Acronym | ... |
Name | Fxox3xoxf3oFxx *b3oxfo&#zx |
Face vector | 336, 1200, 1176, 312 |
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 fo(-x)o3xoxf3(-x)foo *b3oxfo&#zx (other faceting, still same vertex set). Then a Stott expansion wrt. the first and third 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
Fxox3xoxf3oFxx *b3oxfo&#zx → all heights = 0 – except those of the not existing lacing(1,2) resp. lacing(1,3) o...3o...3o... *b3o... | 48 * * * | 4 2 0 0 0 0 0 0 0 0 0 | 2 2 4 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | 1 2 2 0 0 0 0 0 0 .o..3.o..3.o.. *b3.o.. | * 96 * * | 0 0 2 2 2 2 0 0 0 0 0 | 0 0 1 0 1 2 1 2 1 2 2 2 0 0 0 0 0 | 0 1 1 1 1 2 2 0 0 ..o.3..o.3..o. *b3..o. | * * 96 * | 0 0 0 0 2 0 2 1 2 0 0 | 0 0 0 0 0 0 0 1 2 0 0 2 1 2 1 2 0 | 0 0 2 0 1 0 1 1 1 ...o3...o3...o *b3...o | * * * 96 | 0 1 0 0 0 2 0 0 2 1 1 | 0 0 2 1 0 0 0 0 0 2 1 2 0 0 2 2 1 | 0 1 2 0 0 1 2 0 2 ---------------------------+-------------+-------------------------------------+-----------------------------------------------------+------------------------ .... x... .... .... | 2 0 0 0 | 96 * * * * * * * * * * | 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 1 1 1 0 0 0 0 0 0 o..o3o..o3o..o *b3o..o&#x | 1 0 0 1 | * 96 * * * * * * * * * | 0 0 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | 0 1 2 0 0 0 0 0 0 .x.. .... .... .... | 0 2 0 0 | * * 96 * * * * * * * * | 0 0 0 0 1 1 0 1 0 1 0 0 0 0 0 0 0 | 0 0 0 1 1 1 1 0 0 .... .... .... .x.. | 0 2 0 0 | * * * 96 * * * * * * * | 0 0 0 0 0 1 1 0 0 0 1 0 0 0 0 0 0 | 0 1 0 1 0 1 0 0 0 .oo.3.oo.3.oo. *b3.oo.&#x | 0 1 1 0 | * * * * 192 * * * * * * | 0 0 0 0 0 0 0 1 1 0 0 1 0 0 0 0 0 | 0 0 1 0 1 0 1 0 0 .o.o3.o.o3.o.o *b3.o.o&#x | 0 1 0 1 | * * * * * 192 * * * * * | 0 0 1 0 0 0 0 0 0 1 1 1 0 0 0 0 0 | 0 1 1 0 0 1 1 0 0 .... ..x. .... .... | 0 0 2 0 | * * * * * * 96 * * * * | 0 0 0 0 0 0 0 0 1 0 0 0 1 1 0 0 0 | 0 0 1 0 1 0 0 1 0 .... .... ..x. .... | 0 0 2 0 | * * * * * * * 48 * * * | 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 2 0 | 0 0 2 0 0 0 0 1 1 ..oo3..oo3..oo *b3..oo&#x | 0 0 1 1 | * * * * * * * * 192 * * | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0 | 0 0 1 0 0 0 1 0 1 ...x .... .... .... | 0 0 0 2 | * * * * * * * * * 48 * | 0 0 0 0 0 0 0 0 0 2 0 0 0 0 2 0 1 | 0 0 0 0 0 1 2 0 2 .... .... ...x .... | 0 0 0 2 | * * * * * * * * * * 48 | 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 2 1 | 0 0 2 0 0 0 0 0 2 ---------------------------+-------------+-------------------------------------+-----------------------------------------------------+------------------------ .... x...3o... .... | 3 0 0 0 | 3 0 0 0 0 0 0 0 0 0 0 | 32 * * * * * * * * * * * * * * * * | 1 0 1 0 0 0 0 0 0 .... x... .... *b3o... | 3 0 0 0 | 3 0 0 0 0 0 0 0 0 0 0 | * 32 * * * * * * * * * * * * * * * | 1 1 0 0 0 0 0 0 0 .... xo.f .... ....&#xt | 2 1 0 2 | 1 2 0 0 0 2 0 0 0 0 0 | * * 96 * * * * * * * * * * * * * * | 0 1 1 0 0 0 0 0 0 tower: B-D-A .... .... o..x ....