Acronym | ... |
Name | oFFxx3xxoxf3Fxxox3oofFx&#zx |
Face vector | 330, 1170, 1150, 310 |
Confer |
|
The relation to ex runs as follows: ex in pentic subsymmetry can be given as xffoo3oxoof3fooxo3ooffx&#zx. That will be transformed into (-x)ffoo3xxoof3fooxo3ooffx&#zx. Then into (-x)ffoo3xxoxf3foo(-x)o3oofFx&#zx. Finally a Stott expansion wrt. the first and third node produces this polychoron.
The non-existing lacings calculate to vertex distances according to f=(1+sqrt(5))/2.
Incidence matrix according to Dynkin symbol
oFFxx3xxoxf3Fxxox3oofFx&#zx → all heights = 0 – except those of the not existing lacing(1,2), lacing(1,3), lacing(1,4), and lacing(2,4) o....3o....3o....3o.... | 30 * * * * | 2 4 0 0 0 0 0 0 0 0 0 0 0 0 0 | 1 2 2 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 1 2 2 0 0 0 0 0 0 0 0 0 .o...3.o...3.o...3.o... | * 60 * * * | 0 0 1 2 2 2 0 0 0 0 0 0 0 0 0 | 0 0 0 0 2 1 2 2 2 1 2 0 0 0 0 0 0 0 0 0 0 0 0 | 0 1 0 1 2 1 2 0 0 0 0 0 ..o..3..o..3..o..3..o.. | * * 60 * * | 0 0 0 0 2 0 2 2 2 0 0 0 0 0 0 | 0 0 0 1 0 0 1 2 0 0 2 1 1 2 2 2 0 0 0 0 0 0 0 | 0 1 1 0 1 0 2 1 2 0 0 0 ...o.3...o.3...o.3...o. | * * * 60 * | 0 0 0 0 0 0 0 2 0 1 2 2 0 0 0 | 0 0 0 0 0 0 0 0 0 0 0 0 2 1 0 2 2 1 2 1 0 0 0 | 0 0 2 0 0 0 0 1 1 1 1 0 ....o3....o3....o3....o | * * * * 120 | 0 1 0 0 0 1 0 0 1 0 0 1 1 1 1 | 0 1 1 1 0 0 0 0 1 1 1 0 0 0 1 1 0 0 1 1 1 1 1 | 1 1 1 0 0 1 1 0 1 0 1 1 ----------------------------+-----------------+----------------------------------------------------+------------------------------------------------------------------------+---------------------------------- ..... x.... ..... ..... | 2 0 0 0 0 | 30 * * * * * * * * * * * * * * | 1 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 0 1 2 0 0 0 0 0 0 0 0 0 o...o3o...o3o...o3o...o&#x | 1 0 0 0 1 | * 120 * * * * * * * * * * * * * | 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 1 1 1 0 0 0 0 0 0 0 0 0 ..... .x... ..... ..... | 0 2 0 0 0 | * * 30 * * * * * * * * * * * * | 0 0 0 0 2 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 0 1 0 1 2 0 0 0 0 0 0 0 ..... ..... .x... ..... | 0 2 0 0 0 | * * * 60 * * * * * * * * * * * | 0 0 0 0 1 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 0 0 0 1 1 1 1 0 0 0 0 0 .oo..3.oo..3.oo..3.oo..&#x | 0 1 1 0 0 | * * * * 120 * * * * * * * * * * | 0 0 0 0 0 0 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 | 0 1 0 0 1 0 1 0 0 0 0 0 .o..o3.o..o3.o..o3.o..o&#x | 0 1 0 0 1 | * * * * * 120 * * * * * * * * * | 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 | 0 1 0 0 0 1 1 0 0 0 0 0 ..... ..... ..x.. ..... | 0 0 2 0 0 | * * * * * * 60 * * * * * * * * | 0 0 0 0 0 0 0 1 0 0 0 1 0 1 1 0 0 0 0 0 0 0 0 | 0 0 0 0 1 0 1 1 1 0 0 0 ..oo.3..oo.3..oo.3..oo.&#x | 0 0 1 1 0 | * * * * * * * 120 * * * * * * * | 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 0 0 0 0 0 | 0 0 1 0 0 0 0 1 1 0 0 0 ..o.o3..o.o3..o.o3..o.o&#x | 0 0 1 0 1 | * * * * * * * * 120 * * * * * * | 0 0 0 1 0 0 0 0 0 0 1 0 0 0 1 1 0 0 0 0 0 0 0 | 0 1 1 0 0 0 1 0 1 0 0 0 ...x. ..... ..... ..... | 0 0 0 2 0 | * * * * * * * * * 30 * * * * * | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 2 0 0 0 0 | 0 0 2 0 0 0 0 0 0 1 1 0 ..... ...x. ..... ..... | 0 0 0 2 0 | * * * * * * * * * * 60 * * * * | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 0 0 0 0 0 | 0 0 1 0 0 0 0 1 0 1 0 0 ...oo3...oo3...oo3...oo&#x | 0 0 0 1 1 | * * * * * * * * * * * 120 * * * | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0 0 0 | 0 0 1 0 0 0 0 0 1 0 1 0 ....x ..... ..... ..... | 0 0 0 0 2 | * * * * * * * * * * * * 60 * * | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 | 1 0 1 0 0 0 0 0 0 0 1 1 ..... ..... ....x ..... | 0 0 0 0 2 | * * * * * * * * * * * * * 60 * | 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 1 1 0 1 | 0 0 0 0 0 1 1 0 1 0 1 1 ..... ..... ..... ....x | 0 0 0 0 2 | * * * * * * * * * * * * * * 60 | 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 1 | 1 1 0 0 0 1 0 0 0 0 0 1 ----------------------------+-----------------+----------------------------------------------------+------------------------------------------------------------------------+---------------------------------- o....3x.... ..... ..... | 3 0 0 0 0 | 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 10 * * * * * * * * * * * * * * * * * * * * * * | 0 0 2 0 0 0 0 0 0 0 0 0 o...x ..... ..... .....&#x | 1 0 0 0 2 | 0 2 0 0 0 0 0 0 0 0 0 0 1 0 0 | * 60 * * * * * * * * * * * * * * * * * * * * * | 1 0 1 0 0 0 0 0 0 0 0 0 ..... ..... ..... o...x&#x | 1 0 0 0 2 | 0 2 0 0 0 0 0 0 0 0 0 0 0 0 1 | * * 60 * * * * * * * * * * * * * * * * * * * * | 1 1 0 0 0 0 0 0 0 0 0 0 ..... x.o.f ..... .....&#zx | 2 0 1 0 2 | 1 2 0 0 0 0 0 0 2 0 0 0 0 0 0 | * * * 60 * * * * * * * * * * * * * * * * * * * | 0 1 1 0 0 0 0 0 0 0 0 0 ..... .x...3.x... ..... | 0 6 0 0 0 | 0 0 3 3 0 0 0 0 0 0 0 0 0 0 0 | * * * * 20 * * * * * * * * * * * * * * * * * * | 0 0 0 1 1 0 0 0 0 0 0 0 ..... ..... .x...3.o... | 0 3 0 0 0 | 0 0 0 3 0 0 0 0 0 0 0 0 0 0 0 | * * * * * 20 * * * * * * * * * * * * * * * * * | 0 0 0 1 0 1 0 0 0 0 0 0 ..... .xo.. ..... .....&#x | 0 2 1 0 0 | 0 0 1 0 2 0 0 0 0 0 0 0 0 0 0 | * * * * * * 60 * * * * * * * * * * * * * * * * | 0 1 0 0 1 0 0 0 0 0 0 0 ..... ..... .xx.. .....&#x | 0 2 2 0 0 | 0 0 0 1 2 0 1 0 0 0 0 0 0 0 0 | * * * * * * * 60 * * * * * * * * * * * * * * * | 0 0 0 0 1 0 1 0 0 0 0 0 ..... ..... .x..x .....&#x | 0 2 0 0 2 | 0 0 0 1 0 2 0 0 0 0 0 0 0 1 0 | * * * * * * * * 60 * * * * * * * * * * * * * * | 0 0 0 0 0 1 1 0 0 0 0 0 ..... ..... ..... .o..x&#x | 0 1 0 0 2 | 0 0 0 0 0 2 0 0 0 0 0 0 0 0 1 | * * * * * * * * * 60 * * * * * * * * * * * * * | 0 1 0 0 0 1 0 0 0 0 0 0 .oo.o3.oo.o3.oo.o3.oo.o&#x | 0 1 1 0 1 | 0 0 0 0 1 1 0 0 1 0 0 0 0 0 0 | * * * * * * * * * * 120 * * * * * * * * * * * * | 0 1 0 0 0 0 1 0 0 0 0 0 ..... ..o..3..x.. ..... | 0 0 3 0 0 | 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 | * * * * * * * * * * * 20 * * * * * * * * * * * | 0 0 0 0 1 0 0 1 0 0 0 0 ..... ..ox. ..... .....&#x | 0 0 1 2 0 | 0 0 0 0 0 0 0 2 0 0 1 0 0 0 0 | * * * * * * * * * * * * 60 * * * * * * * * * * | 0 0 1 0 0 0 0 1 0 0 0 0 ..... ..... ..xo. .....&#x | 0 0 2 1 0 | 0 0 0 0 0 0 1 2 0 0 0 0 0 0 0 | * * * * * * * * * * * * * 60 * * * * * * * * * | 0 0 0 0 0 0 0 1 1 0 0 0 ..... ..... ..x.x .....