Acronym hoct
Name hexagon octahedron duoprism
Circumradius sqrt(3/2) = 1.224745
Confer
more general:
n,oct-dip  
related segmentotera:
hisquippy  
general polytopal classes:
segmentotera  

Incidence matrix according to Dynkin symbol

x6o x3o4o

. . . . . | 36 |  2  4 | 1  8  4 |  4  8 1 | 4 2
----------+----+-------+---------+---------+----
x . . . . |  2 | 36  * | 1  4  0 |  4  4 0 | 4 1
. . x . . |  2 |  * 72 | 0  2  2 |  1  4 1 | 2 2
----------+----+-------+---------+---------+----
x6o . . . |  6 |  6  0 | 6  *  * |  4  0 0 | 4 0
x . x . . |  4 |  2  2 | * 72  * |  1  2 0 | 2 1
. . x3o . |  3 |  0  3 | *  * 48 |  0  2 1 | 1 2
----------+----+-------+---------+---------+----
x6o x . .  12 | 12  6 | 2  6  0 | 12  * * | 2 0
x . x3o .   6 |  3  6 | 0  3  2 |  * 48 * | 1 1
. . x3o4o   6 |  0 12 | 0  0  8 |  *  * 6 | 0 2
----------+----+-------+---------+---------+----
x6o x3o .  18 | 18 18 | 3 18  6 |  3  6 0 | 8 *
x . x3o4o  12 |  6 24 | 0 12 16 |  0  8 2 | * 6

x3x x3o4o

. . . . . | 36 |  1  1  4 | 1  4  4  4 |  4  4  4 1 | 4 1 1
----------+----+----------+------------+------------+------
x . . . . |  2 | 18  *  * | 1  4  0  0 |  4  4  0 0 | 4 1 0
. x . . . |  2 |  * 18  * | 1  0  4  0 |  4  0  4 0 | 4 0 1
. . x . . |  2 |  *  * 72 | 0  1  1  2 |  1  2  2 1 | 2 1 1
----------+----+----------+------------+------------+------
x3x . . . |  6 |  3  3  0 | 6  *  *  * |  4  0  0 0 | 4 0 0
x . x . . |  4 |  2  0  2 | * 36  *  * |  1  2  0 0 | 2 1 0
. x x . . |  4 |  0  2  2 | *  * 36  * |  1  0  2 0 | 2 0 1
. . x3o . |  3 |  0  0  3 | *  *  * 48 |  0  1  1 1 | 1 1 1
----------+----+----------+------------+------------+------
x3x x . .  12 |  6  6  6 | 2  3  3  0 | 12  *  * * | 2 0 0
x . x3o .   6 |  3  0  6 | 0  3  0  2 |  * 24  * * | 1 1 0
. x x3o .   6 |  0  3  6 | 0  0  3  2 |  *  * 24 * | 1 0 1
. . x3o4o   6 |  0  0 12 | 0  0  0  8 |  *  *  * 6 | 0 1 1
----------+----+----------+------------+------------+------
x3x x3o .  18 |  9  9 18 | 3  9  9  6 |  3  3  3 0 | 8 * *
x . x3o4o  12 |  6  0 24 | 0 12  0 16 |  0  8  0 2 | * 3 *
. x x3o4o  12 |  0  6 24 | 0  0 12 16 |  0  0  8 2 | * * 3

x6o o3x3o

. . . . . | 36 |  2  4 | 1  8  2  2 |  4  4  4 1 | 2 2 2
----------+----+-------+------------+------------+------
x . . . . |  2 | 36  * | 1  4  0  0 |  4  2  2 0 | 2 2 1
. . . x . |  2 |  * 72 | 0  2  1  1 |  1  2  2 1 | 1 1 2
----------+----+-------+------------+------------+------
x6o . . . |  6 |  6  0 | 6  *  *  * |  4  0  0 0 | 2 2 0
x . . x . |  4 |  2  2 | * 72  *  * |  1  1  1 0 | 1 1 1
. . o3x . |  3 |  0  3 | *  * 24  * |  0  2  0 1 | 1 0 2
. . . x3o |  3 |  0  3 | *  *  * 24 |  0  0  2 1 | 0 1 2
----------+----+-------+------------+------------+------
x6o . x .  12 | 12  6 | 2  6  0  0 | 12  *  * * | 1 1 0
x . o3x .   6 |  3  6 | 0  3  2  0 |  * 24  * * | 1 0 1
x . . x3o   6 |  3  6 | 0  3  0  2 |  *  * 24 * | 0 1 1
. . o3x3o   6 |  0 12 | 0  0  4  4 |  *  *  * 6 | 0 0 2
----------+----+-------+------------+------------+------
x6o o3x .  18 | 18 18 | 3 18  6  0 |  3  6  0 0 | 4 * *
x6o . x3o  18 | 18 18 | 3 18  0  6 |  3  0  6 0 | * 4 *
x . o3x3o  12 |  6 24 | 0 12  8  8 |  0  4  4 2 | * * 6

