o3x3x    
             
             
             
x3o3x   x3x3x

This polyteron occurs as a wedge of sart. In fact, it is a further diminishing of sripalprip.

Incidence matrix according to Dynkin symbol

oxx3xox3xxx&#x   → height(1,2) = height(1,3) = sqrt(5/8) = 0.790569
                   height(2,3) = 1/sqrt(2) = 0.707107
                   height(1,23) = 1/sqrt(2) = 0.707107 (tut || coatoe)
                   height(12,3) = sqrt(2/5) = 0.632456 (coatut || toe)
                   height(13,2) = sqrt(2/5) = 0.632456 (co || tutatoe)

o..3o..3o..    | 12  *  * |  2 1  2  2  0  0  0  0  0  0 | 1 2  1  2  2  2  1  2  2 0 0 0  0  0  0 0 0 0 | 1 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  2  0  2  2  2  0  0  0 | 0 0  2  1  2  2  0  0  0 1 2 1  2  1  2 0 0 0 | 0 1 2 1  2  1  2 0 0 0 1 1 2 1 0 | 1 1 2 1 0 1
..o3..o3..o    |  *  * 24 |  0 0  0  1  0  0  1  1  1  1 | 0 0  0  0  0  1  1  1  1 0 0 0  1  1  1 1 1 1 | 0 0 0 0  1  1  1 1 1 1 0 1 1 1 1 | 0 1 1 1 1 1
---------------+----------+------------------------------+-----------------------------------------------+----------------------------------+------------
... x.. ...    |  2  0  0 | 12 *  *  *  *  *  *  *  *  * | 1 1  0  1  0  0  0  1  0 0 0 0  0  0  0 0 0 0 | 1 1 0 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  0  2  0  0  0  2 0 0 0  0  0  0 0 0 0 | 1 0 1 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 |  * * 24  *  *  *  *  *  *  * | 0 0  1  1  1  1  0  0  0 0 0 0  0  0  0 0 0 0 | 0 1 1 1  1  1  1 0 0 0 0 0 0 0 0 | 1 1 1 1 0 0
o.o3o.o3o.o&#x |  1  0  1 |  * *  * 24  *  *  *  *  *  * | 0 0  0  0  0  1  1  1  1 0 0 0  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  0 1 1 0  1  0  0 0 0 0 | 0 1 1 0  1  0  0 0 0 0 1 1 1 0 0 | 1 1 1 0 0 1
... ... .x.    |  0  2  0 |  * *  *  *  * 12  *  *  *  * | 0 0  0  0  1  0  0  0  0 0 1 1  0  0  1 0 0 0 | 0 0 1 1  0  0  1 0 0 0 1 0 1 1 0 | 1 0 1 1 0 1
.oo3.oo3.oo&#x |  0  1  1 |  * *  *  *  *  * 24  *  *  * | 0 0  0  0  0  1  0  0  0 0 0 0  1  1  1 0 0 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 |  * *  *  *  *  *  * 12  *  * | 0 0  0  0  0  0  1  0  0 0 0 0  1  0  0 1 1 0 | 0 0 0 0  1  0  0 1 1 0 0 1 1 0 1 | 0 1 1 0 1 1
... ..x ...    |  0  0  2 |  * *  *  *  *  *  *  * 12  * | 0 0  0  0  0  0  0  1  0 0 0 0  0  1  0 1 0 1 | 0 0 0 0  0  1  0 1 0 1 0 1 0 1 1 | 0 1 0 1 1 1
... ... ..x    |  0  0  2 |  * *  *  *  *  *  *  *  * 12 | 0 0  0  0  0  0  0  0  1 0 0 0  0  0  1 0 1 1 | 0 0 0 0  0  0  1 0 1 1 0 0 1 1 1 | 0 0 1 1 1 1
---------------+----------+------------------------------+-----------------------------------------------+----------------------------------+------------
o..3x.. ...    |  3  0  0 |  3 0  0  0  0  0  0  0  0  0 | 4 *  *  *  *  *  *  *  * * * *  *  *  * * * * | 1 1 0 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  0 | * 4  *  *  *  *  *  *  * * * *  *  *  * * * * | 1 0 0 1  0  0  0 0 0 1 0 0 0 0 0 | 1 0 0 1 1 0
