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Acronym
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tedjak (alt.: hexgyt, hexalhin)
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Name
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tridiminished icosiheptaheptacontidipeton,
tridiminished 22,1,
hexadecachoral gyrotrigonism
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Circumradius
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sqrt(2/3) = 0.816497
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Lace city
in approx. ASCII-art
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where:
E N = x3o3o *b3o (hex)
N E = o3o3x *b3o (gyro hex)
O O = o3o3o *b3x (alt. gyro hex)
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Coordinates
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(1/sqrt(8), 1/sqrt(8), 1/sqrt(8), 1/sqrt(8); 1/sqrt(24), 1/sqrt(8)) & all permutations and all even changes of sign in first 4 coords
("even" hex E)
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(1/sqrt(8), 1/sqrt(8), 1/sqrt(8), -1/sqrt(8); 1/sqrt(24), -1/sqrt(8)) & all permutations and all even changes of sign in first 4 coords
("odd" hex O)
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(1/sqrt(2), 0, 0, 0; -1/sqrt(6), 0)
& all permutations and all changes of sign in first 4 coords
("normal" hex N)
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Face vector
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24, 168, 480, 600, 315, 51
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Confer
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- uniform relatives:
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jak
ico
- segmentopeta:
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dijak
hedjak
hinpy
- related CRFs:
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rettidjak
tettidjak
- general polytopal classes:
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segmentopeta
lace simplices
scaliform
gyrotrigonism
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External
links
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Note that the coordinates provided show that the projection of tedjak by reduction of the last 2 coordinates would result in ico.
It should be emphasized that not only all vertices are equivalent, but also all faces are regular triangles. Thence this polypeton allows for some of the same operations as regulars do:
its truncation results in tettidjak and
its rectification results in rettidjak.
Incidence matrix according to Dynkin symbol
xoo3ooo3oxo *b3oox&#x → all pairwise heights = 1/sqrt(2) = 0.707107
o..3o..3o.. *b3o.. | 8 * * ♦ 6 4 4 0 0 0 | 12 12 6 12 6 12 0 0 0 0 | 4 4 12 6 4 12 6 4 24 12 12 0 0 0 0 0 0 0 | 1 4 4 1 4 4 1 12 12 12 4 4 6 0 0 0 0 0 | 1 1 4 4 6 1 0
.o.3.o.3.o. *b3.o. | * 8 * ♦ 0 4 0 6 4 0 | 0 6 12 0 0 12 12 12 6 0 | 0 0 4 6 12 0 0 0 12 24 12 4 4 12 4 6 0 0 | 0 4 1 4 0 0 0 4 12 6 12 4 12 1 4 1 4 0 | 1 0 4 1 6 4 1
..o3..o3..o *b3..o | * * 8 ♦ 0 0 4 0 4 6 | 0 0 0 6 12 12 0 6 12 12 | 0 0 0 0 0 4 6 12 12 12 24 0 0 4 12 6 4 4 | 0 0 0 0 1 4 4 4 6 12 4 12 12 0 1 4 4 1 | 0 1 1 4 6 4 1
