Acronym | hexaco |
Name |
hexadecachoron atop cuboctahedron, 0.147584-luna of rectified triacontiditeron |
Circumradius | 1 |
Lace city in approx. ASCII-art |
x3o3o o3o3x x3o3x |
Face vector | 20, 72, 106, 68, 17 |
Confer |
|
The dihedral angle at co between tetaco and tetaco is arccos(1/6) = 53.130102°, which is 0.147584 of the full circle.
Incidence matrix according to Dynkin symbol
xxo3ooo3oxx&#x → height(1,2) = height(2,3) = sqrt(5/8) = 0.790569 height(1,3) = 1/sqrt(2) = 0.707107 o..3o..3o.. | 4 * * | 3 3 3 0 0 0 0 | 3 6 3 6 3 3 0 0 0 0 0 0 | 1 3 3 1 3 3 1 6 3 0 0 0 0 0 | 1 1 3 3 1 0 .o.3.o.3.o. | * 12 * | 0 1 0 2 2 1 0 | 0 2 2 0 0 1 1 2 1 2 2 0 | 0 1 2 1 0 0 0 2 2 1 1 2 1 0 | 1 0 1 2 1 1 ..o3..o3..o | * * 4 | 0 0 3 0 0 3 3 | 0 0 0 3 6 3 0 0 0 3 6 3 | 0 0 0 0 1 3 3 3 6 0 1 3 3 1 | 0 1 1 3 3 1 ---------------+--------+--------------------+--------------------------------+-------------------------------+------------ x.. ... ... | 2 0 0 | 6 * * * * * * | 2 2 0 2 0 0 0 0 0 0 0 0 | 1 2 1 0 2 1 0 2 0 0 0 0 0 0 | 1 1 2 1 0 0 oo.3oo.3oo.&#x | 1 1 0 | * 12 * * * * * | 0 2 2 0 0 1 0 0 0 0 0 0 | 0 1 2 1 0 0 0 2 2 0 0 0 0 0 | 1 0 1 2 1 0 o.o3o.o3o.o&#x | 1 0 1 | * * 12 * * * * | 0 0 0 2 2 1 0 0 0 0 0 0 | 0 0 0 0 1 2 1 2 2 0 0 0 0 0 | 0 1 1 2 1 0 .x. ... ... | 0 2 0 | * * * 12 * * * | 0 1 0 0 0 0 1 1 0 1 0 0 | 0 1 1 0 0 0 0 1 0 1 1 1 0 0 | 1 0 1 1 0 1 ... ... .x. | 0 2 0 | * * * * 12 * * | 0 0 1 0 0 0 0 1 1 0 1 0 | 0 0 1 1 0 0 0 0 1 1 0 1 1 0 | 1 0 0 1 1 1 .oo3.oo3.oo&#x | 0 1 1 | * * * * * 12 * | 0 0 0 0 0 1 0 0 0 2 2 0 | 0 0 0 0 0 0 0 2 2 0 1 2 1 0 | 0 0 1 2 1 1 ... ... ..x | 0 0 2 | * * * * * * 6 | 0 0 0 0 2 0 0 0 0 0 2 2 | 0 0 0 0 0 1 2 0 2 0 0 1 2 1 | 0 1 0 1 2 1 ---------------+--------+--------------------+--------------------------------+-------------------------------+------------ x..3o.. ... | 3 0 0 | 3 0 0 0 0 0 0 | 4 * * * * * * * * * * * | 1 1 0 0 1 0 0 0 0 0 0 0 0 0 | 1 1 1 0 0 0 xx. ... ...