x3x o3x3o

. . . . . | 36 |  1  1  4 | 1  4  4  2  2 |  4  2  2  2  2 1 | 2 2 1 1
----------+----+----------+---------------+------------------+--------
x . . . . |  2 | 18  *  * | 1  4  0  0  0 |  4  2  2  0  0 0 | 2 2 1 0
. x . . . |  2 |  * 18  * | 1  0  4  0  0 |  4  0  0  2  2 0 | 2 2 0 1
. . . x . |  2 |  *  * 72 | 0  1  1  1  1 |  1  1  1  1  1 1 | 1 1 1 1
----------+----+----------+---------------+------------------+--------
x3x . . . |  6 |  3  3  0 | 6  *  *  *  * |  4  0  0  0  0 0 | 2 2 0 0
x . . x . |  4 |  2  0  2 | * 36  *  *  * |  1  1  1  0  0 0 | 1 1 1 0
. x . x . |  4 |  0  2  2 | *  * 36  *  * |  1  0  0  1  1 0 | 1 1 0 1
. . o3x . |  3 |  0  0  3 | *  *  * 24  * |  0  1  0  1  0 1 | 1 0 1 1
. . . x3o |  3 |  0  0  3 | *  *  *  * 24 |  0  0  1  0  1 1 | 0 1 1 1
----------+----+----------+---------------+------------------+--------
x3x . x .  12 |  6  6  6 | 2  3  3  0  0 | 12  *  *  *  * * | 1 1 0 0
x . o3x .   6 |  3  0  6 | 0  3  0  2  0 |  * 12  *  *  * * | 1 0 1 0
x . . x3o   6 |  3  0  6 | 0  3  0  0  2 |  *  * 12  *  * * | 0 1 1 0
. x o3x .   6 |  0  3  6 | 0  0  3  2  0 |  *  *  * 12  * * | 1 0 0 1
. x . x3o   6 |  0  3  6 | 0  0  3  0  2 |  *  *  *  * 12 * | 0 1 0 1
. . o3x3o   6 |  0  0 12 | 0  0  0  4  4 |  *  *  *  *  * 6 | 0 0 1 1
----------+----+----------+---------------+------------------+--------
x3x o3x .  18 |  9  9 18 | 3  9  9  6  0 |  3  3  0  3  0 0 | 4 * * *
x3x . x3o  18 |  9  9 18 | 3  9  9  0  6 |  3  0  3  0  3 0 | * 4 * *
x . o3x3o  12 |  6  0 24 | 0 12  0  8  8 |  0  4  4  0  0 2 | * * 3 *
. x o3x3o  12 |  0  6 24 | 0  0 12  8  8 |  0  0  0  4  4 2 | * * * 3

xo3ox xx6oo&#x   → height = sqrt(2/3) = 0.816497
(thiddip || {3}-gyro thiddip)