----------------------+-------+-------------------+-------------------------------+-------------------------------------------------+-------------------------------------------+---------------
x.. ... ... ... | 2 0 0 | 24 * * * * * ♦ 4 2 0 2 0 0 0 0 0 0 | 2 2 4 1 0 4 1 0 4 0 0 0 0 0 0 0 0 0 | 1 2 2 0 2 2 0 4 2 2 0 0 0 0 0 0 0 0 | 1 1 2 2 1 0 0
oo.3oo.3oo. *b3oo.&#x | 1 1 0 | * 32 * * * * ♦ 0 3 3 0 0 3 0 0 0 0 | 0 0 3 3 3 0 0 0 6 6 3 0 0 0 0 0 0 0 | 0 3 1 1 0 0 0 3 6 3 3 1 3 0 0 0 0 0 | 1 0 3 1 3 1 0
o.o3o.o3o.o *b3o.o&#x | 1 0 1 | * * 32 * * * ♦ 0 0 0 3 3 3 0 0 0 0 | 0 0 0 0 0 3 3 3 6 3 6 0 0 0 0 0 0 0 | 0 0 0 0 1 3 1 3 3 6 1 3 3 0 0 0 0 0 | 0 1 1 3 3 1 0
... ... .x. ... | 0 2 0 | * * * 24 * * ♦ 0 0 2 0 0 0 4 2 0 0 | 0 0 0 1 4 0 0 0 0 4 0 2 2 4 0 1 0 0 | 0 2 0 2 0 0 0 0 2 0 4 0 2 1 2 0 2 0 | 1 0 2 0 1 2 1
.oo3.oo3.oo *b3.oo&#x | 0 1 1 | * * * * 32 * ♦ 0 0 0 0 0 3 0 3 3 0 | 0 0 0 0 0 0 0 0 3 6 6 0 0 3 3 3 0 0 | 0 0 0 0 0 0 0 1 3 3 3 3 6 0 1 1 3 0 | 0 0 1 1 3 3 1
... ... ... ..x | 0 0 2 | * * * * * 24 ♦ 0 0 0 0 2 0 0 0 2 4 | 0 0 0 0 0 0 1 4 0 0 4 0 0 0 4 1 2 2 | 0 0 0 0 0 2 2 0 0 2 0 4 2 0 0 2 2 1 | 0 1 0 2 1 2 1
----------------------+-------+-------------------+-------------------------------+-------------------------------------------------+-------------------------------------------+---------------
x..3o.. ... ... | 3 0 0 | 3 0 0 0 0 0 | 32 * * * * * * * * * | 1 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 | 1 1 1 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 | 1 1 1 1 0 0 0
xo. ... ... ...&#x | 2 1 0 | 1 2 0 0 0 0 | * 48 * * * * * * * * | 0 0 2 1 0 0 0 0 2 0 0 0 0 0 0 0 0 0 | 0 2 1 0 0 0 0 2 2 1 0 0 0 0 0 0 0 0 | 1 0 2 1 1 0 0
... ... ox. ...&#x | 1 2 0 | 0 2 0 1 0 0 | * * 48 * * * * * * * | 0 0 0 1 2 0 0 0 0 2 0 0 0 0 0 0 0 0 | 0 2 0 1 0 0 0 0 2 0 2 0 1 0 0 0 0 0 | 1 0 2 0 1 1 0
x.o ... ... ...&#x | 2 0 1 | 1 0 2 0 0 0 | * * * 48 * * * * * * | 0 0 0 0 0 2 1 0 2 0 0 0 0 0 0 0 0 0 | 0 0 0 0 1 2 0 2 1 2 0 0 0 0 0 0 0 0 | 0 1 1 2 1 0 0
... ... ... o.x&#x | 1 0 2 | 0 0 2 0 0 1 | * * * * 48 * * * * * | 0 0 0 0 0 0 1 2 0 0 2 0 0 0 0 0 0 0 | 0 0 0 0 0 2 1 0 0 2 0 2 1 0 0 0 0 0 | 0 1 0 2 1 1 0
ooo3ooo3ooo *b3ooo&#x | 1 1 1 | 0 1 1 0 1 0 | * * * * * 96 * * * * ♦ 0 0 0 0 0 0 0 0 2 2 2 0 0 0 0 0 0 0 | 0 0 0 0 0 0 0 1 2 2 1 1 2 0 0 0 0 0 | 0 0 1 1 2 1 0
... .o.3.x. ... | 0 3 0 | 0 0 0 3 0 0 | * * * * * * 32 * * * | 0 0 0 0 1 0 0 0 0 0 0 1 1 1 0 0 0 0 | 0 1 0 1 0 0 0 0 0 0 1 0 0 1 1 0 1 0 | 1 0 1 0 0 1 1
... ... .xo ...&#x | 0 2 1 | 0 0 0 1 2 0 | * * * * * * * 48 * * | 0 0 0 0 0 0 0 0 0 2 0 0 0 2 0 1 0 0 | 0 0 0 0 0 0 0 0 1 0 2 0 2 0 1 0 2 0 | 0 0 1 0 1 2 1
... ... ... .ox&#x | 0 1 2 | 0 0 0 0 2 1 | * * * * * * * * 48 * | 0 0 0 0 0 0 0 0 0 0 2 0 0 0 2 1 0 0 | 0 0 0 0 0 0 0 0 0 1 0 2 2 0 0 1 2 0 | 0 0 0 1 1 2 1
... ..o ... *b3..x | 0 0 3 | 0 0 0 0 0 3 | * * * * * * * * * 32 | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 1 1 | 0 0 0 0 0 1 1 0 0 0 0 1 0 0 0 1 1 1 | 0 1 0 1 0 1 1
