x3x3o       
                   
                   
o3x3x         o3x3x

This polyteron occurs as internal wedge in siphin.

Incidence matrix according to Dynkin symbol

ox ox3xx3xo&#x   → height = 1/2
(tut || inv tuttip)

o. o.3o.3o.    | 12  * |  2 1  4  0  0  0 | 1 2  2  2  4  4 0  0 0 0 | 1  1  2  2 2  2 4 0 0 0 | 1 1 2 2 0
.o .o3.o3.o    |  * 24 |  0 0  2  1  1  2 | 0 0  2  2  2  1 1  2 2 1 | 0  2  2  1 2  1 1 2 1 1 | 2 1 1 1 1
---------------+-------+------------------+--------------------------+-------------------------+----------
.. .. x. ..    |  2  0 | 12 *  *  *  *  * | 1 1  0  0  2  0 0  0 0 0 | 1  0  1  0 2  0 2 0 0 0 | 1 0 1 2 0
.. .. .. x.    |  2  0 |  * 6  *  *  *  * | 0 2  0  0  0  4 0  0 0 0 | 1  0  0  2 0  2 4 0 0 0 | 0 1 2 2 0
oo oo3oo3oo&#x |  1  1 |  * * 48  *  *  * | 0 0  1  1  1  1 0  0 0 0 | 0  1  1  1 1  1 1 0 0 0 | 1 1 1 1 0
.x .. .. ..    |  0  2 |  * *  * 12  *  * | 0 0  2  0  0  0 1  2 0 0 | 0  2  2  1 0  0 0 2 1 0 | 2 1 1 0 1
.. .x .. ..    |  0  2 |  * *  *  * 12  * | 0 0  0  2  0  0 1  0 2 0 | 0  2  0  0 2  1 0 2 0 1 | 2 1 0 1 1
.. .. .x ..    |  0  2 |  * *  *  *  * 24 | 0 0  0  0  1  0 0  1 1 1 | 0  0  1  0 1  0 1 1 1 1 | 1 0 1 1 1
---------------+-------+------------------+--------------------------+-------------------------+----------
.. o.3x. ..    |  3  0 |  3 0  0  0  0  0 | 4 *  *  *  *  * *  * * * | 1  0  0  0 2  0 0 0 0 0 | 1 0 0 2 0
.. .. x.3x.    |  6  0 |  3 3  0  0  0  0 | * 4  *  *  *  * *  * * * | 1  0  0  0 0  0 2 0 0 0 | 0 0 1 2 0
ox .. .. ..&#x |  1  2 |  0 0  2  1  0  0 | * * 24  *  *  * *  * * * | 0  1  1  1 0  0 0 0 0 0 | 1 1 1 0 0
.. ox .. ..&#x |  1  2 |  0 0  2  0  1  0 | * *  * 24  *  * *  * * * | 0  1  0  0 1  1 0 0 0 0 | 1 1 0 1 0
.. .. xx ..&#x |  2  2 |  1 0  2  0  0  1 | * *  *  * 24  * *  * * * | 0  0  1  0 1  0 1 0 0 0 | 1 0 1 1 0
.. .. .. xo&#x |  2  1 |  0 1  2  0  0  0 | * *  *  *  * 24 *  * * * | 0  0  0  1 0  1 1 0 0 0 | 0 1 1 1 0
.x .x .. ..    |  0  4 |  0 0  0  2  2  0 | * *  *  *  *  * 6  * * * | 0  2  0  0 0  0 0 2 0 0 | 2 1 0 0 1
.x .. .x ..    |  0  4 |  0 0  0  2  0  2 | * *  *  *  *  * * 12 * * | 0  0  1  0 0  0 0 1 1 0 | 1 0 1 0 1
.. .x3.x ..    |  0  6 |  0 0  0  0  3  3 | * *  *  *  *  * *  * 8 * | 0  0  0  0 1  0 0 1 0 1 | 1 0 0 1 1
