Acronym | ... |
Name | fooo3xxoF3xfxo *b3oxFo&#zx |
Face vector | 248, 816, 784, 216 |
Confer |
|
The relation to ex runs as follows: ex in demitessic subsymmetry can be given as foxo3ooof3xfoo *b3oxfo&#zx. That will be transformed into fo(-x)o3ooxf3xfoo *b3oxfo&#zx (faceting, same vertex set). This in turn will be transformed into fooo3oo(-x)f3xfxo *b3oxFo&#zx (other faceting, still same vertex set). Then a Stott expansion wrt. the second nodes produces this polychoron.
Both of the non-existing lacings calculate to vertex distances according to f=(1+sqrt(5))/2.
Incidence matrix according to Dynkin symbol
fooo3xxoF3xfxo *b3oxFo&#zx → all heights = 0 – except those of the not existing lacing(1,3) resp. lacing(3,4) o...3o...3o... *b3o... | 96 * * * | 2 1 2 1 0 0 0 0 0 | 2 1 2 1 1 2 0 0 0 0 0 0 | 1 1 1 2 0 0 0 .o..3.o..3.o.. *b3.o.. | * 96 * * | 0 0 2 0 2 1 1 1 0 | 0 0 2 2 0 2 1 2 2 1 1 0 | 0 2 2 2 1 1 0 ..o.3..o.3..o. *b3..o. | * * 32 * ♦ 0 0 0 0 0 0 3 0 3 | 0 0 0 0 0 0 0 0 3 0 3 3 | 0 0 0 3 0 1 1 ...o3...o3...o *b3...o | * * * 24 | 0 0 0 4 0 0 0 4 0 | 0 0 0 0 2 8 0 0 0 2 2 0 | 0 0 4 4 0 0 0 ---------------------------+-------------+-----------------------------+--------------------------------------+------------------ .... x... .... .... | 2 0 0 0 | 96 * * * * * * * * | 1 1 1 0 0 0 0 0 0 0 0 0 | 1 1 0 1 0 0 0 .... .... x... .... | 2 0 0 0 | * 48 * * * * * * * | 2 0 0 0 1 0 0 0 0 0 0 0 | 1 0 0 2 0 0 0 oo..3oo..3oo.. *b3oo..&#x | 1 1 0 0 | * * 192 * * * * * * | 0 0 1 1 0 1 0 0 0 0 0 0 | 0 1 1 1 0 0 0 o..o3o..o3o..o *b3o..o&#x | 1 0 0 1 | * * * 96 * * * * * | 0 0 0 0 1 2 0 0 0 0 0 0 | 0 0 1 2 0 0 0 .... .x.. .... .... | 0 2 0 0 | * * * * 96 * * * * | 0 0 1 0 0 0 1 1 1 0 0 0 | 0 1 0 1 1 1 0 .... .... .... .x.. | 0 2 0 0 | * * * * * 48 * * * | 0 0 0 2 0 0 0 2 0 1 0 0 | 0 2 2 0 1 0 0 .oo.3.oo.3.oo. *b3.oo.&#x | 0 1 1 0 | * * * * * * 96 * * | 0 0 0 0 0 0 0 0 2 0 1 0 | 0 0 0 2 0 1 0 .o.o3.o.o3.o.o *b3.o.o&#x | 0 1 0 1 | * * * * * * * 96 * | 0 0 0 0 0 2 0 0 0 1 1 0 | 0 0 2 2 0 0 0 .... .... ..x. .... | 0 0 2 0 | * * * * * * * * 48 | 0 0 0 0 0 0 0 0 0 0 1 2 | 0 0 0 2 0 0 1 ---------------------------+-------------+-----------------------------+--------------------------------------+------------------ .... x...3x... .... | 6 0 0 0 | 3 3 0 0 0 0 0 0 0 | 32 * * * * * * * * * * * | 1 0 0 1 0 0 0 .... x... .... *b3o... | 3 0 0 0 | 3 0 0 0 0 0 0 0 0 | * 32 * * * * * * * * * * | 1 1 0 0 0 0 0 .... xx.. .... ....&#x | 2 2 0 0 | 1 0 2 0 1 0 0 0 0 | * * 96 * * * * * * * * * | 0 1 0 1 0 0 0 .... .... .... ox..&#x | 1 2 0 0 | 0 0 2 0 0 1 0 0 0 | * * * 96 * * * * * * * * | 0 1 1 0 0 0 0 .... .... x..o ....&#x | 2 0 0 1 | 0 1 0 2 0 0 0 0 0 | * * * * 48 * * * * * * * | 0 0 0 2 0 0 0 oo.o3oo.o3oo.o *b3oo.o&#x | 1 1 0 1 | 0 0 1 1 0 0 0 1 0 | * * * * * 192 * * * * * * | 0 0 1 1 0 0 0 .o..3.x.. .... .... | 0 3 0 0 | 0 0 0 0 3 0 0 0 0 | * * * * * * 32 * * * * * | 0 0 0 0 1 1 0 .... .x.. .... *b3.x.. | 0 6 0 0 | 0 0 0 0 3 3 0 0 0 | * * * * * * * 32 * * * * | 0 1 0 0 1 0 0 .... .xo. .... ....&#x | 0 2 1 0 | 0 0 0 0 1 0 2 0 0 | * * * * * * * * 96 * * * | 0 0 0 1 0 1 0 .... .... .... .x.o&#x | 0 2 0 1 | 0 0 0 0 0 1 0 2 0 | * * * * * * * * * 48 * * | 0 0 2 0 0 0 0 .... .... .fxo ....&#xt | 0 2 2 1 | 0 0 0 0 0 0 2 2 1 | * * * * * * * * * * 48 * | 0 0 0 2 0 0 0 tower: D-B-C .... ..o.3..x. .... | 0 0 3 0 | 0 0 0 0 0 0 0 0 3 | * * * * * * * * * * * 32 | 0 0 0 1 0 0 1 ---------------------------+-------------+-----------------------------+--------------------------------------+------------------ .... x...3x... *b3o... ♦ 12 0 0 0 | 12 6 0 0 0 0 0 0 0 | 4 4 0 0 0 0 0 0 0 0 0 0 | 8 * * * * * * .... xx.. .... *b3ox..&#x ♦ 3 6 0 0 | 3 0 6 0 3 3 0 0 0 | 0 1 3 3 0 0 0 1 0 0 0 0 | * 32 * * * * * .... .... .... ox.o&#x ♦ 1 2 0 1 | 0 0 2 1 0 1 0 2 0 | 0 0 0 1 0 2 0 0 0 1 0 0 | * * 96 * * * * .... xxoF3xfxo ....&#xt ♦ 6 6 3 3 | 3 3 6 6 3 0 6 6 3 | 1 0 3 0 3 6 0 0 3 0 3 1 | * * * 32 * * * tower: A-D-B-C .o..3.x.. .... *b3.x.. ♦ 0 12 0 0 | 0 0 0 0 12 6 0 0 0 | 0 0 0 0 0 0 4 4 0 0 0 0 | * * * * 8 * * .oo.3.xo. .... ....&#x ♦ 0 3 1 0 | 0 0 0 0 3 0 3 0 0 | 0 0 0 0 0 0 1 0 3 0 0 0 | * * * * * 32 * ..o.3..o.3..x. .... ♦ 0 0 4 0 | 0 0 0 0 0 0 0 0 6 | 0 0 0 0 0 0 0 0 0 0 0 4 | * * * * * * 8
© 2004-2024 | top of page |