&#x | 2 2 0 | 1 2 0 1 0 0 0 | * 12 * * * * * * * * * * | 0 1 1 0 0 0 0 1 0 0 0 0 0 0 | 1 0 1 1 0 0 ... ... ox.&#x | 1 2 0 | 0 2 0 0 1 0 0 | * * 12 * * * * * * * * * | 0 0 1 1 0 0 0 0 1 0 0 0 0 0 | 1 0 0 1 1 0 x.o ... ...&#x | 2 0 1 | 1 0 2 0 0 0 0 | * * * 12 * * * * * * * * | 0 0 0 0 1 1 0 1 0 0 0 0 0 0 | 0 1 1 1 0 0 ... ... o.x&#x | 1 0 2 | 0 0 2 0 0 0 1 | * * * * 12 * * * * * * * | 0 0 0 0 0 1 1 0 1 0 0 0 0 0 | 0 1 0 1 1 0 ooo3ooo3ooo&#x | 1 1 1 | 0 1 1 0 0 1 0 | * * * * * 12 * * * * * * | 0 0 0 0 0 0 0 2 2 0 0 0 0 0 | 0 0 1 2 1 0 .x.3.o. ... | 0 3 0 | 0 0 0 3 0 0 0 | * * * * * * 4 * * * * * | 0 1 0 0 0 0 0 0 0 1 1 0 0 0 | 1 0 1 0 0 1 .x. ... .x. | 0 4 0 | 0 0 0 2 2 0 0 | * * * * * * * 6 * * * * | 0 0 1 0 0 0 0 0 0 1 0 1 0 0 | 1 0 0 1 0 1 ... .o.3.x. | 0 3 0 | 0 0 0 0 3 0 0 | * * * * * * * * 4 * * * | 0 0 0 1 0 0 0 0 0 1 0 0 1 0 | 1 0 0 0 1 1 .xo ... ...&#x | 0 2 1 | 0 0 0 1 0 2 0 | * * * * * * * * * 12 * * | 0 0 0 0 0 0 0 1 0 0 1 1 0 0 | 0 0 1 1 0 1 ... ... .xx&#x | 0 2 2 | 0 0 0 0 1 2 1 | * * * * * * * * * * 12 * | 0 0 0 0 0 0 0 0 1 0 0 1 1 0 | 0 0 0 1 1 1 ... ..o3..x | 0 0 3 | 0 0 0 0 0 0 3 | * * * * * * * * * * * 4 | 0 0 0 0 0 0 1 0 0 0 0 0 1 1 | 0 1 0 0 1 1 ---------------+--------+--------------------+--------------------------------+-------------------------------+------------ x..3o..3o.. ♦ 4 0 0 | 6 0 0 0 0 0 0 | 4 0 0 0 0 0 0 0 0 0 0 0 | 1 * * * * * * * * * * * * * | 1 1 0 0 0 0 xx.3oo. ...&#x ♦ 3 3 0 | 3 3 0 3 0 0 0 | 1 3 0 0 0 0 1 0 0 0 0 0 | * 4 * * * * * * * * * * * * | 1 0 1 0 0 0 xx. ... ox.&#x ♦ 2 4 0 | 1 4 0 2 2 0 0 | 0 2 2 0 0 0 0 1 0 0 0 0 | * * 6 * * * * * * * * * * * | 1 0 0 1 0 0 ... oo.3ox.&#x ♦ 1 3 0 | 0 3 0 0 3 0 0 | 0 0 3 0 0 0 0 0 1 0 0 0 | * * * 4 * * * * * * * * * * | 1 0 0 0 1 0 x.o3o.o ...&#x ♦ 3 0 1 | 3 0 3 0 0 0 0 | 1 0 0 3 0 0 0 0 0 0 0 0 | * * * * 4 * * * * * * * * * | 0 1 1 0 0 0 x.o ... o.x&#x ♦ 2 0 2 | 1 0 4 0 0 0 1 | 0 0 0 2 2 0 0 0 0 0 0 0 | * * * * * 6 * * * * * * * * | 0 1 0 1 0 0 ... o.o3o.x&#x ♦ 1 0 3 | 0 0 3 0 0 0 3 | 0 0 0 0 3 0 0 0 0 0 0 1 | * * * * * * 4 * * * * * * * | 0 1 0 0 1 0 xxo ... ...