----------------------+-------+-------------------+-------------------------------+-------------------------------------------------+-------------------------------------------+---------------
x..3o..3o.. ... ♦ 4 0 0 | 6 0 0 0 0 0 | 4 0 0 0 0 0 0 0 0 0 | 8 * * * * * * * * * * * * * * * * * | 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | 1 1 1 0 0 0 0
x..3o.. ... *b3o.. ♦ 4 0 0 | 6 0 0 0 0 0 | 4 0 0 0 0 0 0 0 0 0 | * 8 * * * * * * * * * * * * * * * * | 1 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 | 1 1 0 1 0 0 0
xo.3oo. ... ...&#x ♦ 3 1 0 | 3 3 0 0 0 0 | 1 3 0 0 0 0 0 0 0 0 | * * 32 * * * * * * * * * * * * * * * | 0 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 | 1 0 1 1 0 0 0
xo. ... ox. ...&#x ♦ 2 2 0 | 1 4 0 1 0 0 | 0 2 2 0 0 0 0 0 0 0 | * * * 24 * * * * * * * * * * * * * * | 0 2 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 | 1 0 2 0 1 0 0
... oo.3ox. ...&#x ♦ 1 3 0 | 0 3 0 3 0 0 | 0 0 3 0 0 0 1 0 0 0 | * * * * 32 * * * * * * * * * * * * * | 0 1 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 | 1 0 1 0 0 1 0
x.o3o.o ... ...&#x ♦ 3 0 1 | 3 0 3 0 0 0 | 1 0 0 3 0 0 0 0 0 0 | * * * * * 32 * * * * * * * * * * * * | 0 0 0 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 | 0 1 1 1 0 0 0
x.o ... ... o.x&#x ♦ 2 0 2 | 1 0 4 0 0 1 | 0 0 0 2 2 0 0 0 0 0 | * * * * * * 24 * * * * * * * * * * * | 0 0 0 0 0 2 0 0 0 2 0 0 0 0 0 0 0 0 | 0 1 0 2 1 0 0
... o.o ... *b3o.x&#x ♦ 1 0 3 | 0 0 3 0 0 3 | 0 0 0 0 3 0 0 0 0 1 | * * * * * * * 32 * * * * * * * * * * | 0 0 0 0 0 1 1 0 0 0 0 1 0 0 0 0 0 0 | 0 1 0 1 0 1 0
xoo ... ... ...&#x ♦ 2 1 1 | 1 2 2 0 1 0 | 0 1 0 1 0 2 0 0 0 0 | * * * * * * * * 96 * * * * * * * * * | 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 | 0 0 1 1 1 0 0
... ... oxo ...&#x ♦ 1 2 1 | 0 2 1 1 2 0 | 0 0 1 0 0 2 0 1 0 0 | * * * * * * * * * 96 * * * * * * * * | 0 0 0 0 0 0 0 0 1 0 1 0 1 0 0 0 0 0 | 0 0 1 0 1 1 0
... ... ... oox&#x ♦ 1 1 2 | 0 1 2 0 2 1 | 0 0 0 0 1 2 0 0 1 0 | * * * * * * * * * * 96 * * * * * * * | 0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 0 0 0 | 0 0 0 1 1 1 0
.o.3.o.3.x. ... ♦ 0 4 0 | 0 0 0 6 0 0 | 0 0 0 0 0 0 4 0 0 0 | * * * * * * * * * * * 8 * * * * * * | 0 1 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 | 1 0 1 0 0 0 1
... .o.3.x. *b3.o. ♦ 0 4 0 | 0 0 0 6 0 0 | 0 0 0 0 0 0 4 0 0 0 | * * * * * * * * * * * * 8 * * * * * | 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 1 0 | 1 0 0 0 0 1 1
... .oo3.xo ...&#x ♦ 0 3 1 | 0 0 0 3 3 0 | 0 0 0 0 0 0 1 3 0 0 | * * * * * * * * * * * * * 32 * * * * | 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 1 0 | 0 0 1 0 0 1 1
... .oo ... *b3.ox&#x ♦ 0 1 3 | 0 0 0 0 3 3 | 0 0 0 0 0 0 0 0 3 1 | * * * * * * * * * * * * * * 32 * * * | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 0 | 0 0 0 1 0 1 1
... ... .xo .ox&#x ♦ 0 2 2 | 0 0 0 1 4 1 | 0 0 0 0 0 0 0 2 2 0 | * * * * * * * * * * * * * * * 24 * * | 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 2 0 | 0 0 0 0 1 2 1
..o3..o ... *b3..x ♦ 0 0 4 | 0 0 0 0 0 6 | 0 0 0 0 0 0 0 0 0 4 | * * * * * * * * * * * * * * * * 8 * | 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 1 | 0 1 0 1 0 0 1