&#x | 1 0 0 2 | 0 2 0 0 0 0 0 0 0 0 1 | * * * 48 * * * * * * * * * * * * * | 0 0 2 0 0 0 0 0 0 .x..3.o.. .... .... | 0 3 0 0 | 0 0 3 0 0 0 0 0 0 0 0 | * * * * 32 * * * * * * * * * * * * | 0 0 0 1 1 0 0 0 0 .x.. .... .... .x.. | 0 4 0 0 | 0 0 2 2 0 0 0 0 0 0 0 | * * * * * 48 * * * * * * * * * * * | 0 0 0 1 0 1 0 0 0 .... .o.. .... *b3.x.. | 0 3 0 0 | 0 0 0 3 0 0 0 0 0 0 0 | * * * * * * 32 * * * * * * * * * * | 0 1 0 1 0 0 0 0 0 .xo. .... .... ....&#x | 0 2 1 0 | 0 0 1 0 2 0 0 0 0 0 0 | * * * * * * * 96 * * * * * * * * * | 0 0 0 0 1 0 1 0 0 .... .ox. .... ....&#x | 0 1 2 0 | 0 0 0 0 2 0 1 0 0 0 0 | * * * * * * * * 96 * * * * * * * * | 0 0 1 0 1 0 0 0 0 .x.x .... .... ....&#x | 0 2 0 2 | 0 0 1 0 0 2 0 0 0 1 0 | * * * * * * * * * 96 * * * * * * * | 0 0 0 0 0 1 1 0 0 .... .... .... .x.o&#x | 0 2 0 1 | 0 0 0 1 0 2 0 0 0 0 0 | * * * * * * * * * * 96 * * * * * * | 0 1 0 0 0 1 0 0 0 .ooo3.ooo3.ooo *b3.ooo&#x | 0 1 1 1 | 0 0 0 0 1 1 0 0 1 0 0 | * * * * * * * * * * * 192 * * * * * | 0 0 1 0 0 0 1 0 1 ..o.3..x. .... .... | 0 0 3 0 | 0 0 0 0 0 0 3 0 0 0 0 | * * * * * * * * * * * * 32 * * * * | 0 0 0 0 1 0 0 1 0 .... ..x.3..x. .... | 0 0 6 0 | 0 0 0 0 0 0 3 3 0 0 0 | * * * * * * * * * * * * * 32 * * * | 0 0 1 0 0 0 0 1 0 ..ox .... .... ....&#x | 0 0 1 2 | 0 0 0 0 0 0 0 0 2 1 0 | * * * * * * * * * * * * * * 96 * * | 0 0 0 0 0 0 1 0 1 .... .... ..xx ....&#x | 0 0 2 2 | 0 0 0 0 0 0 0 1 2 0 1 | * * * * * * * * * * * * * * * 96 * | 0 0 1 0 0 0 0 0 1 ...x .... ...x .... | 0 0 0 4 | 0 0 0 0 0 0 0 0 0 2 2 | * * * * * * * * * * * * * * * * 24 | 0 0 0 0 0 0 0 0 2 ---------------------------+-------------+-------------------------------------+-----------------------------------------------------+------------------------ .... x...3o... *b3o... ♦ 6 0 0 0 | 12 0 0 0 0 0 0 0 0 0 0 | 4 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 8 * * * * * * * * .... xo.f3.... *b3ox.o&#xt ♦ 3 3 0 3 | 3 3 0 3 0 6 0 0 0 0 0 | 0 1 3 0 0 0 1 0 0 0 3 0 0 0 0 0 0 | * 32 * * * * * * * tower: B-D-A .... xoxf3oFxx ....&#xt ♦ 3 3 6 6 | 3 6 0 0 6 6 3 3 6 0 3 | 1 0 3 3 0 0 0 0 3 0 0 6 0 1 0 3 0 | * * 32 * * * * * * tower: C-B-D-A .x..3.o.. .... *b3.x.. ♦ 0 12 0 0 | 0 0 12 12 0 0 0 0 0 0 0 | 0 0 0 0 4 6 4 0 0 0 0 0 0 0 0 0 0 | * * * 8 * * * * * .xo.3.ox. .... ....&#x ♦ 0 3 3 0 | 0 0 3 0 6 0 3 0 0 0 0 | 0 0 0 0 1 0 0 3 3 0 0 0 1 0 0 0 0 | * * * * 32 * * * * .x.x .... .... .x.o&#x ♦ 0 4 0 2 | 0 0 2 2 0 4 0 0 0 1 0 | 0 0 0 0 0 1 0 0 0 2 2 0 0 0 0 0 0 | * * * * * 48 * * * .xox .... .... ....&#x ♦ 0 2 1 2 | 0 0 1 0 2 2 0 0 2 1 0 | 0 0 0 0 0 0 0 1 0 1 0 2 0 0 1 0 0 | * * * * * * 96 * * ..o.3..x.3..x. .... ♦ 0 0 12 0 | 0 0 0 0 0 0 12 6 0 0 0 | 0 0 0 0 0 0 0 0 0 0 0 0 4 4 0 0 0 | * * * * * * * 8 * ..ox .... ..xx ....&#x ♦ 0 0 2 4 | 0 0 0 0 0 0 0 1 4 2 2 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 1 | * * * * * * * * 48
© 2004-2024 | top of page |