&#x ♦ 2 2 1 | 1 2 2 1 0 2 0 | 0 1 0 1 0 2 0 0 0 1 0 0 | * * * * * * * 12 * * * * * * | 0 0 1 1 0 0 ... ... oxx&#x ♦ 1 2 2 | 0 2 2 0 1 2 1 | 0 0 1 0 1 2 0 0 0 0 1 0 | * * * * * * * * 12 * * * * * | 0 0 0 1 1 0 .x.3.o.3.x. ♦ 0 12 0 | 0 0 0 12 12 0 0 | 0 0 0 0 0 0 4 6 4 0 0 0 | * * * * * * * * * 1 * * * * | 1 0 0 0 0 1 .xo3.oo ...&#x ♦ 0 3 1 | 0 0 0 3 0 3 0 | 0 0 0 0 0 0 1 0 0 3 0 0 | * * * * * * * * * * 4 * * * | 0 0 1 0 0 1 .xo ... .xx&#x ♦ 0 4 2 | 0 0 0 2 2 4 1 | 0 0 0 0 0 0 0 1 0 2 2 0 | * * * * * * * * * * * 6 * * | 0 0 0 1 0 1 ... .oo3.xx&#x ♦ 0 3 3 | 0 0 0 0 3 3 3 | 0 0 0 0 0 0 0 0 1 0 3 1 | * * * * * * * * * * * * 4 * | 0 0 0 0 1 1 ..o3..o3..x ♦ 0 0 4 | 0 0 0 0 0 0 6 | 0 0 0 0 0 0 0 0 0 0 0 4 | * * * * * * * * * * * * * 1 | 0 1 0 0 0 1 ---------------+--------+--------------------+--------------------------------+-------------------------------+------------ xx.3oo.3ox.&#x ♦ 4 12 0 | 6 12 0 12 12 0 0 | 4 12 12 0 0 0 4 6 4 0 0 0 | 1 4 6 4 0 0 0 0 0 1 0 0 0 0 | 1 * * * * * x.o3o.o3o.x&#x ♦ 4 0 4 | 6 0 12 0 0 0 6 | 4 0 0 12 12 0 0 0 0 0 0 4 | 1 0 0 0 4 6 4 0 0 0 0 0 0 1 | * 1 * * * * xxo3ooo ...&#x ♦ 3 3 1 | 3 3 3 3 0 3 0 | 1 3 0 3 0 3 1 0 0 3 0 0 | 0 1 0 0 1 0 0 3 0 0 1 0 0 0 | * * 4 * * * xxo ... oxx&#x ♦ 2 4 2 | 1 4 4 2 2 4 1 | 0 2 2 2 2 4 0 1 0 2 2 0 | 0 0 1 0 0 1 0 2 2 0 0 1 0 0 | * * * 6 * * ... ooo3oxx&#x ♦ 1 3 3 | 0 3 3 0 3 3 3 | 0 0 3 0 3 3 0 0 1 0 3 1 | 0 0 0 1 0 0 1 0 3 0 0 0 1 0 | * * * * 4 * .xo3.oo3.xx&#x ♦ 0 12 4 | 0 0 0 12 12 12 6 | 0 0 0 0 0 0 4 6 4 12 12 4 | 0 0 0 0 0 0 0 0 0 1 4 6 4 1 | * * * * * 1
x.o3o.o3o.x&#x || .x.3.o.3.x. → height = 1/sqrt(2) = 0.707107 (hex || co) o..3o..3o.. & | 8 * | 3 3 3 0 | 3 6 3 9 3 0 0 | 1 3 3 1 4 3 9 0 | 1 1 4 3 .o.3.o.3.o. | * 12 | 0 2 0 4 | 0 4 4 0 1 2 2 | 0 2 4 2 0 0 4 1 | 2 0 2 2 -----------------+------+-------------+-------------------+-------------------+-------- x.. ... ... & | 2 0 | 12 * * * | 2 2 0 2 0 0 0 | 1 2 1 0 2 1 2 0 | 1 1 2 1 oo.3oo.3oo.