 * * | 0 0 1 1 0
.o3.x .x ..    ♦  0  6 |  0  0  0  6  3 | 0  0 0  0  0  0 2  3 0 | * * *  *  * * n * | 0 1 0 0 1
.. .x .xn.o    ♦  0 2n |  0  0  0  n 2n | 0  0 0  0  0  0 0  n 2 | * * *  *  * * * 3 | 0 0 0 1 1
---------------+-------+----------------+------------------------+-------------------+----------
x.3o. x.no.    ♦ 3n  0 | 3n 3n  0  0  0 | n 3n 3  0  0  0 0  0 0 | n 3 0  0  0 0 0 0 | 1 * * * *
xo3ox xx ..&#x ♦  6  6 |  6  6  6  6  6 | 2  3 0  6  6  6 2  3 0 | 1 0 2  3  3 0 1 0 | * n * * *
xo .. xxnoo&#x ♦ 2n  n |  n 2n 2n  0  n | 0  n 2  n  0 2n 0  0 1 | 0 1 0  n  0 2 0 0 | * * 3 * *
.. ox xxnoo&#x ♦  n 2n |  0  n 2n  n 2n | 0  0 1  0  n 2n 0  n 2 | 0 0 0  0  n 2 0 1 | * * * 3 *
.o3.x .xn.o    ♦  0 3n |  0  0  0 3n 3n | 0  0 0  0  0  0 n 3n 3 | 0 0 0  0  0 0 n 3 | * * * * 1
```