... ..o3..o *b3..x ♦ 0 0 4 | 0 0 0 0 0 6 | 0 0 0 0 0 0 0 0 0 4 | * * * * * * * * * * * * * * * * * 8 | 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 1 | 0 1 0 0 0 1 1
----------------------+-------+-------------------+-------------------------------+-------------------------------------------------+-------------------------------------------+---------------
x..3o..3o.. *b3o.. ♦ 8 0 0 | 24 0 0 0 0 0 | 32 0 0 0 0 0 0 0 0 0 | 8 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 1 * * * * * * * * * * * * * * * * * | 1 1 0 0 0 0 0
xo.3oo.3ox. ...&#x ♦ 4 4 0 | 6 12 0 6 0 0 | 4 12 12 0 0 0 4 0 0 0 | 1 0 4 6 4 0 0 0 0 0 0 1 0 0 0 0 0 0 | * 8 * * * * * * * * * * * * * * * * | 1 0 1 0 0 0 0
xo.3oo. ... *b3oo.&#x ♦ 4 1 0 | 6 4 0 0 0 0 | 4 6 0 0 0 0 0 0 0 0 | 0 1 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | * * 8 * * * * * * * * * * * * * * * | 1 0 0 1 0 0 0
... oo.3ox. *b3oo.&#x ♦ 1 4 0 | 0 4 0 6 0 0 | 0 0 6 0 0 0 4 0 0 0 | 0 0 0 0 4 0 0 0 0 0 0 0 1 0 0 0 0 0 | * * * 8 * * * * * * * * * * * * * * | 1 0 0 0 0 1 0
x.o3o.o3o.o ...&#x ♦ 4 0 1 | 6 0 4 0 0 0 | 4 0 0 6 0 0 0 0 0 0 | 1 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 | * * * * 8 * * * * * * * * * * * * * | 0 1 1 0 0 0 0
x.o3o.o ... *b3o.x&#x ♦ 4 0 4 | 6 0 12 0 0 6 | 4 0 0 12 12 0 0 0 0 4 | 0 1 0 0 0 4 6 4 0 0 0 0 0 0 0 0 1 0 | * * * * * 8 * * * * * * * * * * * * | 0 1 0 1 0 0 0
... o.o3o.o *b3o.x&#x ♦ 1 0 4 | 0 0 4 0 0 6 | 0 0 0 0 6 0 0 0 0 4 | 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 1 | * * * * * * 8 * * * * * * * * * * * | 0 1 0 0 0 1 0
xoo3ooo ... ...&#x ♦ 3 1 1 | 3 3 3 0 1 0 | 1 3 0 3 0 3 0 0 0 0 | 0 0 1 0 0 1 0 0 3 0 0 0 0 0 0 0 0 0 | * * * * * * * 32 * * * * * * * * * * | 0 0 1 1 0 0 0
xoo ... oxo ...&#x ♦ 2 2 1 | 1 4 2 1 2 0 | 0 2 2 1 0 4 0 1 0 0 | 0 0 0 1 0 0 0 0 2 2 0 0 0 0 0 0 0 0 | * * * * * * * * 48 * * * * * * * * * | 0 0 1 0 1 0 0
xoo ... ... oox&#x ♦ 2 1 2 | 1 2 4 0 2 1 | 0 1 0 2 2 4 0 0 1 0 | 0 0 0 0 0 0 1 0 2 0 2 0 0 0 0 0 0 0 | * * * * * * * * * 48 * * * * * * * * | 0 0 0 1 1 0 0
... ooo3oxo ...&#x ♦ 1 3 1 | 0 3 1 3 3 0 | 0 0 3 0 0 3 1 3 0 0 | 0 0 0 0 1 0 0 0 0 3 0 0 0 1 0 0 0 0 | * * * * * * * * * * 32 * * * * * * * | 0 0 1 0 0 1 0
... ooo ... *b3oox&#x ♦ 1 1 3 | 0 1 3 0 3 3 | 0 0 0 0 3 3 0 0 3 1 | 0 0 0 0 0 0 0 1 0 0 3 0 0 0 1 0 0 0 | * * * * * * * * * * * 32 * * * * * * | 0 0 0 1 0 1 0
... ... oxo oox&#x ♦ 1 2 2 | 0 2 2 1 4 1 | 0 0 1 0 1 4 0 2 2 0 | 0 0 0 0 0 0 0 0 0 2 2 0 0 0 0 1 0 0 | * * * * * * * * * * * * 48 * * * * * | 0 0 0 0 1 1 0
.o.3.o.3.x. *b3.o. ♦ 0 8 0 | 0 0 0 24 0 0 | 0 0 0 0 0 0 32 0 0 0 | 0 0 0 0 0 0 0 0 0 0 0 8 8 0 0 0 0 0 | * * * * * * * * * * * * * 1 * * * * | 1 0 0 0 0 0 1
.oo3.oo3.xo ...&#x ♦ 0 4 1 | 0 0 0 6 4 0 | 0 0 0 0 0 0 4 6 0 0 | 0 0 0 0 0 0 0 0 0 0 0 1 0 4 0 0 0 0 | * * * * * * * * * * * * * * 8 * * * | 0 0 1 0 0 0 1
.oo3.oo ... *b3.ox&#x ♦ 0 1 4 | 0 0 0 0 4 6 | 0 0 0 0 0 0 0 0 6 4 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 1 0 | * * * * * * * * * * * * * * * 8 * * | 0 0 0 1 0 0 1
... .oo3.xo *b3.ox&#x ♦ 0 4 4 | 0 0 0 6 12 6 | 0 0 0 0 0 0 4 12 12 4 | 0 0 0 0 0 0 0 0 0 0 0 0 1 4 4 6 0 1 | * * * * * * * * * * * * * * * * 8 * | 0 0 0 0 0 1 1
