4  
      
h     H   -- hin

        \
         +-- tedhin
wobei 
4 = {4}
h = hex
H = gyro hex

The icosiheptaheptacontidipeton (jak) could be given as point || hin || tac. Its tridiminishing (tedjak) chops off 3 hinpies, in fact one vertex from the first layer and two opposite ones from the third layer, leaving there the equatorial hex only. That one then will be gyrated to either of the other two hexes, from which hin could be thought of as a segmentoteron. If this remaining hex of the third layer is being thought of as a tegum sum of 2 perp. squares, and the vertices of one such square are being omitted as well, then this polyexon will be derived.

Incidence matrix according to Dynkin symbol

xoo3ooo3oxo xox oxx&#x   → height(1,2) = 0
                           height(1,3) = height(2,3) = sqrt(3/8) = 0.612372
(hin || part. para square)

o..3o..3o.. o.. o..    & | 16 * |  3 1  6  2 0 |  3 18  9  6  2  1  6 0 | 1  8  6 12  3  6  3 1 18  9 | 2  5 3 2  3  8  6 12  3 | 1 1 2  5 3
..o3..o3..o ..o ..o      |  * 4 |  0 0  0  8 2 |  0  0  0 12  8  8 12 1 | 0  0  0  0  0  8 12 8 24 24 | 0  0 0 2  8  8  6 24 12 | 0 2 1  8 6
-------------------------+------+--------------+------------------------+-----------------------------+-------------------------+-----------
x.. ... ... ... ...    & |  2 0 | 24 *  *  * * |  2  4  0  2  0  0  0 0 | 1  4  2  2  0  4  1 0  4  0 | 2  2 1 2  2  4  2  2  0 | 1 1 2  2 1
... ... ... x.. ...    & |  2 0 |  * 8  *  * * |  0  0  6  0  2  0  0 0 | 0  0  0  6  3  0  0 1  0  6 | 0  2 3 0  0  0  0  6  3 | 1 0 0  2 3
oo.3oo.3oo. oo. oo.&#x   |  2 0 |  * * 48  * * |  0  4  2  0  0  0  1 0 | 0  2  2  4  1  0  0 0  4  2 | 1  2 2 0  0  2  2  4  1 | 1 0 1  2 2
o.o3o.o3o.o o.o o.o&#x & |  1 1 |  * *  * 32 * |  0  0  0  3  1  1  3 0 | 0  0  0  0  0  3  3 1  9  6 | 0  0 0 1  3  4  3  9  3 | 0 1 1  4 3
... ... ... ..x ...    & |  0 2 |  * *  *  * 4 |  0  0  0  0  4  4  0 1 | 0  0  0  0  0  0  6 8  0 12 | 0  0 0 0  4  0  0 12 12 | 0 1 0  4 6
-------------------------+------+--------------+------------------------+-----------------------------+-------------------------+-----------
x..3o.. ... ... ...    & |  3 0 |  3 0  0  0 0 | 16  *  *  *  *  *  * * | 1  2  0  0  0  2  0 0  0  0 | 2  1 0 2  1  2  0  0  0 | 1 1 2  1 0
xo. ... ... ... ...&#x & |  3 0 |  1 0  2  0 0 |  * 96  *  *  *  *  * * | 0  1  1  1  0  0  0 0  1  0 | 1  1 1 0  0  1  1  1  0 | 1 0 1  1 1
