Acronym owoct
Name octagon octahedron duoprism
Circumradius sqrt[(3+sqrt(2))/2] = 1.485633
Confer
more general:
n,oct-dip  
general polytopal classes:
segmentotera  

Incidence matrix according to Dynkin symbol

x8o x3o4o

. . . . . | 48 |  2  4 | 1  8  4 |  4  8 1 | 4 2
----------+----+-------+---------+---------+----
x . . . . |  2 | 48  * | 1  4  0 |  4  4 0 | 4 1
. . x . . |  2 |  * 96 | 0  2  2 |  1  4 1 | 2 2
----------+----+-------+---------+---------+----
x8o . . . |  8 |  8  0 | 6  *  * |  4  0 0 | 4 0
x . x . . |  4 |  2  2 | * 96  * |  1  2 0 | 2 1
. . x3o . |  3 |  0  3 | *  * 64 |  0  2 1 | 1 2
----------+----+-------+---------+---------+----
x8o x . .  16 | 16  8 | 2  8  0 | 12  * * | 2 0
x . x3o .   6 |  3  6 | 0  3  2 |  * 64 * | 1 1
. . x3o4o   6 |  0 12 | 0  0  8 |  *  * 8 | 0 2
----------+----+-------+---------+---------+----
x8o x3o .  24 | 24 24 | 3 24  8 |  3  8 0 | 8 *
x . x3o4o  12 |  6 24 | 0 12 16 |  0  8 2 | * 8

x4x x3o4o

. . . . . | 48 |  1  1  4 | 1  4  4  4 |  4  4  4 1 | 4 1 1
----------+----+----------+------------+------------+------
x . . . . |  2 | 24  *  * | 1  4  0  0 |  4  4  0 0 | 4 1 0
. x . . . |  2 |  * 24  * | 1  0  4  0 |  4  0  4 0 | 4 0 1
. . x . . |  2 |  *  * 96 | 0  1  1  2 |  1  2  2 1 | 2 1 1
----------+----+----------+------------+------------+------
x4x . . . |  8 |  4  4  0 | 6  *  *  * |  4  0  0 0 | 4 0 0
x . x . . |  4 |  2  0  2 | * 48  *  * |  1  2  0 0 | 2 1 0
. x x . . |  4 |  0  2  2 | *  * 48  * |  1  0  2 0 | 2 0 1
. . x3o . |  3 |  0  0  3 | *  *  * 64 |  0  1  1 1 | 1 1 1
----------+----+----------+------------+------------+------
x4x x . .  16 |  8  8  8 | 2  4  4  0 | 12  *  * * | 2 0 0
x . x3o .   6 |  3  0  6 | 0  3  0  2 |  * 32  * * | 1 1 0
. x x3o .   6 |  0  3  6 | 0  0  3  2 |  *  * 32 * | 1 0 1
. . x3o4o   6 |  0  0 12 | 0  0  0  8 |  *  *  * 8 | 0 1 1
----------+----+----------+------------+------------+------
x4x x3o .  24 | 12 12 24 | 3 12 12  8 |  3  4  4 0 | 8 * *
x . x3o4o  12 |  6  0 24 | 0 12  0 16 |  0  8  0 2 | * 4 *
. x x3o4o  12 |  0  6 24 | 0  0 12 16 |  0  0  8 2 | * * 4

x8o o3x3o

. . . . . | 48 |  2  4 | 1  8  2  2 |  4  4  4 1 | 2 2 2
----------+----+-------+------------+------------+------
x . . . . |  2 | 48  * | 1  4  0  0 |  4  2  2 0 | 2 2 1
. . . x . |  2 |  * 96 | 0  2  1  1 |  1  2  2 1 | 1 1 2
----------+----+-------+------------+------------+------
x8o . . . |  8 |  8  0 | 6  *  *  * |  4  0  0 0 | 2 2 0
x . . x . |  4 |  2  2 | * 96  *  * |  1  1  1 0 | 1 1 1
. . o3x . |  3 |  0  3 | *  * 32  * |  0  2  0 1 | 1 0 2
. . . x3o |  3 |  0  3 | *  *  * 32 |  0  0  2 1 | 0 1 2
----------+----+-------+------------+------------+------
x8o . x .  16 | 16  8 | 2  8  0  0 | 12  *  * * | 1 1 0
x . o3x .   6 |  3  6 | 0  3  2  0 |  * 32  * * | 1 0 1
x . . x3o   6 |  3  6 | 0  3  0  2 |  *  * 32 * | 0 1 1
. . o3x3o   6 |  0 12 | 0  0  4  4 |  *  *  * 8 | 0 0 2
----------+----+-------+------------+------------+------
x8o o3x .  24 | 24 24 | 3 24  8  0 |  3  8  0 0 | 4 * *
x8o . x3o  24 | 24 24 | 3 24  0  8 |  3  0  8 0 | * 4 *
x . o3x3o  12 |  6 24 | 0 12  8  8 |  0  4  4 2 | * * 8