..o3..o2..o *b3..x ♦ 0 0 8 | 0 0 0 0 0 24 | 0 0 0 0 0 0 0 0 0 32 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8 8 | * * * * * * * * * * * * * * * * * 1 | 0 1 0 0 0 0 1
----------------------+-------+-------------------+-------------------------------+-------------------------------------------------+-------------------------------------------+---------------
xo.3oo.3ox. *b3oo.&#x ♦ 8 8 0 | 24 32 0 24 0 0 | 32 48 48 0 0 0 32 0 0 0 | 8 8 32 24 32 0 0 0 0 0 0 8 8 0 0 0 0 0 | 1 8 8 8 0 0 0 0 0 0 0 0 0 1 0 0 0 0 | 1 * * * * * *
x.o3o.o3o.o *b3o.x&#x ♦ 8 0 8 | 24 0 32 0 0 24 | 32 0 0 48 48 0 0 0 0 32 | 8 8 0 0 0 32 24 32 0 0 0 0 0 0 0 0 8 8 | 1 0 0 0 8 8 8 0 0 0 0 0 0 0 0 0 0 1 | * 1 * * * * *
xoo3ooo3oxo ...&#x ♦ 4 4 1 | 6 12 4 6 4 0 | 4 12 12 6 0 12 4 6 0 0 | 1 0 4 6 4 4 0 0 12 12 0 1 0 4 0 0 0 0 | 0 1 0 0 1 0 0 4 6 0 4 0 0 0 1 0 0 0 | * * 8 * * * *
xoo3ooo ... *b3oox&#x ♦ 4 1 4 | 6 4 12 0 4 6 | 4 6 0 12 12 12 0 0 6 4 | 0 1 4 0 0 4 6 4 12 0 12 0 0 0 4 0 1 0 | 0 0 1 0 0 1 0 4 0 6 0 4 0 0 0 1 0 0 | * * * 8 * * *
xoo ... oxo oox&#x ♦ 2 2 2 | 1 4 4 1 4 1 | 0 2 2 2 2 8 0 2 2 0 | 0 0 0 1 0 0 1 0 4 4 4 0 0 0 0 1 0 0 | 0 0 0 0 0 0 0 0 2 2 0 0 2 0 0 0 0 0 | * * * * 24 * *
... ooo3oxo *b3oox&#x ♦ 1 4 4 | 0 4 4 6 12 6 | 0 0 6 0 6 12 4 12 12 4 | 0 0 0 0 4 0 0 4 0 12 12 0 1 4 4 6 0 1 | 0 0 0 1 0 0 1 0 0 0 4 4 6 0 0 0 1 0 | * * * * * 8 *
.oo3.oo3.xo *b3.ox&#x ♦ 0 8 8 | 0 0 0 24 32 24 | 0 0 0 0 0 0 32 48 48 32 | 0 0 0 0 0 0 0 0 0 0 0 8 8 32 32 24 8 8 | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 8 8 8 1 | * * * * * * 1
or
o..3o..3o.. *b3o.. & | 24 ♦ 6 8 | 12 36 12 | 8 32 12 48 | 1 8 10 20 30 | 2 9 6
------------------------+----+-------+-----------+---------------+----------------+--------
x.. ... ... ... & | 2 | 72 * ♦ 4 4 0 | 4 8 2 4 | 1 4 4 4 4 | 2 4 1
oo.3oo.3oo. *b3oo.&#x & | 2 | * 96 ♦ 0 6 3 | 0 6 3 15 | 0 3 2 7 12 | 1 5 3
------------------------+----+-------+-----------+---------------+----------------+--------
x..3o.. ... ... & | 3 | 3 0 | 96 * * | 2 2 0 0 | 1 2 2 1 0 | 2 2 0
xo. ... ... ...&#x & | 3 | 1 2 | * 288 * | 0 2 1 2 | 0 2 1 2 3 | 1 3 1
ooo3ooo3ooo *b3ooo&#x | 3 | 0 3 | * * 96 ♦ 0 0 0 6 | 0 0 0 3 6 | 0 3 2
------------------------+----+-------+-----------+---------------+----------------+--------
x..3o..3o.. ... & ♦ 4 | 6 0 | 4 0 0 | 48 * * * | 1 1 1 0 0 | 2 1 0
xo.3oo. ... ...&#x & ♦ 4 | 3 3 | 1 3 0 | * 192 * * | 0 1 1 1 0 | 1 2 0
xo. ... ox. ...&#x & ♦ 4 | 2 4 | 0 4 0 | * * 72 * | 0 2 0 0 2 | 1 2 1
xoo ... ... ...&#x & ♦ 4 | 1 5 | 0 2 2 | * * * 288 | 0 0 0 1 2 | 0 2 1
------------------------+----+-------+-----------+---------------+----------------+--------
x..3o..3o.. *b3o.. & ♦ 8 | 24 0 | 32 0 0 | 16 0 0 0 | 3 * * * * | 2 0 0
xo.3oo.3ox. ...&#x & ♦ 8 | 12 12 | 8 24 0 | 2 8 6 0 | * 24 * * * | 1 1 0
xo.3oo. ... *b3oo.&#x & ♦ 5 | 6 4 | 4 6 0 | 1 4 0 0 | * * 48 * * | 1 1 0
xoo3ooo ... ...&#x & ♦ 5 | 3 7 | 1 6 3 | 0 2 0 3 | * * * 96 * | 0 2 0
xoo ... oxo ...&#x & ♦ 5 | 2 8 | 0 6 4 | 0 0 1 4 | * * * * 144 | 0 1 1
------------------------+----+-------+-----------+---------------+----------------+--------
