| Acronym | odinaq (alt.: hexgyo) |
| Name |
octa-diminished naq, hexadecachoral gyro-octahedronism |
| Circumradius | sqrt(3)/2 = 0.866025 |
|
Lace hyper city in approx. ASCII-art |
N
//|\
/ / | \
/ _O--+----_E - x3o3o *b3o3o (hin)
/_- | | _- /
E-----+--O / - o3o3x *b3o3o (alt. hin)
\ | / /
\|//
N
where:
N = o3o3o *b3x (hex)
E = x3o3o *b3o (gyro hex)
O = o3o3x *b3o (alt. gyro hex)
|
| Face vector | 48, 552, 2496, 5280, 5478, 2508, 320 |
| Confer |
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External links |
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This scaliform polyexon is obtained from naq, when, in the same D4 × A1 × A1 × A1 symmetry representation, as given in the lace hyper city display above, the 8 vertices of the encasing cube of position subspace, there representing a single point in object subspace each, will be chopped off.
Alternatively it could be obtained as the tegum sum of 3 mutually gyrated and lacing orthogonal hexips. Those then show up in the lace hyper city display as the 3 diagonals (N-N, E-E, O-O) of the oct of position subspace.
Incidence matrix according to Dynkin symbol
xoo oxo oox oxo3ooo3oox *e3xoo&#zx → all heights = 0 (tegum sum of 3 mutually gyrated, lacings-orthogonal hexips) o.. o.. o.. o..3o..3o.. *e3o.. & | 48 | 1 6 16 | 12 24 72 48 | 8 8 48 64 24 96 192 | 1 40 20 16 60 240 80 120 | 12 4 12 72 96 72 36 24 | 6 28 20 4 ------------------------------------+----+------------+------------------+-----------------------------+--------------------------------+------------------------------+------------ x.. ... ... ... ... ... ... & | 2 | 24 * * | 0 16 0 0 | 0 8 24 0 0 48 0 | 0 16 0 0 48 96 0 0 | 4 0 12 48 32 24 0 0 | 6 16 4 0 ... ... ... ... ... ... x.. & | 2 | * 144 * | 4 0 8 0 | 4 0 4 16 4 0 16 | 1 8 8 8 0 16 16 16 | 4 4 0 4 16 8 16 4 | 1 4 8 4 oo. oo. oo. oo.3oo.3oo. *e3oo.&#x & | 2 | * * 384 | 0 2 6 6 | 0 1 6 6 3 15 30 | 0 6 2 3 12 48 14 24 | 2 1 3 18 22 18 10 6 | 3 8 7 2 ------------------------------------+----+------------+------------------+-----------------------------+--------------------------------+------------------------------+------------ ... ... ... ... o.. ... *e3x.. & | 3 | 0 3 0 | 192 * * * | 2 0 0 4 0 0 0 | 1 2 4 4 0 0 4 0 | 2 4 0 0 4 0 8 0 | 0 1 4 4 xo. ... ... ... ... ... ...&#x & | 3 | 1 0 2 | * 384 * * | 0 1 3 0 0 6 0 | 0 3 0 0 9 18 0 0 | 1 0 3 12 8 6 0 0 | 3 5 2 0 ... ... ... ox. ... ... ...&#x & | 3 | 0 1 2 | * * 1152 * | 0 0 1 2 1 0 4 | 0 2 1 2 0 6 4 6 | 1 1 0 2 6 4 6 2 | 1 2 4 2 ooo ooo ooo ooo3ooo3ooo *e3ooo&#x | 3 | 0 0 3 | * * * 768 | 0 0 0 0 0 3 6 | 0 0 0 0 3 12 3 6 | 0 0 1 6 6 6 3 2 | 2 3 3 1 ------------------------------------+----+------------+------------------+-----------------------------+--------------------------------+------------------------------+------------ ... ... ... o..3o.. ... *e3x.. & ♦ 4 | 0 6 0 | 4 0 0 0 | 96 * * * * * * | 1 0 2 2 0 0 0 0 | 1 4 0 0 0 0 4 0 | 0 0 2 4 xo. ox. ... ... ... ... ...&#x & ♦ 4 | 2 0 4 | 0 4 0 0 | * 96 * * * * * ♦ 0 0 0 0 6 0 0 0 | 0 0 3 6 0 0 0 0 | 3 2 0 0 xo. ... ... ox. ... ... ...&#x & ♦ 4 | 1 1 4 | 0 2 2 0 | * * 576 * * * * | 0 2 0 0 0 4 0 0 | 1 0 0 2 4 2 0 0 | 1 2 2 0 ... ... ... ox.3oo. ... ...&#x & ♦ 4 | 0 3 3 | 1 0 3 0 | * * * 768 * * * | 0 1 1 1 0 0 2 0 | 1 1 0 0 3 0 4 0 | 0 1 3 2 ... ... ... ox. ... ... xo.&#x & ♦ 4 | 0 2 4 | 0 0 4 0 | * * * * 288 * * | 0 0 0 2 0 0 0 4 | 0 1 0 0 0 2 4 2 | 1 0 2 2 xoo ... ... ... ... ... ...