ox. ... ...&#x |  1  2  0 |  0 0  2  0  1  0  0  0  0  0 | * * 12  *  *  *  *  *  * * * *  *  *  * * * * | 0 1 1 0  1  0  0 0 0 0 0 0 0 0 0 | 1 1 1 0 0 0
... xo. ...&#x |  2  1  0 |  1 0  2  0  0  0  0  0  0  0 | * *  * 12  *  *  *  *  * * * *  *  *  * * * * | 0 1 0 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  0 | * *  *  * 12  *  *  *  * * * *  *  *  * * * * | 0 0 1 1  0  0  1 0 0 0 0 0 0 0 0 | 1 0 1 1 0 0
ooo3ooo3ooo&#x |  1  1  1 |  0 0  1  1  0  0  1  0  0  0 | * *  *  *  * 24  *  *  * * * *  *  *  * * * * | 0 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  0 | * *  *  *  *  * 12  *  * * * *  *  *  * * * * | 0 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  0 | * *  *  *  *  *  * 12  * * * *  *  *  * * * * | 0 0 0 0  0  1  0 1 0 1 0 0 0 0 0 | 0 1 0 1 1 0
... ... x.x&#x |  2  0  2 |  0 1  0  2  0  0  0  0  0  1 | * *  *  *  *  *  *  * 12 * * *  *  *  * * * * | 0 0 0 0  0  0  1 0 1 1 0 0 0 0 0 | 0 0 1 1 1 0
.x.3.o. ...    |  0  3  0 |  0 0  0  0  3  0  0  0  0  0 | * *  *  *  *  *  *  *  * 4 * *  *  *  * * * * | 0 1 0 0  0  0  0 0 0 0 1 1 0 0 0 | 1 1 0 0 0 1
.x. ... .x.    |  0  4  0 |  0 0  0  0  2  2  0  0  0  0 | * *  *  *  *  *  *  *  * * 6 *  *  *  * * * * | 0 0 1 0  0  0  0 0 0 0 1 0 1 0 0 | 1 0 1 0 0 1
... .o.3.x.    |  0  3  0 |  0 0  0  0  0  3  0  0  0  0 | * *  *  *  *  *  *  *  * * * 4  *  *  * * * * | 0 0 0 1  0  0  0 0 0 0 1 0 0 1 0 | 1 0 0 1 0 1
.xx ... ...&#x |  0  2  2 |  0 0  0  0  1  0  2  1  0  0 | * *  *  *  *  *  *  *  * * * * 12  *  * * * * | 0 0 0 0  1  0  0 0 0 0 0 1 1 0 0 | 0 1 1 0 0 1
... .ox ...&#x |  0  1  2 |  0 0  0  0  0  0  2  0  1  0 | * *  *  *  *  *  *  *  * * * *  * 12  * * * * | 0 0 0 0  0  1  0 0 0 0 0 1 0 1 0 | 0 1 0 1 0 1
... ... .xx&#x |  0  2  2 |  0 0  0  0  0  1  2  0  0  1 | * *  *  *  *  *  *  *  * * * *  *  * 12 * * * | 0 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  0 | * *  *  *  *  *  *  *  * * * *  *  *  * 4 * * | 0 0 0 0  0  0  0 1 0 0 0 1 0 0 1 | 0 1 0 0 1 1
..x ... ..x    |  0  0  4 |  0 0  0  0  0  0  0  2  0  2 | * *  *  *  *  *  *  *  * * * *  *  *  * * 6 * | 0 0 0 0  0  0  0 0 1 0 0 0 1 0 1 | 0 0 1 0 1 1
... ..x3..x    |  0  0  6 |  0 0  0  0  0  0  0  0  3  3 | * *  *  *  *  *  *  *  * * * *  *  *  * * * 4 | 0 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  0 | 4 4  0  0  0  0  0  0  0 0 0 0  0  0  0 0 0 0 | 1 * * *  *  *  * * * * * * * * * | 1 0 0 0 1 0
ox.3xo. ...&#x ♦  3  3  0 |  3 0  6  0  3  0  0  0  0  0 | 1 0  3  3  0  0  0  0  0 1 0 0  0  0  0 0 0 0 | * 4 * *  *  *  * * * * * * * * * | 1 1 0 0 0 0
ox. ... xx.&#x ♦  2  4  0 |  0 1  4  0  2  2  0  0  0  0 | 0 0  2  0  2  0  0  0  0 0 1 0  0  0  0 0 0 0 | * * 6 *  *  *  * * * * * * * * * | 1 0 1 0 0 0