.. .. .x3.o    |  0  3 |  0 0  0  0  0  3 | * *  *  *  *  * *  * * 8 | 0  0  0  0 0  0 1 0 1 1 | 0 0 1 1 1
---------------+-------+------------------+--------------------------+-------------------------+----------
.. o.3x.3x.    ♦ 12  0 | 12 6  0  0  0  0 | 4 4  0  0  0  0 0  0 0 0 | 1  *  *  * *  * * * * * | 0 0 0 2 0
ox ox .. ..&#x ♦  1  4 |  0 0  4  2  2  0 | 0 0  2  2  0  0 1  0 0 0 | * 12  *  * *  * * * * * | 1 1 0 0 0
ox .. xx ..&#x ♦  2  4 |  1 0  4  2  0  2 | 0 0  2  0  2  0 0  1 0 0 | *  * 12  * *  * * * * * | 1 0 1 0 0
ox .. .. xo&#x ♦  2  2 |  0 1  4  1  0  0 | 0 0  2  0  0  2 0  0 0 0 | *  *  * 12 *  * * * * * | 0 1 1 0 0
.. ox3xx ..&#x ♦  3  6 |  3 0  6  0  3  3 | 1 0  0  3  3  0 0  0 1 0 | *  *  *  * 8  * * * * * | 1 0 0 1 0
.. ox .. xo&#x ♦  2  2 |  0 1  4  0  1  0 | 0 0  0  2  0  2 0  0 0 0 | *  *  *  * * 12 * * * * | 0 1 0 1 0
.. .. xx3xo&#x ♦  6  3 |  3 3  6  0  0  3 | 0 1  0  0  3  3 0  0 0 1 | *  *  *  * *  * 8 * * * | 0 0 1 1 0
.x .x3.x ..    ♦  0 12 |  0 0  0  6  6  6 | 0 0  0  0  0  0 3  3 2 0 | *  *  *  * *  * * 4 * * | 1 0 0 0 1
.x .. .x3.o    ♦  0  6 |  0 0  0  3  0  6 | 0 0  0  0  0  0 0  3 0 2 | *  *  *  * *  * * * 4 * | 0 0 1 0 1
.. .x3.x3.o    ♦  0 12 |  0 0  0  0  6 12 | 0 0  0  0  0  0 0  0 4 4 | *  *  *  * *  * * * * 2 | 0 0 0 1 1
---------------+-------+------------------+--------------------------+-------------------------+----------
ox ox3xx ..&#x ♦  3 12 |  3 0 12  6  6  6 | 1 0  6  6  6  0 3  3 2 0 | 0  3  3  0 2  0 0 1 0 0 | 4 * * * *
ox ox .. xo&#x ♦  2  4 |  0 1  8  2  2  0 | 0 0  4  4  0  4 1  0 0 0 | 0  2  0  2 0  2 0 0 0 0 | * 6 * * *
ox .. xx3xo&#x ♦  6  6 |  3 3 12  3  0  6 | 0 1  6  0  6  6 0  3 0 2 | 0  0  3  3 0  0 2 0 1 0 | * * 4 * *
.. ox3xx3xo&#x ♦ 12 12 | 12 6 24  0  6 12 | 4 4  0 12 12 12 0  0 4 4 | 1  0  0  0 4  6 4 0 0 1 | * * * 2 *
.x .x3.x3.o    ♦  0 24 |  0 0  0 12 12 24 | 0 0  0  0  0  0 6 12 8 8 | 0  0  0  0 0  0 0 4 4 2 | * * * * 1

oox3xxx3xxo&#x   → height(1,2) = 1
                 height(1,3) = height(2,3) = 1/sqrt(2) = 0.707107

o..3o..3o..    | 12  *  * |  2 1  1  2  0 0  0 0  0 | 1 2  2 1  2  1  2  2 0 0  0  0  0 0 0 | 1 1 2  1  2  2 1 1 2 0 0 0 0 0 | 1 1 1 2 1 0
.o.3.o.3.o.    |  * 12  * |  0 0  1  0  2 1  2 0  0 | 0 0  2 1  2  0  0  0 1 2  1  2  2 0 0 | 0 1 2  1  2  2 0 0 0 1 1 1 2 0 | 1 1 1 2 0 1