&#x & | 1 1 | * 24 * * | 0 2 2 0 1 0 0 | 0 1 2 1 0 0 4 0 | 1 0 2 2 o.o3o.o3o.o&#x | 2 0 | * * 12 * | 0 0 0 4 1 0 0 | 0 0 0 0 2 2 4 0 | 0 1 2 2 .x. ... ... & | 0 2 | * * * 24 | 0 1 1 0 0 1 1 | 0 1 2 1 0 0 1 1 | 2 0 1 1 -----------------+------+-------------+-------------------+-------------------+-------- x..3o.. ... & | 3 0 | 3 0 0 0 | 8 * * * * * * | 1 1 0 0 1 0 0 0 | 1 1 1 0 xx. ... ...&#x & | 2 2 | 1 2 0 1 | * 24 * * * * * | 0 1 1 0 0 0 1 0 | 1 0 1 1 ... ... ox.&#x & | 1 2 | 0 2 0 1 | * * 24 * * * * | 0 0 1 1 0 0 1 0 | 1 0 1 1 x.o ... ...&#x & | 3 0 | 1 0 2 0 | * * * 24 * * * | 0 0 0 0 1 1 1 0 | 0 1 1 1 ooo3ooo3ooo&#x | 2 1 | 0 2 1 0 | * * * * 12 * * | 0 0 0 0 0 0 4 0 | 0 0 2 2 .x.3.o. ... & | 0 3 | 0 0 0 3 | * * * * * 8 * | 0 1 0 1 0 0 0 1 | 2 0 1 0 .x. ... .x. | 0 4 | 0 0 0 4 | * * * * * * 6 | 0 0 2 0 0 0 0 1 | 2 0 0 1 -----------------+------+-------------+-------------------+-------------------+-------- x..3o..3o.. & ♦ 4 0 | 6 0 0 0 | 4 0 0 0 0 0 0 | 2 * * * * * * * | 1 1 0 0 xx.3oo. ...&#x & ♦ 3 3 | 3 3 0 3 | 1 3 0 0 0 1 0 | * 8 * * * * * * | 1 0 1 0 xx. ... ox.&#x & ♦ 2 4 | 1 4 0 4 | 0 2 2 0 0 0 1 | * * 12 * * * * * | 1 0 0 1 ... oo.3ox.&#x & ♦ 1 3 | 0 3 0 3 | 0 0 3 0 0 1 0 | * * * 8 * * * * | 1 0 1 0 x.o3o.o ...&#x & ♦ 4 0 | 3 0 3 0 | 1 0 0 3 0 0 0 | * * * * 8 * * * | 0 1 1 0 x.o ... o.x&#x ♦ 4 0 | 2 0 4 0 | 0 0 0 4 0 0 0 | * * * * * 6 * * | 0 1 0 1 xxo ... ...&#x & ♦ 3 2 | 1 4 2 1 | 0 1 1 1 2 0 0 | * * * * * * 24 * | 0 0 1 1 .x.3.o.3.x. ♦ 0 12 | 0 0 0 24 | 0 0 0 0 0 8 6 | * * * * * * * 1 | 2 0 0 0 -----------------+------+-------------+-------------------+-------------------+-------- xx.3oo.3ox.&#x & ♦ 4 12 | 6 12 0 24 | 4 12 12 0 0 8 6 | 1 4 6 4 0 0 0 1 | 2 * * * x.o3o.o3o.x&#x ♦ 8 0 | 12 0 12 0 | 8 0 0 24 0 0 0 | 2 0 0 0 8 6 0 0 | * 1 * * xxo3ooo ...&#x & ♦ 4 3 | 3 6 3 3 | 1 3 3 3 3 1 0 | 0 1 0 1 1 0 3 0 | * * 8 * xxo ... oxx&#x ♦ 4 4 | 2 8 4 4 | 0 4 4 4 4 0 1 | 0 0 2 0 0 1 4 0 | * * * 6
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