xo.3oo.3ox. *b3oo.&#x & ♦ 16 | 48 32 | 64 96 0 | 32 64 24 0 | 2 8 16 0 0 | 3 * *
xoo3ooo3oxo ...&#x & ♦ 9 | 12 20 | 8 36 12 | 2 16 6 24 | 0 1 2 8 6 | * 24 *
xoo ... oxo oox&#x ♦ 6 | 3 12 | 0 12 8 | 0 0 3 12 | 0 0 0 0 6 | * * 24
(xo)(xo)(ox) (xo)(ox)(xo) (ox)(xo)(xo) (ox)(ox)(ox)&#x - height(12,34) = height(12,56) = height(34,56) = 1/sqrt(2) = 0.707107
height(1,2) = height(3,4) = height(5,6) = 0
(gyrotrigonism of 3 tegum sums of 2 squares each)
(o.)(..)(..) (o.)(..)(..) (o.)(..)(..) (o.)(..)(..) & | 24 ♦ 2 4 8 | 12 12 24 4 8 | 8 32 4 16 0 0 | 1 10 8 20 10 20 | 2 9 2 4
----------------------------------------------------------+----+----------+-----------------+---------------------+------------------+----------
(x.)(..)(..) (..)(..)(..) (..)(..)(..) (..)(..)(..) & | 2 | 24 * * ♦ 4 4 0 0 0 | 4 8 2 4 0 0 | 1 4 4 4 4 0 | 2 4 1 0
(oo)(..)(..) (oo)(..)(..) (oo)(..)(..) (oo)(..)(..)&#x & | 2 | * 48 * ♦ 4 0 4 0 0 | 4 8 0 0 2 4 | 1 4 4 4 0 4 | 2 4 0 1
(o.)(o.)(..) (o.)(o.)(..) (o.)(o.)(..) (o.)(o.)(..)&#x & | 2 | * * 96 ♦ 0 2 4 1 2 | 0 6 1 5 2 10 | 0 2 3 7 4 8 | 1 5 1 2
----------------------------------------------------------+----+----------+-----------------+---------------------+------------------+----------
(xo)(..)(..) (..)(..)(..) (..)(..)(..) (..)(..)(..)&#x & | 3 | 1 2 0 | 96 * * * * | 2 2 0 0 0 0 | 1 2 2 1 0 0 | 2 2 0 0
(x.)(.o)(..) (..)(..)(..) (..)(..)(..) (..)(..)(..)&#x & | 3 | 1 0 2 | * 96 * * * | 0 2 1 2 0 0 | 0 1 2 2 3 0 | 1 3 1 0
(oo)(o.)(..) (oo)(o.)(..) (oo)(o.)(..) (oo)(o.)(..)&#x & | 3 | 0 1 2 | * * 192 * * | 0 2 0 0 1 2 | 0 1 2 2 0 3 | 1 3 0 1
(o.)(o.)(o.) (o.)(o.)(o.) (o.)(o.)(o.) (o.)(o.)(o.)&#x & | 3 | 0 0 3 | * * * 64 * ♦ 0 0 0 3 0 3 | 0 0 0 3 3 3 | 0 3 1 1
(.o)(o.)(o.) (.o)(o.)(o.) (.o)(o.)(o.) (.o)(o.)(o.)&#x & | 3 | 0 0 3 | * * * * 32 ♦ 0 0 0 0 0 6 | 0 0 0 3 0 6 | 0 3 0 2
----------------------------------------------------------+----+----------+-----------------+---------------------+------------------+----------
(xo)(..)(..) (..)(..)(..) (ox)(..)(..) (..)(..)(..)&#x & ♦ 4 | 2 4 0 | 4 0 0 0 0 | 48 * * * * * | 1 1 1 0 0 0 | 2 1 0 0
(xo)(.o)(..) (..)(..)(..) (..)(..)(..) (..)(..)(..)&#x & ♦ 4 | 1 2 3 | 1 1 2 0 0 | * 192 * * * * | 0 1 1 1 0 0 | 1 2 0 0
(x.)(.o)(..) (..)(..)(..) (..)(..)(..) (o.)(.x)(..)&#x & ♦ 4 | 2 0 4 | 0 4 0 0 0 | * * 24 * * * | 0 0 2 0 2 0 | 1 2 1 0
(x.)(.o)(o.) (..)(..)(..) (..)(..)(..) (..)(..)(..)&#x & ♦ 4 | 1 0 5 | 0 2 0 2 0 | * * * 96 * * | 0 0 0 1 2 0 | 0 2 1 0
(oo)(oo)(..) (oo)(oo)(..) (oo)(oo)(..) (oo)(oo)(..)&#x & ♦ 4 | 0 2 4 | 0 0 4 0 0 | * * * * 48 * | 0 0 2 0 0 2 | 1 2 0 1
(oo)(o.)(o.) (oo)(o.)(o.) (oo)(o.)(o.) (oo)(o.)(o.)&#x & ♦ 4 | 0 1 5 | 0 0 2 1 1 | * * * * * 192 | 0 0 0 1 0 2 | 0 2 0 1
----------------------------------------------------------+----+----------+-----------------+---------------------+------------------+----------
(xo)(..)(..) (xo)(..)(..) (ox)(..)(..) (ox)(..)(..)&#zx & ♦ 8 | 8 16 0 | 32 0 0 0 0 | 16 0 0 0 0 0 | 3 * * * * * | 2 0 0 0
(xo)(.o)(..) (..)(..)(..) (ox)(.o)(..) (..)(..)(..)&#x & ♦ 5 | 2 4 4 | 4 2 4 0 0 | 1 4 0 0 0 0 | * 48 * * * * | 1 1 0 0