x4x o3x3o

. . . . . | 48 |  1  1  4 | 1  4  4  2  2 |  4  2  2  2  2 1 | 2 2 1 1
----------+----+----------+---------------+------------------+--------
x . . . . |  2 | 24  *  * | 1  4  0  0  0 |  4  2  2  0  0 0 | 2 2 1 0
. x . . . |  2 |  * 24  * | 1  0  4  0  0 |  4  0  0  2  2 0 | 2 2 0 1
. . . x . |  2 |  *  * 96 | 0  1  1  1  1 |  1  1  1  1  1 1 | 1 1 1 1
----------+----+----------+---------------+------------------+--------
x4x . . . |  8 |  4  4  0 | 6  *  *  *  * |  4  0  0  0  0 0 | 2 2 0 0
x . . x . |  4 |  2  0  2 | * 48  *  *  * |  1  1  1  0  0 0 | 1 1 1 0
. x . x . |  4 |  0  2  2 | *  * 48  *  * |  1  0  0  1  1 0 | 1 1 0 1
. . o3x . |  3 |  0  0  3 | *  *  * 32  * |  0  1  0  1  0 1 | 1 0 1 1
. . . x3o |  3 |  0  0  3 | *  *  *  * 32 |  0  0  1  0  1 1 | 0 1 1 1
----------+----+----------+---------------+------------------+--------
x4x . x .  16 |  8  8  8 | 2  4  4  0  0 | 12  *  *  *  * * | 1 1 0 0
x . o3x .   6 |  3  0  6 | 0  3  0  2  0 |  * 16  *  *  * * | 1 0 1 0
x . . x3o   6 |  3  0  6 | 0  3  0  0  2 |  *  * 16  *  * * | 0 1 1 0
. x o3x .   6 |  0  3  6 | 0  0  3  2  0 |  *  *  * 16  * * | 1 0 0 1
. x . x3o   6 |  0  3  6 | 0  0  3  0  2 |  *  *  *  * 16 * | 0 1 0 1
. . o3x3o   6 |  0  0 12 | 0  0  0  4  4 |  *  *  *  *  * 8 | 0 0 1 1
----------+----+----------+---------------+------------------+--------
x4x o3x .  24 | 12 12 24 | 3 12 12  8  0 |  3  4  0  4  0 0 | 4 * * *
x4x . x3o  24 | 12 12 24 | 3 12 12  0  8 |  3  0  4  0  4 0 | * 4 * *
x . o3x3o  12 |  6  0 24 | 0 12  0  8  8 |  0  4  4  0  0 2 | * * 4 *
. x o3x3o  12 |  0  6 24 | 0  0 12  8  8 |  0  0  0  4  4 2 | * * * 4

xo3ox xx8oo&#x   → height = sqrt(2/3) = 0.816497
(todip || {3}-gyro todip)

o.3o. o.8o.    | 24  * |  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 .o8.o    |  * 24 |  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 | 24  *  *  *  * | 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 |  * 24  *  *  * | 0  2 1  0  0  2 0  0 0 | 1 2 0  2  1 2 0 0 | 1 2 2 1 0
oo3oo oo8oo&#x |  1  1 |  *  * 48  *  * | 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 |  *  *  * 24  * | 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 |  *  *  *  * 24 | 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 | 8  * *  *  *  * *  * * | 2 0 1  0  0 0 0 0 | 1 2 0 0 0
x. .. x. ..    |  4  0 |  2  2  0  0  0 | * 24 *  *  *  * *  * * | 1 1 0  1  0 0 0 0 | 1 1 1 0 0
.. .. x.8o.    |  8  0 |  0  8  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 | *  * * 24  *  * *  * * | 0 0 1  2  0 0 0 0 | 0 2 1 0 0
.. ox .. ..&#x |  1  2 |  0  0  2  1  0 | *  * *  * 24  * *  * * | 0 0 1  0  2 0 0 0 | 0 2 0 1 0
.. .. xx ..&#x |  2  2 |  0  1  2  0  1 | *  * *  *  * 48 *  * * | 0 0 0  1  1 1 0 0 | 0 1 1 1 0
.o3.x .. ..    |  0  3 |  0  0  0  3  0 | *  * *  *  *  * 8  * * | 0 0 1  0  0 0 2 0 | 0 2 0 0 1
.. .x .x ..    |  0  4 |  0  0  0  2  2 | *  * *  *  *  * * 24 * | 0 0 0  0  1 0 1 1 | 0 1 0 1 1
.. .. .x8.o    |  0  8 |  0  0  0  0  8 | *  * *  *  *  * *  * 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 | 8 * *  *  * * * * | 1 1 0 0 0
x. .. x.8o.     16  0 |  8 16  0  0  0 | 0  8 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 | * * 8  *  * * * * | 0 2 0 0 0
xo .. xx ..&#x   4  2 |  2  2  4  0  1 | 0  1 0  2  0  2 0  0 0 | * * * 24  * * * * | 0 1 1 0 0
.. ox xx ..&#x   2  4 |  0  1  4  2  2 | 0  0 0  0  2  2 0  1 0 | * * *  * 24 * * * | 0 1 0 1 0
.. .. xx8oo&#x   8  8 |  0  8  8  0  8 | 0  0 1  0  0  8 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 | * * *  *  * * 8 * | 0 1 0 0 1
.. .x .x8.o      0 16 |  0  0  0  8 16 | 0  0 0  0  0  0 0  8 2 | * * *  *  * * * 3 | 0 0 0 1 1
---------------+-------+----------------+------------------------+-------------------+----------
x.3o. x.8o.     24  0 | 24 24  0  0  0 | 8 24 3  0  0  0 0  0 0 | 8 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 | * 8 * * *
xo .. xx8oo&#x  16  8 |  8 16 16  0  8 | 0  8 2  8  0 16 0  0 1 | 0 1 0  8  0 2 0 0 | * * 3 * *
.. ox xx8oo&#x   8 16 |  0  8 16  8 16 | 0  0 1  0  8 16 0  8 2 | 0 0 0  0  8 2 0 1 | * * * 3 *
.o3.x .x8.o      0 24 |  0  0  0 24 24 | 0  0 0  0  0  0 8 24 3 | 0 0 0  0  0 0 8 3 | * * * * 1

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