... ... ... xo. ...&#x & |  3 0 |  0 1  2  0 0 |  *  * 48  *  *  *  * * | 0  0  0  2  1  0  0 0  0  1 | 0  1 2 0  0  0  0  2  1 | 1 0 0  1 2
x.o ... ... ... ...&#x & |  2 1 |  1 0  0  2 0 |  *  *  * 48  *  *  * * | 0  0  0  0  0  2  1 0  2  0 | 0  0 0 1  2  2  1  2  0 | 0 1 1  2 1
... ... ... x.x ...&#x & |  2 2 |  0 1  0  2 1 |  *  *  *  * 16  *  * * | 0  0  0  0  0  0  0 1  0  3 | 0  0 0 0  0  0  0  3  3 | 0 0 0  1 3
... ... ... ... o.x&#x & |  1 2 |  0 0  0  2 1 |  *  *  *  *  * 16  * * | 0  0  0  0  0  0  3 1  0  3 | 0  0 0 0  3  0  0  6  3 | 0 1 0  3 3
ooo3ooo3ooo ooo ooo&#x   |  2 1 |  0 0  1  2 0 |  *  *  *  *  *  * 48 * | 0  0  0  0  0  0  0 0  4  2 | 0  0 0 0  0  2  2  4  1 | 0 0 1  2 2
... ... ... ..x ..x      |  0 4 |  0 0  0  0 4 |  *  *  *  *  *  *  * 1 ♦ 0  0  0  0  0  0  0 8  0  0 | 0  0 0 0  0  0  0  0 12 | 0 0 0  0 6
-------------------------+------+--------------+------------------------+-----------------------------+-------------------------+-----------
x..3o..3o.. ... ...    & ♦  4 0 |  6 0  0  0 0 |  4  0  0  0  0  0  0 0 | 4  *  *  *  *  *  * *  *  * | 2  0 0 2  0  0  0  0  0 | 1 1 2  0 0
xo.3oo. ... ... ...&#x & ♦  4 0 |  3 0  3  0 0 |  1  3  0  0  0  0  0 0 | * 32  *  *  *  *  * *  *  * | 1  1 0 0  0  1  0  0  0 | 1 0 1  1 0
xo. ... ox. ... ...&#x   ♦  4 0 |  2 0  4  0 0 |  0  4  0  0  0  0  0 0 | *  * 24  *  *  *  * *  *  * | 1  0 1 0  0  0  1  0  0 | 1 0 1  0 1
xo. ... ... ... ox.&#x & ♦  4 0 |  1 1  4  0 0 |  0  2  2  0  0  0  0 0 | *  *  * 48  *  *  * *  *  * | 0  1 1 0  0  0  0  1  0 | 1 0 0  1 1
... ... ... xo. ox.&#x   ♦  4 0 |  0 2  4  0 0 |  0  0  4  0  0  0  0 0 | *  *  *  * 12  *  * *  *  * | 0  0 2 0  0  0  0  0  1 | 1 0 0  0 2
x.o3o.o ... ... ...&#x & ♦  3 1 |  3 0  0  3 0 |  1  0  0  3  0  0  0 0 | *  *  *  *  * 32  * *  *  * | 0  0 0 1  1  1  0  0  0 | 0 1 1  1 0
x.o ... ... ... o.x&#x & ♦  2 2 |  1 0  0  4 1 |  0  0  0  2  0  2  0 0 | *  *  *  *  *  * 24 *  *  * | 0  0 0 0  2  0  0  2  0 | 0 1 0  2 1
... ... ... x.x o.x&#x & ♦  2 4 |  0 1  0  4 4 |  0  0  0  0  2  2  0 1 | *  *  *  *  *  *  * 8  *  * | 0  0 0 0  0  0  0  0  3 | 0 0 0  0 3
xoo ... ... ... ...&#x & ♦  3 1 |  1 0  2  3 0 |  0  1  0  1  0  0  2 0 | *  *  *  *  *  *  * * 96  * | 0  0 0 0  0  1  1  1  0 | 0 0 1  1 1
