x x3o3o     x o3o3x
                   
                   
                   
      o x3o3x      

This polypeton is a diminished rag, in fact, the hexipaico already was a monostratic wedge thereof. This one now diminishes the latter further on, omitting a pair of opposite bases of the formerly central ico.

Incidence matrix according to Dynkin symbol

xxo xox3ooo3oxx&#x   → height(1,2) = 1/sqrt(2) = 0.707107
                       height(1,3) = height(2,3) = sqrt(3/8) = 0.612372
(hexip || co)

o.. o..3o..3o..    & | 16  * | 1  3  3  3  0 |  3  3  3  9  3  3  6  3 0 0 | 3 1  9  4  3  3  9  6  3  3  3  1 0 | 1 4 3 1  9  4  3 3  3 1 1 | 1 4 3 1 1
..o ..o3..o3..o      |  * 12 | 0  0  0  4  4 |  0  0  0  0  2  2  8  8 2 2 | 0 0  0  0  0  1  8  4  4  4  8  4 1 | 0 0 0 0  4  4  4 2  4 2 4 | 0 2 2 2 2
---------------------+-------+---------------+-----------------------------+-------------------------------------+---------------------------+----------
x.. ... ... ...    & |  2  0 | 8  *  *  *  * |  3  0  3  0  0  3  0  0 0 0 | 3 0  9  0  0  3  0  6  3  0  0  0 0 | 1 4 3 0  9  0  0 3  3 1 0 | 1 4 3 0 1
... x.. ... ...    & |  2  0 | * 24  *  *  * |  1  2  0  2  0  0  2  0 0 0 | 2 1  2  2  1  0  2  2  0  2  1  0 0 | 1 2 1 1  2  2  1 2  1 0 1 | 1 2 1 1 1
oo. oo.3oo.3oo.&#x   |  2  0 | *  * 24  *  * |  0  0  1  4  1  0  0  0 0 0 | 0 0  4  2  2  1  4  0  0  0  0  0 0 | 0 2 2 1  4  2  2 0  0 0 0 | 1 2 2 1 0
o.o o.o3o.o3o.o&#x & |  1  1 | *  *  * 48  * |  0  0  0  0  1  1  2  2 0 0 | 0 0  0  0  0  1  4  2  2  1  2  1 0 | 0 0 0 0  4  2  2 1  2 1 1 | 0 2 2 1 1
... ..x ... ...    & |  0  2 | *  *  *  * 24 |  0  0  0  0  0  0  2  2 1 1 | 0 0  0  0  0  0  2  1  1  2  4  2 1 | 0 0 0 0  1  2  2 1  2 1 4 | 0 1 1 2 2
---------------------+-------+---------------+-----------------------------+-------------------------------------+---------------------------+----------
x.. x.. ... ...    & |  4  0 | 2  2  0  0  0 | 12  *  *  *  *  *  *  * * * | 2 0  2  0  0  0  0  2  0  0  0  0 0 | 1 2 1 0  2  0  0 2  1 0 0 | 1 2 1 0 1
... x..3o.. ...    & |  3  0 | 0  3  0  0  0 |  * 16  *  *  *  *  *  * * * | 1 1  0  1  0  0  0  0  0  1  0  0 0 | 1 1 0 1  0  1  0 1  0 0 1 | 1 1 0 1 1
xx. ... ... ...&#x   |  4  0 | 2  0  2  0  0 |  *  * 12  *  *  *  *  * * * | 0 0  4  0  0  1  0  0  0  0  0  0 0 | 0 2 2 0  4  0  0 0  0 0 0 | 1 2 2 0 0
... xo. ... ...&#x & |  3  0 | 0  1  2  0  0 |  *  *  * 48  *  *  *  * * * | 0 0  1  1  1  0  1  0  0  0  0  0 0 | 0 1 1 1  1  1  1 0  0 0 0 | 1 1 1 1 0
ooo ooo3ooo3ooo&#x   |  2  1 | 0  0  1  2  0 |  *  *  *  * 24  *  *  * * * | 0 0  0  0  0  1  4  0  0  0  0  0 0 | 0 0 0 0  4  2  2 0  0 0 0 | 0 2 2 1 0
x.o ... ... ...&#x & |  2  1 | 1  0  0  2  0 |  *  *  *  *  * 24  *  * * * | 0 0  0  0  0  1  0  2  2  0  0  0 0 | 0 0 0 0  4  0  0 1  2 1 0 | 0 2 2 0 1