(..)(..)(..) (xo)(ox)(..) (ox)(xo)(..) (..)(..)(..)&#x & ♦ 8 | 4 8 12 | 8 8 16 0 0 | 2 8 2 0 4 0 | * * 24 * * * | 1 1 0 0
(xo)(.o)(o.) (..)(..)(..) (..)(..)(..) (..)(..)(..)&#x & ♦ 5 | 1 2 7 | 1 2 4 2 1 | 0 2 0 1 0 2 | * * * 96 * * | 0 2 0 0
(x.)(.o)(o.) (..)(..)(..) (..)(..)(..) (o.)(.x)(o.)&#x & ♦ 5 | 2 0 8 | 0 6 0 4 0 | 0 0 1 4 0 0 | * * * * 48 * | 0 1 1 0
(oo)(oo)(o.) (oo)(oo)(o.) (oo)(oo)(o.) (oo)(oo)(o.)&#x & ♦ 5 | 0 2 8 | 0 0 6 2 2 | 0 0 0 0 1 4 | * * * * * 96 | 0 1 0 1
----------------------------------------------------------+----+----------+-----------------+---------------------+------------------+----------
(xo)(xo)(..) (xo)(ox)(..) (ox)(xo)(..) (ox)(ox)(..)&#x & ♦ 16 | 16 32 32 | 64 32 64 0 0 | 32 64 8 0 16 0 | 2 16 8 0 0 0 | 3 * * *
(..)(..)(..) (xo)(ox)(.o) (ox)(xo)(.o) (..)(..)(..)&#x & ♦ 9 | 4 8 20 | 8 12 24 8 4 | 2 16 2 8 4 16 | 0 2 1 8 2 4 | * 24 * *
(x.)(.o)(o.) (..)(..)(..) (o.)(.o)(x.) (o.)(.x)(o.)&#x & ♦ 6 | 3 0 12 | 0 12 0 8 0 | 0 0 3 12 0 0 | 0 0 0 0 6 0 | * * 8 *
(oo)(oo)(oo) (oo)(oo)(oo) (oo)(oo)(oo) (oo)(oo)(oo)&#x ♦ 6 | 0 3 12 | 0 0 12 4 4 | 0 0 0 0 3 12 | 0 0 0 0 0 6 | * * * 16
x..3o..3o.. *b3o.. || .oo3.oo3.xo *b3.ox&#x → height = sqrt(3/8) = 0.612372
hex || hin
o..3o..3o.. *b3o.. | 8 * ♦ 6 8 0 0 | 12 24 12 12 0 0 | 8 24 12 8 24 24 0 0 0 0 | 1 8 8 2 12 24 8 6 0 0 0 | 2 8 6 1 0
.o.3.o.3.o. *b3.o. & | * 16 ♦ 0 4 6 4 | 0 6 12 12 12 18 | 0 4 6 12 12 36 4 4 16 6 | 0 4 1 4 4 18 16 12 1 5 4 | 1 5 6 4 1
------------------------+------+-------------+-------------------+--------------------------------+-------------------------------+------------
x.. ... ... ... | 2 0 | 24 * * * ♦ 4 4 0 0 0 0 | 4 8 2 0 4 0 0 0 0 0 | 1 4 4 0 4 4 0 0 0 0 0 | 1 4 1 0 0
oo.3oo.3oo. *b3oo.&#x & | 1 1 | * 64 * * ♦ 0 3 3 3 0 0 | 0 3 3 3 6 9 0 0 0 0 | 0 3 1 1 3 9 4 3 0 0 0 | 1 4 3 1 0
... ... .x. ... & | 0 2 | * * 48 * ♦ 0 0 2 0 4 2 | 0 0 1 4 0 4 2 2 4 1 | 0 2 0 2 0 2 4 2 1 2 2 | 1 2 1 2 1
.oo3.oo3.oo *b3.oo&#x | 0 2 | * * * 32 ♦ 0 0 0 3 0 6 | 0 0 0 0 3 12 0 0 6 3 | 0 0 0 0 1 6 6 6 0 2 3 | 0 2 3 3 1
------------------------+------+-------------+-------------------+--------------------------------+-------------------------------+------------
x..3o.. ... ... | 3 0 | 3 0 0 0 | 32 * * * * * | 2 2 0 0 0 0 0 0 0 0 | 1 2 2 0 1 0 0 0 0 0 0 | 2 2 0 0 0
xo. ... ... ...&#x & | 2 1 | 1 2 0 0 | * 96 * * * * | 0 2 1 0 2 0 0 0 0 0 | 0 2 1 0 2 3 0 0 0 0 0 | 1 3 1 0 0
... ... ox. ...&#x & | 1 2 | 0 2 1 0 | * * 96 * * * | 0 0 1 2 0 2 0 0 0 0 | 0 2 0 1 0 2 2 1 0 0 0 | 1 2 1 1 0
ooo3ooo3ooo *b3ooo&#x | 1 2 | 0 2 0 1 | * * * 96 * * ♦ 0 0 0 0 2 4 0 0 0 0 | 0 0 0 0 1 4 2 2 0 0 0 | 0 2 2 1 0
... .o.3.x. ... & | 0 3 | 0 0 3 0 | * * * * 64 * | 0 0 0 1 0 0 1 1 1 0 | 0 1 0 1 0 0 1 0 1 1 1 | 1 1 0 1 1
... ... .xo ...&#x & | 0 3 | 0 0 1 2 | * * * * * 96 | 0 0 0 0 0 2 0 0 2 1 | 0 0 0 0 0 1 2 2 0 1 2 | 0 1 1 2 1
------------------------+------+-------------+-------------------+--------------------------------+-------------------------------+------------
x..3o..3o.. ... & ♦ 4 0 | 6 0 0 0 | 4 0 0 0 0 0 | 16 * * * * * * * * * | 1 1 1 0 0 0 0 0 0 0 0 | 2 1 0 0 0
