x x o3o      
                   
                   
                   
x o o3x     o x o3x

This polypeton indeed is a pentadiminished ril, in fact, the octa tratet already was a monostratic segment thereof, rejecting 3 vertices therefrom. This one now diminishes the latter further on, omitting a pair of opposite vertices of the top oct.

Incidence matrix according to Dynkin symbol

xxo xox ooo3oxx&#x   → height(1,2) = height(1,3) = sqrt(5/12) = 0.645497
                       height(2,3) = 1/sqrt(2) = 0.707107
({4} || tratet)

o.. o.. o..3o..      | 4  * | 2  6 0  0  0 | 1  6  6  6  3 0 0  0  0 | 6  6  6 2  6  3 0 0  0 0 | 6 2 2 3  6 1 0 0 | 2 3 2 0
.o. .o. .o.3.o.    & | * 12 | 0  2 1  2  2 | 0  2  1  4  2 2 1  3  4 | 1  4  2 2  3  4 1 1  6 2 | 2 2 1 1  6 2 2 3 | 1 2 3 1
---------------------+------+--------------+-------------------------+--------------------------+------------------+--------
x.. ... ... ...    & | 2  0 | 4  * *  *  * | 1  3  3  0  0 0 0  0  0 | 6  3  3 0  3  0 0 0  0 0 | 6 1 1 3  3 0 0 0 | 2 3 1 0
oo. oo. oo.3oo.&#x & | 1  1 | * 24 *  *  * | 0  1  1  2  1 0 0  0  0 | 1  2  2 1  2  2 0 0  0 0 | 2 1 1 1  4 1 0 0 | 1 2 2 0
.x. ... ... ...    & | 0  2 | *  * 6  *  * | 0  2  0  0  0 2 0  2  0 | 1  4  0 0  2  0 1 1  4 0 | 2 2 0 1  4 0 2 2 | 1 2 2 1
... ... ... .x.    & | 0  2 | *  * * 12  * | 0  0  0  2  0 1 1  0  2 | 0  2  1 2  0  2 1 0  3 2 | 1 2 1 0  3 2 1 3 | 1 1 3 1
.oo .oo .oo3.oo&#x   | 0  2 | *  * *  * 12 | 0  0  0  0  1 0 0  2  2 | 0  0  0 0  2  2 0 1  4 1 | 0 0 0 1  4 1 2 2 | 0 2 2 1
---------------------+------+--------------+-------------------------+--------------------------+------------------+--------
x.. x.. ... ...      | 4  0 | 4  0 0  0  0 | 1  *  *  *  * * *  *  * | 6  0  0 0  0  0 0 0  0 0 | 6 0 0 3  0 0 0 0 | 2 3 0 0
xx. ... ... ...&#x & | 2  2 | 1  2 1  0  0 | * 12  *  *  * * *  *  * | 1  2  0 0  1  0 0 0  0 0 | 2 1 0 1  2 0 0 0 | 1 2 1 0
... xo. ... ...&#x & | 2  1 | 1  2 0  0  0 | *  * 12  *  * * *  *  * | 1  0  2 0  1  0 0 0  0 0 | 2 0 1 1  2 0 0 0 | 1 2 1 0
... ... ... ox.&#x & | 1  2 | 0  2 0  1  0 | *  *  * 24  * * *  *  * | 0  1  1 1  0  1 0 0  0 0 | 1 1 1 0  2 1 0 0 | 1 1 2 0
ooo ooo ooo3ooo&#x   | 1  2 | 0  2 0  0  1 | *  *  *  * 12 * *  *  * | 0  0  0 0  2  2 0 0  0 0 | 0 0 0 1  4 1 0 0 | 0 2 2 0
.x. ... ... .x.    & | 0  4 | 0  0 2  2  0 | *  *  *  *  * 6 *  *  * | 0  2  0 0  0  0 1 0  2 0 | 1 2 0 0  2 0 1 2 | 1 1 2 1
... ... .o.3.x.    & | 0  3 | 0  0 0  3  0 | *  *  *  *  * * 4  *  * | 0  0  0 2  0  0 1 0  0 2 | 0 2 1 0  0 2 0 3 | 1 0 3 1
.xo ... ... ...&#x & | 0  3 | 0  0 1  0  2 | *  *  *  *  * * * 12  * | 0  0  0 0  1  0 0 1  2 0 | 0 0 0 1  2 0 2 1 | 0 2 1 1
... ... ... .xx&#x   | 0  4 | 0  0 0  2  2 | *  *  *  *  * * *  * 12 | 0  0  0 0  0  1 0 0  2 1 | 0 0 0 0  2 1 1 2 | 0 1 2 1
---------------------+------+--------------+-------------------------+--------------------------+------------------+--------