... x.x ... ...&#x & |  2  2 | 0  1  0  2  1 |  *  *  *  *  *  * 48  * * * | 0 0  0  0  0  0  1  1  0  1  1  0 0 | 0 0 0 0  1  1  1 1  1 0 1 | 0 1 1 1 1
... ... ... o.x&#x & |  1  2 | 0  0  0  2  1 |  *  *  *  *  *  *  * 48 * * | 0 0  0  0  0  0  1  0  1  0  1  1 0 | 0 0 0 0  1  1  1 0  1 1 1 | 0 1 1 1 1
... ..x3..o ...    & |  0  3 | 0  0  0  0  3 |  *  *  *  *  *  *  *  * 8 * | 0 0  0  0  0  0  0  0  0  2  0  2 1 | 0 0 0 0  0  2  0 1  0 1 4 | 0 1 0 2 2
... ..x ... ..x      |  0  4 | 0  0  0  0  4 |  *  *  *  *  *  *  *  * * 6 | 0 0  0  0  0  0  0  0  0  0  4  0 1 | 0 0 0 0  0  0  2 0  2 0 4 | 0 0 1 2 2
---------------------+-------+---------------+-----------------------------+-------------------------------------+---------------------------+----------
x.. x..3o.. ...    & ♦  6  0 | 3  6  0  0  0 |  3  2  0  0  0  0  0  0 0 0 | 8 *  *  *  *  *  *  *  *  *  *  * * | 1 1 0 0  0  0  0 1  0 0 0 | 1 1 0 0 1
... x..3o..3o..    & ♦  4  0 | 0  6  0  0  0 |  0  4  0  0  0  0  0  0 0 0 | * 4  *  *  *  *  *  *  *  *  *  * * | 1 0 0 1  0  0  0 0  0 0 1 | 1 0 0 1 1
xx. xo. ... ...&#x & ♦  6  0 | 3  2  4  0  0 |  1  0  2  2  0  0  0  0 0 0 | * * 24  *  *  *  *  *  *  *  *  * * | 0 1 1 0  1  0  0 0  0 0 0 | 1 1 1 0 0
... xo.3oo. ...&#x & ♦  4  0 | 0  3  3  0  0 |  0  1  0  3  0  0  0  0 0 0 | * *  * 16  *  *  *  *  *  *  *  * * | 0 1 0 1  0  1  0 0  0 0 0 | 1 1 0 1 0
... xo. ... ox.&#x   ♦  4  0 | 0  2  4  0  0 |  0  0  0  4  0  0  0  0 0 0 | * *  *  * 12  *  *  *  *  *  *  * * | 0 0 1 1  0  0  1 0  0 0 0 | 1 0 1 1 0
xxo ... ... ...&#x   ♦  4  1 | 2  0  2  4  0 |  0  0  1  0  2  2  0  0 0 0 | * *  *  *  * 12  *  *  *  *  *  * * | 0 0 0 0  4  0  0 0  0 0 0 | 0 2 2 0 0
... xox ... ...&#x & ♦  3  2 | 0  1  2  4  1 |  0  0  0  1  2  0  1  1 0 0 | * *  *  *  *  * 48  *  *  *  *  * * | 0 0 0 0  1  1  1 0  0 0 0 | 0 1 1 1 0
x.o x.x ... ...&#x & ♦  4  2 | 2  2  0  4  1 |  1  0  0  0  0  2  2  0 0 0 | * *  *  *  *  *  * 24  *  *  *  * * | 0 0 0 0  1  0  0 1  1 0 0 | 0 1 1 0 1
x.o ... ... o.x&#x & ♦  2  2 | 1  0  0  4  1 |  0  0  0  0  0  2  0  2 0 0 | * *  *  *  *  *  *  * 24  *  *  * * | 0 0 0 0  1  0  0 0  1 1 0 | 0 1 1 0 1
... x.x3o.o ...&#x & ♦  3  3 | 0  3  0  3  3 |  0  1  0  0  0  0  3  0 1 0 | * *  *  *  *  *  *  *  * 16  *  * * | 0 0 0 0  0  1  0 1  0 0 1 | 0 1 0 1 1
... x.x ... o.x&#x & ♦  2  4 | 0  1  0  4  4 |  0  0  0  0  0  0  2  2 0 1 | * *  *  *  *  *  *  *  *  * 24  * * | 0 0 0 0  0  0  1 0  1 0 1 | 0 0 1 1 1
... ... o.o3o.x&#x & ♦  1  3 | 0  0  0  3  3 |  0  0  0  0  0  0  0  3 1 0 | * *  *  *  *  *  *  *  *  *  * 16 * | 0 0 0 0  0  1  0 0  0 1 1 | 0 1 0 1 1
... ..x3..o3..x      ♦  0 12 | 0  0  0  0 24 |  0  0  0  0  0  0  0  0 8 6 | * *  *  *  *  *  *  *  *  *  *  * 1 | 0 0 0 0  0  0  0 0  0 0 4 | 0 0 0 2 2