xo.3oo. ... ...&#x & ♦ 3 1 | 3 3 0 0 | 1 3 0 0 0 0 | * 64 * * * * * * * * | 0 1 1 0 1 0 0 0 0 0 0 | 1 2 0 0 0
xo. ... ox. ...&#x & ♦ 2 2 | 1 4 1 0 | 0 2 2 0 0 0 | * * 48 * * * * * * * | 0 2 0 0 0 2 0 0 0 0 0 | 1 2 1 0 0
... oo.3ox. ...&#x & ♦ 1 3 | 0 3 3 0 | 0 0 3 0 1 0 | * * * 64 * * * * * * | 0 1 0 1 0 0 1 0 0 0 0 | 1 1 0 1 0
xoo ... ... ...&#x ♦ 2 2 | 1 4 0 1 | 0 2 0 2 0 0 | * * * * 96 * * * * * | 0 0 0 0 1 2 0 0 0 0 0 | 0 2 1 0 0
... ... oxo ...&#x & ♦ 1 3 | 0 3 1 2 | 0 0 1 2 0 1 | * * * * * 192 * * * * | 0 0 0 0 0 1 1 1 0 0 0 | 0 1 1 1 0
.o.3.o.3.x. ... & ♦ 0 4 | 0 0 6 0 | 0 0 0 0 4 0 | * * * * * * 16 * * * | 0 1 0 0 0 0 0 0 1 1 0 | 1 1 0 0 1
... .o.3.x. *b3.o. & ♦ 0 4 | 0 0 6 0 | 0 0 0 0 4 0 | * * * * * * * 16 * * | 0 0 0 1 0 0 0 0 1 0 1 | 1 0 0 1 1
... .oo3.xo ...&#x & ♦ 0 4 | 0 0 3 3 | 0 0 0 0 1 3 | * * * * * * * * 64 * | 0 0 0 0 0 0 1 0 0 1 1 | 0 1 0 1 1
... ... .xo .ox&#x ♦ 0 4 | 0 0 2 4 | 0 0 0 0 0 4 | * * * * * * * * * 24 | 0 0 0 0 0 0 0 2 0 0 2 | 0 0 1 2 1
------------------------+------+-------------+-------------------+--------------------------------+-------------------------------+------------
x..3o..3o.. *b3o.. ♦ 8 0 | 24 0 0 0 | 32 0 0 0 0 0 | 16 0 0 0 0 0 0 0 0 0 | 1 * * * * * * * * * * | 2 0 0 0 0
xo.3oo.3ox. ...&#x & ♦ 4 4 | 6 12 6 0 | 4 12 12 0 4 0 | 1 4 6 4 0 0 1 0 0 0 | * 16 * * * * * * * * * | 1 1 0 0 0
xo.3oo. ... *b3oo.&#x & ♦ 4 1 | 6 4 0 0 | 4 6 0 0 0 0 | 1 4 0 0 0 0 0 0 0 0 | * * 16 * * * * * * * * | 1 1 0 0 0
... oo.3ox. *b3oo.&#x & ♦ 1 4 | 0 4 6 0 | 0 0 6 0 4 0 | 0 0 0 4 0 0 0 1 0 0 | * * * 16 * * * * * * * | 1 0 0 1 0
xoo3ooo ... ...&#x ♦ 3 2 | 3 6 0 1 | 1 6 0 3 0 0 | 0 2 0 0 3 0 0 0 0 0 | * * * * 32 * * * * * * | 0 2 0 0 0
xoo ... oxo ...&#x & ♦ 2 3 | 1 6 1 2 | 0 3 2 4 0 1 | 0 0 1 0 2 2 0 0 0 0 | * * * * * 96 * * * * * | 0 1 1 0 0
... ooo3oxo ...&#x & ♦ 1 4 | 0 4 3 3 | 0 0 3 3 1 3 | 0 0 0 1 0 3 0 0 1 0 | * * * * * * 64 * * * * | 0 1 0 1 0
... ... oxo oox&#x ♦ 1 4 | 0 4 2 4 | 0 0 2 4 0 4 | 0 0 0 0 0 4 0 0 0 1 | * * * * * * * 48 * * * | 0 0 1 1 0
.o.3.o.3.x. *b3.o. & ♦ 0 8 | 0 0 24 0 | 0 0 0 0 32 0 | 0 0 0 0 0 0 8 8 0 0 | * * * * * * * * 2 * * | 1 0 0 0 1
.oo3.oo3.xo ...&#x & ♦ 0 5 | 0 0 6 4 | 0 0 0 0 4 6 | 0 0 0 0 0 0 1 0 4 0 | * * * * * * * * * 16 * | 0 1 0 0 1
... .oo3.xo *b3.ox&#x ♦ 0 8 | 0 0 12 12 | 0 0 0 0 8 24 | 0 0 0 0 0 0 0 2 8 6 | * * * * * * * * * * 8 | 0 0 0 1 1
------------------------+------+-------------+-------------------+--------------------------------+-------------------------------+------------
xo.3oo.3ox. *b3oo.&#x & ♦ 8 8 | 24 32 24 0 | 32 48 48 0 32 0 | 16 32 24 32 0 0 8 8 0 0 | 1 8 8 8 0 0 0 0 1 0 0 | 2 * * * *
xoo3ooo3oxo ...&#x & ♦ 4 5 | 6 16 6 4 | 4 18 12 12 4 6 | 1 8 6 4 12 12 1 0 4 0 | 0 1 1 0 4 6 4 0 0 1 0 | * 16 * * *
xoo ... oxo oox&#x ♦ 2 4 | 1 8 2 4 | 0 4 4 8 0 4 | 0 0 2 0 4 8 0 0 0 1 | 0 0 0 0 0 4 0 2 0 0 0 | * * 24 * *
... ooo3oxo *b3oox&#x ♦ 1 8 | 0 8 12 12 | 0 0 12 12 8 24 | 0 0 0 8 0 24 0 2 8 6 | 0 0 0 2 0 0 8 6 0 0 1 | * * * 8 *
.oo3.oo3.xo *b3.ox&#x ♦ 0 16 | 0 0 48 32 | 0 0 0 0 64 96 | 0 0 0 0 0 0 16 16 64 24 | 0 0 0 0 0 0 0 0 2 16 8 | * * * * 1