... ... ... xox ...&#x & ♦  3 2 |  0 1  2  4 1 |  0  0  1  0  1  1  2 0 | *  *  *  *  *  *  * *  * 48 | 0  0 0 0  0  0  0  2  1 | 0 0 0  1 2
-------------------------+------+--------------+------------------------+-----------------------------+-------------------------+-----------
xo.3oo.3ox. ... ...&#x   ♦  8 0 | 12 0 12  0 0 |  8 24  0  0  0  0  0 0 | 2  8  6  0  0  0  0 0  0  0 | 4  * * *  *  *  *  *  * | 1 0 1  0 0
xo.3oo. ... ... ox.&#x & ♦  5 0 |  3 1  6  0 0 |  1  6  3  0  0  0  0 0 | 0  2  0  3  0  0  0 0  0  0 | * 16 * *  *  *  *  *  * | 1 0 0  1 0
xo. ... ox. xo. ox.&#zx  ♦  8 0 |  4 4 16  0 0 |  0 16 16  0  0  0  0 0 | 0  0  4  8  4  0  0 0  0  0 | *  * 6 *  *  *  *  *  * | 1 0 0  0 1
x.o3o.o3o.o ... ...&#x & ♦  4 1 |  6 0  0  4 0 |  4  0  0  6  0  0  0 0 | 1  0  0  0  0  4  0 0  0  0 | *  * * 8  *  *  *  *  * | 0 1 1  0 0
x.o3o.o ... ... o.x&#x & ♦  3 2 |  3 0  0  6 1 |  1  0  0  6  0  3  0 0 | 0  0  0  0  0  2  3 0  0  0 | *  * * * 16  *  *  *  * | 0 1 0  1 0
xoo3ooo ... ... ...&#x & ♦  4 1 |  3 0  3  4 0 |  1  3  0  3  0  0  3 0 | 0  1  0  0  0  1  0 0  3  0 | *  * * *  * 32  *  *  * | 0 0 1  1 0
xoo ... oxo ... ...&#x & ♦  4 1 |  2 0  4  4 0 |  0  4  0  2  0  0  4 0 | 0  0  1  0  0  0  0 0  4  0 | *  * * *  *  * 24  *  * | 0 0 1  0 1
xoo ... ... ... oxx&#x & ♦  4 2 |  1 1  4  6 1 |  0  2  2  2  1  2  4 0 | 0  0  0  1  0  0  1 0  2  2 | *  * * *  *  *  * 48  * | 0 0 0  1 1
... ... ... xox oxx&#x   ♦  4 4 |  0 2  4  8 4 |  0  0  4  0  4  4  4 1 | 0  0  0  0  1  0  0 2  0  4 | *  * * *  *  *  *  * 12 | 0 0 0  0 2
-------------------------+------+--------------+------------------------+-----------------------------+-------------------------+-----------
xo.3oo.3ox. xo. ox.&#zx  ♦ 16 0 | 24 8 48  0 0 | 16 96 48  0  0  0  0 0 | 4 32 24 48 12  0  0 0  0  0 | 4 16 6 0  0  0  0  0  0 | 1 * *  * *
x.o3o.o3o.o ... o.x&#x & ♦  4 2 |  6 0  0  8 1 |  4  0  0 12  0  4  0 0 | 1  0  0  0  0  8  6 0  0  0 | 0  0 0 2  4  0  0  0  0 | * 4 *  * *
xoo3ooo3oxo ... ...&#x   ♦  8 1 | 12 0 12  8 0 |  8 24  0 12  0  0 12 0 | 2  8  6  0  0  8  0 0 24  0 | 1  0 0 2  0  8  6  0  0 | * * 4  * *
xoo3ooo ... ... oxx&#x & ♦  5 2 |  3 1  6  8 1 |  1  6  3  6  1  3  6 0 | 0  2  0  3  0  2  3 0  6  3 | 0  1 0 0  1  2  0  3  0 | * * * 16 *
xoo ... oxo xox oxx&#x   ♦  8 4 |  4 4 16 16 4 |  0 16 16  8  8  8 16 1 | 0  0  4  8  4  0  4 4 16 16 | 0  0 1 0  0  0  4  8  4 | * * *  * 6