&#x & ♦ 4 | 1 0 5 | 0 2 0 2 | * * * * * 1152 * | 0 0 0 0 2 4 0 0 | 0 0 1 4 2 2 0 0 | 2 2 1 0 ... ... ... oxo ... ... ...&#x & ♦ 4 | 0 1 5 | 0 0 2 2 | * * * * * * 2304 | 0 0 0 0 0 2 1 2 | 0 0 0 1 2 2 2 1 | 1 1 2 1 ------------------------------------+----+------------+------------------+-----------------------------+--------------------------------+------------------------------+------------ ... ... ... o..3o..3o.. *e3x.. & ♦ 8 | 0 24 0 | 32 0 0 0 | 16 0 0 0 0 0 0 | 6 * * * * * * * | 0 4 0 0 0 0 0 0 | 0 0 0 4 xo. ... ... ox.3oo. ... ...&#x & ♦ 5 | 1 3 6 | 1 3 6 0 | 0 0 3 2 0 0 0 | * 384 * * * * * * | 1 0 0 0 2 0 0 0 | 0 1 2 0 ... ... ... ox.3oo.3oo. ...&#x & ♦ 5 | 0 6 4 | 4 0 6 0 | 1 0 0 4 0 0 0 | * * 192 * * * * * | 1 1 0 0 0 0 2 0 | 0 0 2 2 ... ... ... ox.3oo. ... *e3xo.&#x & ♦ 8 | 0 12 12 | 8 0 24 0 | 2 0 0 8 6 0 0 | * * * 96 * * * * | 0 1 0 0 0 0 2 0 | 0 0 1 2 xoo oxo ... ... ... ... ...&#x & ♦ 5 | 2 0 8 | 0 6 0 4 | 0 1 0 0 0 4 0 | * * * * 576 * * * | 0 0 1 2 0 0 0 0 | 2 1 0 0 xoo ... ... oxo ... ... ...&#x & ♦ 5 | 1 1 8 | 0 3 3 4 | 0 0 1 0 0 2 2 | * * * * * 2304 * * | 0 0 0 1 1 1 0 0 | 1 1 1 0 ... ... ... oxo3ooo ... ...&#x & ♦ 5 | 0 3 7 | 1 0 6 3 | 0 0 0 2 0 0 3 | * * * * * * 768 * | 0 0 0 0 2 0 2 0 | 0 1 2 1 ... ... ... oxo ... oox ...&#x & ♦ 5 | 0 2 8 | 0 0 6 4 | 0 0 0 0 1 0 4 | * * * * * * * 1152 | 0 0 0 0 0 1 1 1 | 1 0 1 1 ------------------------------------+----+------------+------------------+-----------------------------+--------------------------------+------------------------------+------------ xo. ... ... ox.3oo.3oo. ...&#x & ♦ 6 | 1 6 8 | 4 4 12 0 | 1 0 6 8 0 0 0 | 0 4 2 0 0 0 0 0 | 96 * * * * * * * | 0 0 2 0 ... ... ... ox.3oo.3oo. *e3xo.&#x & ♦ 16 | 0 48 32 | 64 0 96 0 | 32 0 0 64 24 0 0 | 2 0 16 8 0 0 0 0 | * 12 * * * * * * | 0 0 0 2 xoo oxo oox ... ... ... ...&#x ♦ 6 | 3 0 12 | 0 12 0 8 | 0 3 0 0 0 12 0 | 0 0 0 0 6 0 0 0 | * * 96 * * * * * | 2 0 0 0 xoo oxo ... ... ... oox ...&#x & ♦ 6 | 2 1 12 | 0 8 4 8 | 0 1 2 0 0 8 4 | 0 0 0 0 2 4 0 0 | * * * 576 * * * * | 1 1 0 0 xoo ... ... oxo3ooo ... ...&#x & ♦ 6 | 1 3 11 | 1 4 9 6 | 0 0 3 3 0 3 6 | 0 1 0 0 0 3 2 0 | * * * * 768 * * * | 0 1 1 0 xoo ... ... oxo ... oox ...&#x & ♦ 6 | 1 2 12 | 0 4 8 8 | 0 0 2 0 1 4 8 | 0 0 0 0 0 4 0 2 | * * * * * 576 * * | 1 0 1 0 ... ... ... oxo3ooo3oox ...&#x & ♦ 9 | 0 12 20 | 8 0 36 12 | 2 0 0 16 6 0 24 | 0 0 2 1 0 0 8 6 | * * * * * * 192 * | 0 0 1 1 ... ... ... oxo ... oox xoo&#x ♦ 6 | 0 3 12 | 0 0 12 8 | 0 0 0 0 3 0 12 | 0 0 0 0 0 0 0 6 | * * * * * * * 192 | 1 0 0 1 ------------------------------------+----+------------+------------------+-----------------------------+--------------------------------+------------------------------+------------ xoo oxo oox xoo ... oxo oox&#zx ♦ 12 | 6 6 48 | 0 48 48 64 | 0 12 24 0 12 96 96 | 0 0 0 0 48 96 0 48 | 0 0 8 24 0 24 0 8 | 24 * * * xoo oxo ... ... ooo3oox ...&#x & ♦ 7 | 2 3 16 | 1 10 12 12 | 0 1 6 4 0 12 12 | 0 2 0 0 3 12 4 0 | 0 0 0 3 4 0 0 0 | * 192 * * xoo ... ... oxo3ooo3oox ...&#x & ♦ 10 | 1 12 28 | 8 8 48 24 | 2 0 12 24 6 12 48 | 0 8 4 1 0 24 16 12 | 2 0 0 0 8 6 2 0 | * * 96 * ... ... ... oxo3ooo3oox *e3xoo&#x ♦ 24 | 0 72 96 | 96 0 288 96 | 48 0 0 192 72 0 288 | 3 0 48 24 0 0 96 144 | 0 3 0 0 0 0 24 24 | * * * 8
o(xo)o o(ox)o o(xo)o3o(oo)o3o(ox)o *d3x(oo)x&#xt → both heights = 1/2 (hex || tegum sum of 2 relatively and mutually gyrated, lacings-orthogonal hexips || hex) ...
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