..o3..o3..o    |  *  * 12 |  0 0  0  2  0 0  2 1  2 | 0 0  0 0  2  2  2  1 0 0  2  2  1 2 1 | 0 0 0  2  2  1 2 1 1 0 2 1 1 1 | 0 2 1 1 1 1
---------------+----------+-------------------------+---------------------------------------+--------------------------------+------------
... x.. ...    |  2  0  0 | 12 *  *  *  * *  * *  * | 1 1  1 0  0  0  1  0 0 0  0  0  0 0 0 | 1 1 1  0  1  0 1 0 1 0 0 0 0 0 | 1 1 0 1 1 0
... ... x..    |  2  0  0 |  * 6  *  *  * *  * *  * | 0 2  0 1  0  0  0  2 0 0  0  0  0 0 0 | 1 0 2  0  0  2 0 1 2 0 0 0 0 0 | 1 0 1 2 1 0
oo.3oo.3oo.&#x |  1  1  0 |  * * 12  *  * *  * *  * | 0 0  2 1  2  0  0  0 0 0  0  0  0 0 0 | 0 1 2  1  2  2 0 0 0 0 0 0 0 0 | 1 1 1 2 0 0
o.o3o.o3o.o&#x |  1  0  1 |  * *  * 24  * *  * *  * | 0 0  0 0  1  1  1  1 0 0  0  0  0 0 0 | 0 0 0  1  1  1 1 1 1 0 0 0 0 0 | 0 1 1 1 1 0
... .x. ...    |  0  2  0 |  * *  *  * 12 *  * *  * | 0 0  1 0  0  0  0  0 1 1  0  1  0 0 0 | 0 1 1  0  1  0 0 0 0 1 1 0 1 0 | 1 1 0 1 0 1
... ... .x.    |  0  2  0 |  * *  *  *  * 6  * *  * | 0 0  0 1  0  0  0  0 0 2  0  0  2 0 0 | 0 0 2  0  0  2 0 0 0 1 0 1 2 0 | 1 0 1 2 0 1
.oo3.oo3.oo&#x |  0  1  1 |  * *  *  *  * * 24 *  * | 0 0  0 0  1  0  0  0 0 0  1  1  1 0 0 | 0 0 0  1  1  1 0 0 0 0 1 1 1 0 | 0 1 1 1 0 1
..x ... ...    |  0  0  2 |  * *  *  *  * *  * 6  * | 0 0  0 0  0  2  0  0 0 0  2  0  0 2 0 | 0 0 0  2  0  0 2 1 0 0 2 1 0 1 | 0 2 1 0 1 1
... ..x ...    |  0  0  2 |  * *  *  *  * *  * * 12 | 0 0  0 0  0  0  1  0 0 0  0  1  0 1 1 | 0 0 0  0  1  0 1 0 1 0 1 0 1 1 | 0 1 0 1 1 1
---------------+----------+-------------------------+---------------------------------------+--------------------------------+------------
o..3x.. ...    |  3  0  0 |  3 0  0  0  0 0  0 0  0 | 4 *  * *  *  *  *  * * *  *  *  * * * | 1 1 0  0  0  0 1 0 0 0 0 0 0 0 | 1 1 0 0 1 0
... x..3x..    |  6  0  0 |  3 3  0  0  0 0  0 0  0 | * 4  * *  *  *  *  * * *  *  *  * * * | 1 0 1  0  0  0 0 0 1 0 0 0 0 0 | 1 0 0 1 1 0
... xx. ...&#x |  2  2  0 |  1 0  2  0  1 0  0 0  0 | * * 12 *  *  *  *  * * *  *  *  * * * | 0 1 1  0  1  0 0 0 0 0 0 0 0 0 | 1 1 0 1 0 0
... ... xx.&#x |  2  2  0 |  0 1  2  0  0 1  0 0  0 | * *  * 6  *  *  *  * * *  *  *  * * * | 0 0 2  0  0  2 0 0 0 0 0 0 0 0 | 1 0 1 2 0 0