o.3o. o.6o.    | 18  * |  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 .o6.o    |  * 18 |  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 | 18  *  *  *  * | 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 |  * 18  *  *  * | 0  2 1  0  0  2 0  0 0 | 1 2 0  2  1 2 0 0 | 1 1 2 1 0
oo3oo oo6oo&#x |  1  1 |  *  * 36  *  * | 0  0 0  1  1  2 0  0 0 | 0 0 1  2  2 1 0 0 | 0 2 1 1 0
.. .x .. ..    |  0  2 |  *  *  * 18  * | 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 |  *  *  *  * 18 | 0  0 0  0  0  2 0  2 1 | 0 0 0  1  2 2 1 2 | 0 1 1 2 1
---------------+-------+----------------+------------------------+-------------------+----------
x.3o. .. ..    |  3  0 |  3  0  0  0  0 | 6  * *  *  *  * *  * * | 2 0 1  0  0 0 0 0 | 1 2 0 0 0
x. .. x. ..    |  4  0 |  2  2  0  0  0 | * 18 *  *  *  * *  * * | 1 1 0  1  0 0 0 0 | 1 1 1 0 0
.. .. x.6o.    |  6  0 |  0  6  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 | *  * * 18  *  * *  * * | 0 0 1  2  0 0 0 0 | 0 2 1 0 0
.. ox .. ..&#x |  1  2 |  0  0  2  1  0 | *  * *  * 18  * *  * * | 0 0 1  0  2 0 0 0 | 0 2 0 1 0
.. .. xx ..&#x |  2  2 |  0  1  2  0  1 | *  * *  *  * 36 *  * * | 0 0 0  1  1 1 0 0 | 0 1 1 1 0
.o3.x .. ..    |  0  3 |  0  0  0  3  0 | *  * *  *  *  * 6  * * | 0 0 1  0  0 0 2 0 | 0 2 0 0 1
.. .x .x ..    |  0  4 |  0  0  0  2  2 | *  * *  *  *  * * 18 * | 0 0 0  0  1 0 1 1 | 0 1 0 1 1
.. .. .x6.o    |  0  6 |  0  0  0  0  6 | *  * *  *  *  * *  * 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 | 6 * *  *  * * * * | 1 1 0 0 0
x. .. x.6o.     12  0 |  6 12  0  0  0 | 0  6 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 | * * 6  *  * * * * | 0 2 0 0 0
xo .. xx ..&#x   4  2 |  2  2  4  0  1 | 0  1 0  2  0  2 0  0 0 | * * * 18  * * * * | 0 1 1 0 0
.. ox xx ..&#x   2  4 |  0  1  4  2  2 | 0  0 0  0  2  2 0  1 0 | * * *  * 18 * * * | 0 1 0 1 0
.. .. xx6oo&#x   6  6 |  0  6  6  0  6 | 0  0 1  0  0  6 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 | * * *  *  * * 6 * | 0 1 0 0 1
.. .x .x6.o      0 12 |  0  0  0  6 12 | 0  0 0  0  0  0 0  6 2 | * * *  *  * * * 3 | 0 0 0 1 1
---------------+-------+----------------+------------------------+-------------------+----------
x.3o. x.6o.     18  0 | 18 18  0  0  0 | 6 18 3  0  0  0 0  0 0 | 6 3 0  0  0 0 0 0 | 1 * * * *
xo3ox xx ..&#x   6  6 |  6  3 12  6  3 | 2  3 0  6  6  6 2  3 0 | 1 0 2  3  3 0 1 0 | * 6 * * *
xo .. xx6oo&#x  12  6 |  6 12 12  0  6 | 0  6 2  6  0 12 0  0 1 | 0 1 0  6  0 2 0 0 | * * 3 * *
.. ox xx6oo&#x   6 12 |  0  6 12  6 12 | 0  0 1  0  6 12 0  6 2 | 0 0 0  0  6 2 0 1 | * * * 3 *
.o3.x .x6.o      0 18 |  0  0  0 18 18 | 0  0 0  0  0  0 6 18 3 | 0 0 0  0  0 0 6 3 | * * * * 1

xo3ox xx3xx&#x   → height = sqrt(2/3) = 0.816497
(thiddip || {3}-gyro thiddip)