---------------------+-------+---------------+-----------------------------+-------------------------------------+---------------------------+----------
x.. x..3o..3o..    & ♦  8  0 | 4 12  0  0  0 |  6  8  0  0  0  0  0  0 0 0 | 4 2  0  0  0  0  0  0  0  0  0  0 0 | 2 * * *  *  *  * *  * * * | 1 0 0 0 1
xx. xo.3oo. ...&#x & ♦  8  0 | 4  6  6  0  0 |  3  2  3  6  0  0  0  0 0 0 | 1 0  3  2  0  0  0  0  0  0  0  0 0 | * 8 * *  *  *  * *  * * * | 1 1 0 0 0
xx. xo. ... ox.&#x   ♦  8  0 | 4  4  8  0  0 |  2  0  4  8  0  0  0  0 0 0 | 0 0  4  0  2  0  0  0  0  0  0  0 0 | * * 6 *  *  *  * *  * * * | 1 0 1 0 0
... xo.3oo.3ox.&#x   ♦  8  0 | 0 12 12  0  0 |  0  8  0 24  0  0  0  0 0 0 | 0 2  0  8  6  0  0  0  0  0  0  0 0 | * * * 2  *  *  * *  * * * | 1 0 0 1 0
xxo xox ... ...&#x & ♦  6  2 | 3  2  4  8  1 |  1  0  2  2  4  4  2  2 0 0 | 0 0  1  0  0  2  2  2  1  0  0  0 0 | * * * * 24  *  * *  * * * | 0 1 1 0 0
... xox3ooo ...&#x & ♦  4  3 | 0  3  3  6  3 |  0  1  0  3  3  0  3  3 1 0 | 0 0  0  1  0  0  3  0  0  1  0  1 0 | * * * *  * 16  * *  * * * | 0 1 0 1 0
... xox ... oxx&#x   ♦  4  4 | 0  2  4  8  4 |  0  0  0  4  4  0  4  4 0 1 | 0 0  0  0  1  0  4  0  0  0  2  0 0 | * * * *  *  * 12 *  * * * | 0 0 1 1 0
x.o x.x3o.o ...&#x & ♦  6  3 | 3  6  0  6  3 |  3  2  0  0  0  3  6  0 1 0 | 1 0  0  0  0  0  0  3  0  2  0  0 0 | * * * *  *  *  * 8  * * * | 0 1 0 0 1
x.o x.x ... o.x&#x & ♦  4  4 | 2  2  0  8  4 |  1  0  0  0  0  4  4  4 0 1 | 0 0  0  0  0  0  0  2  2  0  2  0 0 | * * * *  *  *  * * 12 * * | 0 0 1 0 1
x.o ... o.o3o.x&#x & ♦  2  3 | 1  0  0  6  3 |  0  0  0  0  0  3  0  6 1 0 | 0 0  0  0  0  0  0  0  3  0  0  2 0 | * * * *  *  *  * *  * 8 * | 0 1 0 0 1
... x.x3o.o3o.x&#x & ♦  4 12 | 0  6  0 12 24 |  0  4  0  0  0  0 12 12 8 6 | 0 1  0  0  0  0  0  0  0  4  6  4 1 | * * * *  *  *  * *  * * 4 | 0 0 0 1 1
---------------------+-------+---------------+-----------------------------+-------------------------------------+---------------------------+----------
xx. xo.3oo.3ox.&#x   ♦ 16  0 | 8 24 24  0  0 | 12 16 12 48  0  0  0  0 0 0 | 8 4 24 16 12  0  0  0  0  0  0  0 0 | 2 8 6 2  0  0  0 0  0 0 0 | 1 * * * *
xxo xox3ooo ...&#x & ♦  8  3 | 4  6  6 12  3 |  3  2  3  6  6  6  6  6 1 0 | 1 0  3  2  0  3  6  3  3  2  0  2 0 | 0 1 0 0  3  2  0 1  0 1 0 | * 8 * * *
xxo xox ... oxx&#x   ♦  8  4 | 4  4  8 16  4 |  2  0  4  8  8  8  8  8 0 1 | 0 0  4  0  2  4  8  4  4  0  4  0 0 | 0 0 1 0  4  0  2 0  2 0 0 | * * 6 * *
... xox3ooo3oxx&#x   ♦  8 12 | 0 12 12 24 24 |  0  8  0 24 12  0 24 24 8 6 | 0 2  0  8  6  0 24  0  0  8 12  8 1 | 0 0 0 1  0  8  6 0  0 0 2 | * * * 2 *
x.o x.x3o.o3o.x&#x & ♦  8 12 | 4 12  0 24 24 |  6  8  0  0  0 12 24 24 8 6 | 4 2  0  0  0  0  0 12 12  8 12  8 1 | 1 0 0 0  0  0  0 4  6 4 2 | * * * * 2