ooo3ooo3ooo&#x |  1  1  1 |  0 0  1  1  0 0  1 0  0 | * *  * * 24  *  *  * * *  *  *  * * * | 0 0 0  1  1  1 0 0 0 0 0 0 0 0 | 0 1 1 1 0 0
o.x ... ...&#x |  1  0  2 |  0 0  0  2  0 0  0 1  0 | * *  * *  * 12  *  * * *  *  *  * * * | 0 0 0  1  0  0 1 1 0 0 0 0 0 0 | 0 1 1 0 1 0
... x.x ...&#x |  2  0  2 |  1 0  0  2  0 0  0 0  1 | * *  * *  *  * 12  * * *  *  *  * * * | 0 0 0  0  1  0 1 0 1 0 0 0 0 0 | 0 1 0 1 1 0
... ... x.o&#x |  2  0  1 |  0 1  0  2  0 0  0 0  0 | * *  * *  *  *  * 12 * *  *  *  * * * | 0 0 0  0  0  1 0 1 1 0 0 0 0 0 | 0 0 1 1 1 0
.o.3.x. ...    |  0  3  0 |  0 0  0  0  3 0  0 0  0 | * *  * *  *  *  *  * 4 *  *  *  * * * | 0 1 0  0  0  0 0 0 0 1 1 0 0 0 | 1 1 0 0 0 1
... .x.3.x.    |  0  6  0 |  0 0  0  0  3 3  0 0  0 | * *  * *  *  *  *  * * 4  *  *  * * * | 0 0 1  0  0  0 0 0 0 1 0 0 1 0 | 1 0 0 1 0 1
.ox ... ...&#x |  0  1  2 |  0 0  0  0  0 0  2 1  0 | * *  * *  *  *  *  * * * 12  *  * * * | 0 0 0  1  0  0 0 0 0 0 1 1 0 0 | 0 1 1 0 0 1
... .xx ...&#x |  0  2  2 |  0 0  0  0  1 0  2 0  1 | * *  * *  *  *  *  * * *  * 12  * * * | 0 0 0  0  1  0 0 0 0 0 1 0 1 0 | 0 1 0 1 0 1
... ... .xo&#x |  0  2  1 |  0 0  0  0  0 1  2 0  0 | * *  * *  *  *  *  * * *  *  * 12 * * | 0 0 0  0  0  1 0 0 0 0 0 1 1 0 | 0 0 1 1 0 1
..x3..x ...    |  0  0  6 |  0 0  0  0  0 0  0 3  3 | * *  * *  *  *  *  * * *  *  *  * 4 * | 0 0 0  0  0  0 1 0 0 0 1 0 0 1 | 0 1 0 0 1 1
... ..x3..o    |  0  0  3 |  0 0  0  0  0 0  0 0  3 | * *  * *  *  *  *  * * *  *  *  * * 4 | 0 0 0  0  0  0 0 0 1 0 0 0 1 1 | 0 0 0 1 1 1
---------------+----------+-------------------------+---------------------------------------+--------------------------------+------------
o..3x..3x..    ♦ 12  0  0 | 12 6  0  0  0 0  0 0  0 | 4 4  0 0  0  0  0  0 0 0  0  0  0 0 0 | 1 * *  *  *  * * * * * * * * * | 1 0 0 0 1 0
oo.3xx. ...&#x ♦  3  3  0 |  3 0  3  0  3 0  0 0  0 | 1 0  3 0  0  0  0  0 1 0  0  0  0 0 0 | * 4 *  *  *  * * * * * * * * * | 1 1 0 0 0 0
... xx.3xx.&#x ♦  6  6  0 |  3 3  6  0  3 3  0 0  0 | 0 1  3 3  0  0  0  0 0 1  0  0  0 0 0 | * * 4  *  *  * * * * * * * * * | 1 0 0 1 0 0
oox ... ...&#x ♦  1  1  2 |  0 0  1  2  0 0  2 1  0 | 0 0  0 0  2  1  0  0 0 0  1  0  0 0 0 | * * * 12  *  * * * * * * * * * | 0 1 1 0 0 0
... xxx ...&#x ♦  2  2  2 |  1 0  2  2  1 0  2 0  1 | 0 0  1 0  2  0  1  0 0 0  0  1  0 0 0 | * * *  * 12  * * * * * * * * * | 0 1 0 1 0 0
