Acronym squoct
Name square-octahedron duoprism
Circumradius 1
Confer n,oct-dip  

Incidence matrix according to Dynkin symbol

x4o x3o4o

. . . . . | 24 |  2  4 | 1  8  4 |  4  8 1 | 4 2
----------+----+-------+---------+---------+----
x . . . . |  2 | 24  * | 1  4  0 |  4  4 0 | 4 1
. . x . . |  2 |  * 48 | 0  2  2 |  1  4 1 | 2 2
----------+----+-------+---------+---------+----
x4o . . . |  4 |  4  0 | 6  *  * |  4  0 0 | 4 0
x . x . . |  4 |  2  2 | * 48  * |  1  2 0 | 2 1
. . x3o . |  3 |  0  3 | *  * 32 |  0  2 1 | 1 2
----------+----+-------+---------+---------+----
x4o x . .   8 |  8  4 | 2  4  0 | 12  * * | 2 0
x . x3o .   6 |  3  6 | 0  3  2 |  * 32 * | 1 1
. . x3o4o   6 |  0 12 | 0  0  8 |  *  * 4 | 0 2
----------+----+-------+---------+---------+----
x4o x3o .  12 | 12 12 | 3 12  4 |  3  4 0 | 8 *
x . x3o4o  12 |  6 24 | 0 12 16 |  0  8 2 | * 4

x4o o3x3o

. . . . . | 24 |  2  4 | 1  8  2  2 |  4  4  4 1 | 2 2 2
----------+----+-------+------------+------------+------
x . . . . |  2 | 24  * | 1  4  0  0 |  4  2  2 0 | 2 2 1
. . . x . |  2 |  * 48 | 0  2  1  1 |  1  2  2 1 | 1 1 2
----------+----+-------+------------+------------+------
x4o . . . |  4 |  4  0 | 6  *  *  * |  4  0  0 0 | 2 2 0
x . . x . |  4 |  2  2 | * 48  *  * |  1  1  1 0 | 1 1 1
. . o3x . |  3 |  0  3 | *  * 16  * |  0  2  0 1 | 1 0 2
. . . x3o |  3 |  0  3 | *  *  * 16 |  0  0  2 1 | 0 1 2
----------+----+-------+------------+------------+------
x4o . x .   8 |  8  4 | 2  4  0  0 | 12  *  * * | 1 1 0
x . o3x .   6 |  3  6 | 0  3  2  0 |  * 16  * * | 1 0 1
x . . x3o   6 |  3  6 | 0  3  0  2 |  *  * 16 * | 0 1 1
. . o3x3o   6 |  0 12 | 0  0  4  4 |  *  *  * 4 | 0 0 2
----------+----+-------+------------+------------+------
x4o o3x .  12 | 12 12 | 3 12  4  0 |  3  4  0 0 | 4 * *
x4o . x3o  12 | 12 12 | 3 12  0  4 |  3  0  4 0 | * 4 *
x . o3x3o  12 |  6 24 | 0 12  8  8 |  0  4  4 2 | * * 4

x x x3o4o

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

x x o3x3o

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

xo3ox xx4oo&#x   → height = sqrt(2/3) = 0.816497
(tisdip || {3}-gyro tisdip)

o.3o. o.4o.    | 12  * |  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 .o4.o    |  * 12 |  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 | 12  *  *  *  * | 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 |  * 12  *  *  * | 0  2 1  0  0  2 0  0 0 | 1 2 0  2  1 2 0 0 | 1 2 2 1 0
oo3oo oo4oo&#x |  1  1 |  *  * 24  *  * | 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 |  *  *  * 12  * | 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 |  *  *  *  * 12 | 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 | 4  * *  *  *  * *  * * | 2 0 1  0  0 0 0 0 | 1 2 0 0 0
x. .. x. ..    |  4  0 |  2  2  0  0  0 | * 12 *  *  *  * *  * * | 1 1 0  1  0 0 0 0 | 1 1 1 0 0
.. .. x.4o.    |  4  0 |  0  4  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 | *  * * 12  *  * *  * * | 0 0 1  2  0 0 0 0 | 0 2 1 0 0
.. ox .. ..&#x |  1  2 |  0  0  2  1  0 | *  * *  * 12  * *  * * | 0 0 1  0  2 0 0 0 | 0 2 0 1 0
.. .. xx ..&#x |  2  2 |  0  1  2  0  1 | *  * *  *  * 24 *  * * | 0 0 0  1  1 1 0 0 | 0 1 1 1 0
.o3.x .. ..    |  0  3 |  0  0  0  3  0 | *  * *  *  *  * 4  * * | 0 0 1  0  0 0 2 0 | 0 2 0 0 1
.. .x .x ..    |  0  4 |  0  0  0  2  2 | *  * *  *  *  * * 12 * | 0 0 0  0  1 0 1 1 | 0 1 0 1 1
.. .. .x4.o    |  0  4 |  0  0  0  0  4 | *  * *  *  *  * *  * 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 | 4 * *  *  * * * * | 1 1 0 0 0
x. .. x.4o.      8  0 |  4  8  0  0  0 | 0  4 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 | * * 4  *  * * * * | 0 2 0 0 0
xo .. xx ..&#x   4  2 |  2  2  4  0  1 | 0  1 0  2  0  2 0  0 0 | * * * 12  * * * * | 0 1 1 0 0
.. ox xx ..&#x   2  4 |  0  1  4  2  2 | 0  0 0  0  2  2 0  1 0 | * * *  * 12 * * * | 0 1 0 1 0
.. .. xx4oo&#x   4  4 |  0  4  4  0  4 | 0  0 1  0  0  4 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 | * * *  *  * * 4 * | 0 1 0 0 1
.. .x .x4.o      0  8 |  0  0  0  4  8 | 0  0 0  0  0  0 0  4 2 | * * *  *  * * * 3 | 0 0 0 1 1
---------------+-------+----------------+------------------------+-------------------+----------
x.3o. x.4o.     12  0 | 12 12  0  0  0 | 4 12 3  0  0  0 0  0 0 | 4 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 | * 4 * * *
xo .. xx4oo&#x   8  4 |  4  8  8  0  4 | 0  4 2  4  0  8 0  0 1 | 0 1 0  4  0 2 0 0 | * * 3 * *
.. ox xx4oo&#x   4  8 |  0  4  8  4  8 | 0  0 1  0  4  8 0  4 2 | 0 0 0  0  4 2 0 1 | * * * 3 *
.o3.x .x4.o      0 12 |  0  0  0 12 12 | 0  0 0  0  0  0 4 12 3 | 0 0 0  0  0 0 4 3 | * * * * 1

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