o.3o. o.3o.    | 18  * |  2 1 1  2  0 0 0 | 1 2 2 1  2  1  2  2 0 0 0 0 | 1 1 2 1 2 2 1 1 2 0 0 0 | 1 1 1 2 1 0
.o3.o .o3.o    |  * 18 |  0 0 0  2  2 1 1 | 0 0 0 0  1  2  2  2 1 2 2 1 | 0 0 0 1 1 1 2 2 2 1 1 2 | 0 1 1 1 2 1
---------------+-------+------------------+-----------------------------+-------------------------+------------
x. .. .. ..    |  2  0 | 18 * *  *  * * * | 1 1 1 0  1  0  0  0 0 0 0 0 | 1 1 1 1 1 1 0 0 0 0 0 0 | 1 1 1 1 0 0
.. .. x. ..    |  2  0 |  * 9 *  *  * * * | 0 2 0 1  0  0  2  0 0 0 0 0 | 1 0 2 0 2 0 1 0 2 0 0 0 | 1 1 0 2 1 0
.. .. .. x.    |  2  0 |  * * 9  *  * * * | 0 0 2 1  0  0  0  2 0 0 0 0 | 0 1 2 0 0 2 0 1 2 0 0 0 | 1 0 1 2 1 0
oo3oo oo3oo&#x |  1  1 |  * * * 36  * * * | 0 0 0 0  1  1  1  1 0 0 0 0 | 0 0 0 1 1 1 1 1 1 0 0 0 | 0 1 1 1 1 0
.. .x .. ..    |  0  2 |  * * *  * 18 * * | 0 0 0 0  0  1  0  0 1 1 1 0 | 0 0 0 1 0 0 1 1 0 1 1 1 | 0 1 1 0 1 1
.. .. .x ..    |  0  2 |  * * *  *  * 9 * | 0 0 0 0  0  0  2  0 0 2 0 1 | 0 0 0 0 1 0 2 0 2 1 0 2 | 0 1 0 1 2 1
.. .. .. .x    |  0  2 |  * * *  *  * * 9 | 0 0 0 0  0  0  0  2 0 0 2 1 | 0 0 0 0 0 1 0 2 2 0 1 2 | 0 0 1 1 2 1
---------------+-------+------------------+-----------------------------+-------------------------+------------
x.3o. .. ..    |  3  0 |  3 0 0  0  0 0 0 | 6 * * *  *  *  *  * * * * * | 1 1 0 1 0 0 0 0 0 0 0 0 | 1 1 1 0 0 0
x. .. x. ..    |  4  0 |  2 2 0  0  0 0 0 | * 9 * *  *  *  *  * * * * * | 1 0 1 0 1 0 0 0 0 0 0 0 | 1 1 0 1 0 0
x. .. .. x.    |  4  0 |  2 0 2  0  0 0 0 | * * 9 *  *  *  *  * * * * * | 0 1 1 0 0 1 0 0 0 0 0 0 | 1 0 1 1 0 0
.. .. x.3x.    |  6  0 |  0 3 3  0  0 0 0 | * * * 3  *  *  *  * * * * * | 0 0 2 0 0 0 0 0 2 0 0 0 | 1 0 0 2 1 0
xo .. .. ..&#x |  2  1 |  1 0 0  2  0 0 0 | * * * * 18  *  *  * * * * * | 0 0 0 1 1 1 0 0 0 0 0 0 | 0 1 1 1 0 0
.. ox .. ..&#x |  1  2 |  0 0 0  2  1 0 0 | * * * *  * 18  *  * * * * * | 0 0 0 1 0 0 1 1 0 0 0 0 | 0 1 1 0 1 0
.. .. xx ..&#x |  2  2 |  0 1 0  2  0 1 0 | * * * *  *  * 18  * * * * * | 0 0 0 0 1 0 1 0 1 0 0 0 | 0 1 0 1 1 0
.. .. .. xx&#x |  2  2 |  0 0 1  2  0 0 1 | * * * *  *  *  * 18 * * * * | 0 0 0 0 0 1 0 1 1 0 0 0 | 0 0 1 1 1 0
.o3.x .. ..    |  0  3 |  0 0 0  0  3 0 0 | * * * *  *  *  *  * 6 * * * | 0 0 0 1 0 0 0 0 0 1 1 0 | 0 1 1 0 0 1
.. .x .x ..    |  0  4 |  0 0 0  0  2 2 0 | * * * *  *  *  *  * * 9 * * | 0 0 0 0 0 0 1 0 0 1 0 1 | 0 1 0 0 1 1
.. .x .. .x    |  0  4 |  0 0 0  0  2 0 2 | * * * *  *  *  *  * * * 9 * | 0 0 0 0 0 0 0 1 0 0 1 1 | 0 0 1 0 1 1