... ... xxo&#x ♦  2  2  1 |  0 1  2  2  0 1  2 0  0 | 0 0  0 1  2  0  0  1 0 0  0  0  1 0 0 | * * *  *  * 12 * * * * * * * * | 0 0 1 1 0 0
o.x3x.x ...&#x ♦  3  0  6 |  3 0  0  6  0 0  0 3  3 | 1 0  0 0  0  3  3  0 0 0  0  0  0 1 0 | * * *  *  *  * 4 * * * * * * * | 0 1 0 0 1 0
o.x ... x.o&#x ♦  2  0  2 |  0 1  0  4  0 0  0 1  0 | 0 0  0 0  0  2  0  2 0 0  0  0  0 0 0 | * * *  *  *  * * 6 * * * * * * | 0 0 1 0 1 0
... x.x3x.o&#x ♦  6  0  3 |  3 3  0  6  0 0  0 0  3 | 0 1  0 0  0  0  3  3 0 0  0  0  0 0 1 | * * *  *  *  * * * 4 * * * * * | 0 0 0 1 1 0
.o.3.x.3.x.    ♦  0 12  0 |  0 0  0  0 12 6  0 0  0 | 0 0  0 0  0  0  0  0 4 4  0  0  0 0 0 | * * *  *  *  * * * * 1 * * * * | 1 0 0 0 0 1
.ox3.xx ...&#x ♦  0  3  6 |  0 0  0  0  3 0  6 3  3 | 0 0  0 0  0  0  0  0 1 0  3  3  0 1 0 | * * *  *  *  * * * * * 4 * * * | 0 1 0 0 0 1
.ox ... .xo&#x ♦  0  2  2 |  0 0  0  0  0 1  4 1  0 | 0 0  0 0  0  0  0  0 0 0  2  0  2 0 0 | * * *  *  *  * * * * * * 6 * * | 0 0 1 0 0 1
... .xx3.xo&#x ♦  0  6  3 |  0 0  0  0  3 3  6 0  3 | 0 0  0 0  0  0  0  0 0 1  0  3  3 0 1 | * * *  *  *  * * * * * * * 4 * | 0 0 0 1 0 1
..x3..x3..o    ♦  0  0 12 |  0 0  0  0  0 0  0 6 12 | 0 0  0 0  0  0  0  0 0 0  0  0  0 4 4 | * * *  *  *  * * * * * * * * 1 | 0 0 0 0 1 1
---------------+----------+-------------------------+---------------------------------------+--------------------------------+------------
oo.3xx.3xx.&#x ♦ 12 12  0 | 12 6 12  0 12 6  0 0  0 | 4 4 12 6  0  0  0  0 4 4  0  0  0 0 0 | 1 4 4  0  0  0 0 0 0 1 0 0 0 0 | 1 * * * * *
oox3xxx ...&#x ♦  3  3  6 |  3 0  3  6  3 0  6 3  3 | 1 0  3 0  6  3  3  0 1 0  3  3  0 1 0 | 0 1 0  3  3  0 1 0 0 0 1 0 0 0 | * 4 * * * *
oox ... xxo&#x ♦  2  2  2 |  0 1  2  4  0 1  4 1  0 | 0 0  0 1  4  2  0  2 0 0  2  0  2 0 0 | 0 0 0  2  0  2 0 1 0 0 0 1 0 0 | * * 6 * * *
... xxx3xxo&#x ♦  6  6  3 |  3 3  6  6  3 3  6 0  3 | 0 1  3 3  6  0  3  3 0 1  0  3  3 0 1 | 0 0 1  0  3  3 0 0 1 0 0 0 1 0 | * * * 4 * *
o.x3x.x3x.o&#x ♦ 12  0 12 | 12 6  0 24  0 0  0 6 12 | 4 4  0 0  0 12 12 12 0 0  0  0  0 4 4 | 1 0 0  0  0  0 4 6 4 0 0 0 0 1 | * * * * 1 *
.ox3.xx3.xo&#x ♦  0 12 12 |  0 0  0  0 12 6 24 6 12 | 0 0  0 0  0  0  0  0 4 4 12 12 12 4 4 | 0 0 0  0  0  0 0 0 0 1 4 6 4 1 | * * * * * 1