﻿ hedjak
 Acronym hedjak Name heptadiminished jak,square || hin Circumradius sqrt(2/3) = 0.816497 Lace cityin approx. ASCII-art ``` 4 h H -- hin \ +-- tedhin wobei 4 = {4} h = hex H = gyro hex ``` Coordinates (1/sqrt(2), 0, 0, 0, 0, -sqrt(3/8))                                     & all permutations, all changes of sign in the first 2 coord.s only (top square layer) (1/sqrt(8), 1/sqrt(8), 1/sqrt(8), 1/sqrt(8), 1/sqrt(8), 0)    & all even changes of sign in one but last coord. (bottom hin layer) Confer uniform relative: jak   segmentopeta: dijak   tedjak   hinpy   general polytopal classes: segmentopeta

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
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