xx. xo. ... ...&#x & ♦ 4  2 | 4  4 1  0  0 | 1  2  2  0  0 0 0  0  0 | 6  *  * *  *  * * *  * * | 2 0 0 1  0 0 0 0 | 1 2 0 0
xx. ... ... ox.&#x & ♦ 2  4 | 1  4 2  2  0 | 0  2  0  2  0 1 0  0  0 | * 12  * *  *  * * *  * * | 1 1 0 0  1 0 0 0 | 1 1 1 0
... xo. ... ox.&#x & ♦ 2  2 | 1  4 0  1  0 | 0  0  2  2  0 0 0  0  0 | *  * 12 *  *  * * *  * * | 1 0 1 0  1 0 0 0 | 1 1 1 0
... ... oo.3ox.&#x & ♦ 1  3 | 0  3 0  3  0 | 0  0  0  3  0 0 1  0  0 | *  *  * 8  *  * * *  * * | 0 1 1 0  0 1 0 0 | 1 0 2 0
xxo ... ... ...&#x & ♦ 2  3 | 1  4 1  0  2 | 0  1  1  0  2 0 0  1  0 | *  *  * * 12  * * *  * * | 0 0 0 1  2 0 0 0 | 0 2 1 0
... ... ... oxx&#x & ♦ 1  4 | 0  4 0  2  2 | 0  0  0  2  2 0 0  0  1 | *  *  * *  * 12 * *  * * | 0 0 0 0  2 1 0 0 | 0 1 2 0
.x. ... .o.3.x.      ♦ 0  6 | 0  0 3  6  0 | 0  0  0  0  0 3 2  0  0 | *  *  * *  *  * 2 *  * * | 0 2 0 0  0 0 0 2 | 1 0 2 1
.xo .ox ... ...&#x   ♦ 0  4 | 0  0 2  0  4 | 0  0  0  0  0 0 0  4  0 | *  *  * *  *  * * 3  * * | 0 0 0 1  0 0 2 0 | 0 2 0 1
.xo ... ... .xx&#x & ♦ 0  6 | 0  0 2  3  4 | 0  0  0  0  0 1 0  2  2 | *  *  * *  *  * * * 12 * | 0 0 0 0  1 0 1 1 | 0 1 1 1
... ... .oo3.xx&#x   ♦ 0  6 | 0  0 0  6  3 | 0  0  0  0  0 0 2  0  3 | *  *  * *  *  * * *  * 4 | 0 0 0 0  0 1 0 2 | 0 0 2 1
---------------------+------+--------------+-------------------------+--------------------------+------------------+--------
xx. xo. ... ox.&#x & ♦ 4  4 | 4  8 2  2  0 | 1  4  4  4  0 1 0  0  0 | 2  2  2 0  0  0 0 0  0 0 | 6 * * *  * * * * | 1 1 0 0
xx. ... oo.3ox.&#x & ♦ 2  6 | 1  6 3  6  0 | 0  3  0  6  0 3 2  0  0 | 0  3  0 2  0  0 1 0  0 0 | * 4 * *  * * * * | 1 0 1 0
... xo. oo.3ox.&#x & ♦ 2  3 | 1  6 0  3  0 | 0  0  3  6  0 0 1  0  0 | 0  0  3 2  0  0 0 0  0 0 | * * 4 *  * * * * | 1 0 1 0
xxo xox ... ...&#x   ♦ 4  4 | 4  8 2  0  4 | 1  4  4  0  4 0 0  4  0 | 2  0  0 0  4  0 0 1  0 0 | * * * 3  * * * * | 0 2 0 0
xxo ... ... oxx&#x & ♦ 2  6 | 1  8 2  3  4 | 0  2  2  4  4 1 0  2  2 | 0  1  1 0  2  2 0 0  1 0 | * * * * 12 * * * | 0 1 1 0
... ... ooo3oxx&#x   ♦ 1  6 | 0  6 0  6  3 | 0  0  0  6  3 0 2  0  3 | 0  0  0 2  0  3 0 0  0 1 | * * * *  * 4 * * | 0 0 2 0
.xo .ox ... .xx&#x   ♦ 0  8 | 0  0 4  4  8 | 0  0  0  0  0 2 0  8  4 | 0  0  0 0  0  0 0 2  4 0 | * * * *  * * 3 * | 0 1 0 1
.xo ... .oo3.xx&#x & ♦ 0  9 | 0  0 3  9  6 | 0  0  0  0  0 3 3  3  6 | 0  0  0 0  0  0 1 0  3 2 | * * * *  * * * 4 | 0 0 1 1
---------------------+------+--------------+-------------------------+--------------------------+------------------+--------
xx. xo. oo.3ox.&#x & ♦ 4  6 | 4 12 3  6  0 | 1  6  6 12  0 3 2  0  0 | 3  6  6 4  0  0 1 0  0 0 | 3 2 2 0  0 0 0 0 | 2 * * *
xxo xox ... oxx&#x   ♦ 4  8 | 4 16 4  4  8 | 1  8  8  8  8 2 0  8  4 | 4  4  4 0  8  4 0 2  4 0 | 2 0 0 2  4 0 1 0 | * 3 * *
xxo ... ooo3oxx&#x & ♦ 2  9 | 1 12 3  9  6 | 0  3  3 12  6 3 3  3  6 | 0  3  3 4  3  6 1 0  3 2 | 0 1 1 0  3 2 0 1 | * * 4 *
.xo .ox .oo3.xx&#x   ♦ 0 12 | 0  0 6 12 12 | 0  0  0  0  0 6 4 12 12 | 0  0  0 0  0  0 2 3 12 4 | 0 0 0 0  0 0 3 4 | * * * 1