.. .. .x3.x    |  0  6 |  0 0 0  0  0 3 3 | * * * *  *  *  *  * * * * 3 | 0 0 0 0 0 0 0 0 2 0 0 2 | 0 0 0 1 2 1
---------------+-------+------------------+-----------------------------+-------------------------+------------
x.3o. x. ..      6  0 |  6 3 0  0  0 0 0 | 2 3 0 0  0  0  0  0 0 0 0 0 | 3 * * * * * * * * * * * | 1 1 0 0 0 0
x.3o. .. x.      6  0 |  6 0 3  0  0 0 0 | 2 0 3 0  0  0  0  0 0 0 0 0 | * 3 * * * * * * * * * * | 1 0 1 0 0 0
x. .. x.3x.     12  0 |  6 6 6  0  0 0 0 | 0 3 3 2  0  0  0  0 0 0 0 0 | * * 3 * * * * * * * * * | 1 0 0 1 0 0
xo3ox .. ..&#x   3  3 |  3 0 0  6  3 0 0 | 1 0 0 0  3  3  0  0 1 0 0 0 | * * * 6 * * * * * * * * | 0 1 1 0 0 0
xo .. xx ..&#x   4  2 |  2 2 0  4  0 1 0 | 0 1 0 0  2  0  2  0 0 0 0 0 | * * * * 9 * * * * * * * | 0 1 0 1 0 0
xo .. .. xx&#x   4  2 |  2 0 2  4  0 0 1 | 0 0 1 0  2  0  0  2 0 0 0 0 | * * * * * 9 * * * * * * | 0 0 1 1 0 0
.. ox xx ..&#x   2  4 |  0 1 0  4  2 2 0 | 0 0 0 0  0  2  2  0 0 1 0 0 | * * * * * * 9 * * * * * | 0 1 0 0 1 0
.. ox .. xx&#x   2  4 |  0 0 1  4  2 0 2 | 0 0 0 0  0  2  0  2 0 0 1 0 | * * * * * * * 9 * * * * | 0 0 1 0 1 0
.. .. xx3xx&#x   6  6 |  0 3 3  6  0 3 3 | 0 0 0 1  0  0  3  3 0 0 0 1 | * * * * * * * * 6 * * * | 0 0 0 1 1 0
.o3.x .x ..      0  6 |  0 0 0  0  6 3 0 | 0 0 0 0  0  0  0  0 2 3 0 0 | * * * * * * * * * 3 * * | 0 1 0 0 0 1
.o3.x .. .x      0  6 |  0 0 0  0  6 0 3 | 0 0 0 0  0  0  0  0 2 0 3 0 | * * * * * * * * * * 3 * | 0 0 1 0 0 1
.. .x .x3.x      0 12 |  0 0 0  0  6 6 6 | 0 0 0 0  0  0  0  0 0 3 3 2 | * * * * * * * * * * * 3 | 0 0 0 0 1 1
---------------+-------+------------------+-----------------------------+-------------------------+------------
x.3o. x.3x.     18  0 | 18 9 9  0  0 0 0 | 6 9 9 3  0  0  0  0 0 0 0 0 | 3 3 3 0 0 0 0 0 0 0 0 0 | 1 * * * * *
xo3ox xx ..&#x   6  6 |  6 3 0 12  6 3 0 | 2 3 0 0  6  6  6  0 2 3 0 0 | 1 0 0 2 3 0 3 0 0 1 0 0 | * 3 * * * *
xo3ox .. xx&#x   6  6 |  6 0 3 12  6 0 3 | 2 0 3 0  6  6  0  6 2 0 3 0 | 0 1 0 2 0 3 0 3 0 0 1 0 | * * 3 * * *
xo .. xx3xx&#x  12  6 |  6 6 6 12  0 3 3 | 0 3 3 2  6  0  6  6 0 0 0 1 | 0 0 1 0 3 3 0 0 2 0 0 0 | * * * 3 * *
.. ox xx3xx&#x   6 12 |  0 3 3 12  6 6 6 | 0 0 0 1  0  6  6  6 0 3 3 2 | 0 0 0 0 0 0 3 3 2 0 0 1 | * * * * 3 *
.o3.x .x3.x      0 18 |  0 0 0  0 18 9 9 | 0 0 0 0  0  0  0  0 6 9 9 3 | 0 0 0 0 0 0 0 0 0 3 3 3 | * * * * * 1

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