Acronym | ... |
Name |
point || hex || gyro hex, Dutour polyteron type A |
Lace city in approx. ASCII-art |
o where: T T = x3o3o (tet) O o t = o3o3x (dual tet) t O = o3x3o (oct) o o = o3o3o (point) | | + o3o3o *b3o (point) | +---- x3o3o *b3o (hex) +-------- o3o3o *b3x (gyro hex) |
Coordinates | |
Dihedral angles
(at margins) | |
Face vector | 17, 88, 184, 144, 33 |
Confer |
|
This polyteron is nothing but an external blend of hin and hexpy, adjoining at an hex. There it just happens that the dihedral angle between some of the pens becomes flat, i.e. they join into a tete each.
Incidence matrix according to Dynkin symbol
oxo3ooo3ooo *b3oox&#xt both heights = 1/sqrt(2) = 0.707107 o..3o..3o.. *b3o.. | 1 * * ♦ 8 0 0 0 | 24 0 0 0 0 | 32 0 0 0 0 0 0 | 8 8 0 0 0 .o.3.o.3.o. *b3.o. | * 8 * | 1 6 4 0 | 6 12 12 6 0 | 12 4 12 6 4 0 0 | 4 4 4 1 0 ..o3..o3..o *b3..o | * * 8 | 0 0 4 6 | 0 0 6 12 12 | 0 0 4 6 12 4 4 | 1 0 4 4 1 -----------------------+-------+------------+----------------+-------------------+---------- oo.3oo.3oo. *b3oo.&#x | 1 1 0 | 8 * * * ♦ 6 0 0 0 0 | 12 0 0 0 0 0 0 | 4 4 0 0 0 .x. ... ... ... | 0 2 0 | * 24 * * | 1 4 2 0 0 | 4 2 4 1 0 0 0 | 2 2 2 0 0 .oo3.oo3.oo *b3.oo&#x | 0 1 1 | * * 32 * | 0 0 3 3 0 | 0 0 3 3 3 0 0 | 1 0 3 1 0 ... ... ... ..x | 0 0 2 | * * * 24 | 0 0 0 2 4 | 0 0 0 1 4 2 2 | 0 0 2 2 1 -----------------------+-------+------------+----------------+-------------------+---------- ox. ... ... ...&#x | 1 2 0 | 2 1 0 0 | 24 * * * * | 4 0 0 0 0 0 0 | 2 2 0 0 0 .x.3.o. ... ... | 0 3 0 | 0 3 0 0 | * 32 * * * | 1 1 1 0 0 0 0 | 1 1 1 0 0 .xo ... ... ...&#x | 0 2 1 | 0 1 2 0 | * * 48 * * | 0 0 2 1 0 0 0 | 1 0 2 0 0 ... ... ... .ox&#x | 0 1 2 | 0 0 2 1 | * * * 48 * | 0 0 0 1 2 0 0 | 0 0 2 1 0 ... ..o ... *b3..x | 0 0 3 | 0 0 0 3 | * * * * 32 | 0 0 0 0 1 1 1 | 0 0 1 1 1 -----------------------+-------+------------+----------------+-------------------+---------- ox.3oo. ... ...&#x ♦ 1 3 0 | 3 3 0 0 | 3 1 0 0 0 | 32 * * * * * * | 1 1 0 0 0 .x.3.o. ... *b3.o. ♦ 0 4 0 | 0 6 0 0 | 0 4 0 0 0 | * 8 * * * * * | 0 1 1 0 0 .xo3.oo ... ...&#x ♦ 0 3 1 | 0 3 3 0 | 0 1 3 0 0 | * * 32 * * * * | 1 0 1 0 0 .xo ... ... .ox&#x ♦ 0 2 2 | 0 1 4 1 | 0 0 2 2 0 | * * * 24 * * * | 0 0 2 0 0 ... .oo ... *b3.ox&#x ♦ 0 1 3 | 0 0 3 3 | 0 0 0 3 1 | * * * * 32 * * | 0 0 1 1 0 ..o3..o ... *b3..x ♦ 0 0 4 | 0 0 0 6 | 0 0 0 0 4 | * * * * * 8 * | 0 0 1 0 1 ... ..o3..o *b3..x ♦ 0 0 4 | 0 0 0 6 | 0 0 0 0 4 | * * * * * * 8 | 0 0 0 1 1 -----------------------+-------+------------+----------------+-------------------+---------- oxo3ooo3ooo ...&#xt ♦ 1 4 1 | 4 6 4 0 | 6 4 6 0 0 | 4 0 4 0 0 0 0 | 8 * * * * ox.3oo. ... *b3oo.&#x ♦ 1 4 0 | 4 6 0 0 | 6 4 0 0 0 | 4 1 0 0 0 0 0 | * 8 * * * .xo3.oo ... *b3.ox&#x ♦ 0 4 4 | 0 6 12 6 | 0 4 12 12 4 | 0 1 4 6 4 1 0 | * * 8 * * ... .oo3.oo *b3.ox&#x ♦ 0 1 4 | 0 0 4 6 | 0 0 0 6 4 | 0 0 0 0 4 0 1 | * * * 8 * ..o3..o3..o *b3..x ♦ 0 0 8 | 0 0 0 24 | 0 0 0 0 32 | 0 0 0 0 0 8 8 | * * * * 1
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