... xo.3xx.&#x ♦  6  3  0 |  3 3  6  0  0  3  0  0  0  0 | 0 1  0  3  3  0  0  0  0 0 0 1  0  0  0 0 0 0 | * * * 4  *  *  * * * * * * * * * | 1 0 0 1 0 0
oxx ... ...&#x ♦  1  2  2 |  0 0  2  2  1  0  2  1  0  0 | 0 0  1  0  0  2  1  0  0 0 0 0  1  0  0 0 0 0 | * * * * 12  *  * * * * * * * * * | 0 1 1 0 0 0
... xox ...&#x ♦  2  1  2 |  1 0  2  2  0  0  2  0  1  0 | 0 0  0  1  0  2  0  1  0 0 0 0  0  1  0 0 0 0 | * * * *  * 12  * * * * * * * * * | 0 1 0 1 0 0
... ... xxx&#x ♦  2  2  2 |  0 1  2  2  0  1  2  0  0  1 | 0 0  0  0  1  2  0  0  1 0 0 0  0  0  1 0 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  0 | 1 0  0  0  0  0  3  3  0 0 0 0  0  0  0 1 0 0 | * * * *  *  *  * 4 * * * * * * * | 0 1 0 0 1 0
o.x ... x.x&#x ♦  2  0  4 |  0 1  0  4  0  0  0  2  0  2 | 0 0  0  0  0  0  2  0  2 0 0 0  0  0  0 0 1 0 | * * * *  *  *  * * 6 * * * * * * | 0 0 1 0 1 0
... x.x3x.x&#x ♦  6  0  6 |  3 3  0  6  0  0  0  0  3  3 | 0 1  0  0  0  0  0  3  3 0 0 0  0  0  0 0 0 1 | * * * *  *  *  * * * 4 * * * * * | 0 0 0 1 1 0
.x.3.o.3.x.    ♦  0 12  0 |  0 0  0  0 12 12  0  0  0  0 | 0 0  0  0  0  0  0  0  0 4 6 4  0  0  0 0 0 0 | * * * *  *  *  * * * * 1 * * * * | 1 0 0 0 0 1
.xx3.ox ...&#x ♦  0  3  6 |  0 0  0  0  3  0  6  3  3  0 | 0 0  0  0  0  0  0  0  0 1 0 0  3  3  0 1 0 0 | * * * *  *  *  * * * * * 4 * * * | 0 1 0 0 0 1
.xx ... .xx&#x ♦  0  4  4 |  0 0  0  0  2  2  4  2  0  2 | 0 0  0  0  0  0  0  0  0 0 1 0  2  0  2 0 1 0 | * * * *  *  *  * * * * * * 6 * * | 0 0 1 0 0 1
... .ox3.xx&#x ♦  0  3  6 |  0 0  0  0  0  3  6  0  3  3 | 0 0  0  0  0  0  0  0  0 0 0 1  0  3  3 0 0 1 | * * * *  *  *  * * * * * * * 4 * | 0 0 0 1 0 1
..x3..x3..x    ♦  0  0 24 |  0 0  0  0  0  0  0 12 12 12 | 0 0  0  0  0  0  0  0  0 0 0 0  0  0  0 4 6 4 | * * * *  *  *  * * * * * * * * 1 | 0 0 0 0 1 1
---------------+----------+------------------------------+-----------------------------------------------+----------------------------------+------------
ox.3xo.3xx.&#x ♦ 12 12  0 | 12 6 24  0 12 12  0  0  0  0 | 4 4 12 12 12  0  0  0  0 4 6 4  0  0  0 0 0 0 | 1 4 6 4  0  0  0 0 0 0 1 0 0 0 0 | 1 * * * * *
oxx3xox ...&#x ♦  3  3  6 |  3 0  6  6  3  0  6  3  3  0 | 1 0  3  3  0  6  3  3  0 1 0 0  3  3  0 1 0 0 | 0 1 0 0  3  3  0 1 0 0 0 1 0 0 0 | * 4 * * * *
oxx ... xxx&#x ♦  2  4  4 |  0 1  4  4  2  2  4  2  0  2 | 0 0  2  0  2  4  2  0  2 0 1 0  2  0  2 0 1 0 | 0 0 1 0  2  0  2 0 1 0 0 0 1 0 0 | * * 6 * * *
... xox3xxx&#x ♦  6  3  6 |  3 3  6  6  0  3  6  0  3  3 | 0 1  0  3  3  6  0  3  3 0 0 1  0  3  3 0 0 1 | 0 0 0 1  0  3  3 0 0 1 0 0 0 1 0 | * * * 4 * *
o.x3x.x3x.x&#x ♦ 12  0 24 | 12 6  0 24  0  0  0 12 12 12 | 4 4  0  0  0  0 12 12 12 0 0 0  0  0  0 4 6 4 | 1 0 0 0  0  0  0 4 6 4 0 0 0 0 1 | * * * * 1 *
.xx3.ox3.xx&#x ♦  0 12 24 |  0 0  0  0 12 12 24 12 12 12 | 0 0  0  0  0  0  0  0  0 4 6 4 12 12 12 4 6 4 | 0 0 0 0  0  0  0 0 0 0 1 4 6 4 1 | * * * * * 1