&#x | 0 0 2 0 2 | 0 0 0 0 0 0 1 0 2 0 0 0 0 1 0 | * * * * * * * * * * * * * * 60 * * * * * * * * | 0 0 0 0 0 0 1 0 1 0 0 0 ..ooo3..ooo3..ooo3..ooo&#x | 0 0 1 1 1 | 0 0 0 0 0 0 0 1 1 0 0 1 0 0 0 | * * * * * * * * * * * * * * * 120 * * * * * * * | 0 0 1 0 0 0 0 0 1 0 0 0 ...x.3...x. ..... ..... | 0 0 0 6 0 | 0 0 0 0 0 0 0 0 0 3 3 0 0 0 0 | * * * * * * * * * * * * * * * * 20 * * * * * * | 0 0 1 0 0 0 0 0 0 1 0 0 ..... ...x.3...o. ..... | 0 0 0 3 0 | 0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 | * * * * * * * * * * * * * * * * * 20 * * * * * | 0 0 0 0 0 0 0 1 0 1 0 0 ...xx ..... ..... .....&#x | 0 0 0 2 2 | 0 0 0 0 0 0 0 0 0 1 0 2 1 0 0 | * * * * * * * * * * * * * * * * * * 60 * * * * | 0 0 1 0 0 0 0 0 0 0 1 0 ..... ..... ...ox .....&#x | 0 0 0 1 2 | 0 0 0 0 0 0 0 0 0 0 0 2 0 1 0 | * * * * * * * * * * * * * * * * * * * 60 * * * | 0 0 0 0 0 0 0 0 1 0 1 0 ....x ..... ....x ..... | 0 0 0 0 4 | 0 0 0 0 0 0 0 0 0 0 0 0 2 2 0 | * * * * * * * * * * * * * * * * * * * * 30 * * | 0 0 0 0 0 0 0 0 0 0 1 1 ....x ..... ..... ....x | 0 0 0 0 4 | 0 0 0 0 0 0 0 0 0 0 0 0 2 0 2 | * * * * * * * * * * * * * * * * * * * * * 30 * | 1 0 0 0 0 0 0 0 0 0 0 1 ..... ..... ....x3....x | 0 0 0 0 6 | 0 0 0 0 0 0 0 0 0 0 0 0 0 3 3 | * * * * * * * * * * * * * * * * * * * * * * 20 | 0 0 0 0 0 1 0 0 0 0 0 1 ----------------------------+-----------------+----------------------------------------------------+------------------------------------------------------------------------+---------------------------------- o...x ..... ..... o...x&#x ♦ 1 0 0 0 4 | 0 4 0 0 0 0 0 0 0 0 0 0 2 0 2 | 0 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 | 30 * * * * * * * * * * * ..... xxo.f ..... oof.x&#zx ♦ 2 2 2 0 4 | 1 4 1 0 4 4 0 0 4 0 0 0 0 0 2 | 0 0 2 2 0 0 2 0 0 2 4 0 0 0 0 0 0 0 0 0 0 0 0 | * 30 * * * * * * * * * * (tower: 1532) o.Fxx3x.oxf ..... .....&#zx ♦ 3 0 3 6 6 | 3 6 0 0 0 0 0 6 6 3 3 6 3 0 0 | 1 3 0 3 0 0 0 0 0 0 0 0 3 0 0 6 1 0 3 0 0 0 0 | * * 20 * * * * * * * * * (tower: 1534) ..... .x...3.x...3.o... ♦ 0 12 0 0 0 | 0 0 6 12 0 0 0 0 0 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 0 0 | * * * 5 * * * * * * * * ..... .xo..3.xx.. .....&#x ♦ 0 6 3 0 0 | 0 0 3 3 6 0 3 0 0 0 0 0 0 0 0 | 0 0 0 0 1 0 3 3 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 | * * * * 20 * * * * * * * ..... ..... .x..x3.o..x&#x ♦ 0 3 0 0 6 | 0 0 0 3 0 6 0 0 0 0 0 0 0 3 3 | 0 0 0 0 0 1 0 0 3 3 0 0 0 0 0 0 0 0 0 0 0 0 1 | * * * * * 20 * * * * * * ..... ..... .xx.x .....&#x ♦ 0 2 2 0 2 | 0 0 0 1 2 2 1 0 2 0 0 0 0 1 0 | 0 0 0 0 0 0 0 1 1 0 2 0 0 0 1 0 0 0 0 0 0 0 0 | * * * * * * 60 * * * * * ..... ..ox.3..xo. .....&#x ♦ 0 0 3 3 0 | 0 0 0 0 0 0 3 6 0 0 3 0 0 0 0 | 0 0 0 0 0 0 0 0 0 0 0 1 3 3 0 0 0 1 0 0 0 0 0 | * * * * * * * 20 * * * * ..... ..... ..xox .....&#x ♦ 0 0 2 1 2 | 0 0 0 0 0 0 1 2 2 0 0 2 0 1 0 | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 2 0 0 0 1 0 0 0 | * * * * * * * * 60 * * * ...x.3...x.3...o. ..... ♦ 0 0 0 12 0 | 0 0 0 0 0 0 0 0 0 6 12 0 0 0 0 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 4 0 0 0 0 0 | * * * * * * * * * 5 * * ...xx ..... ...ox .....&#x ♦ 0 0 0 2 4 | 0 0 0 0 0 0 0 0 0 1 0 4 2 2 0 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 1 0 0 | * * * * * * * * * * 30 * ....x ..... ....x3....x ♦ 0 0 0 0 12 | 0 0 0 0 0 0 0 0 0 0 0 0 6 6 6 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 3 2 | * * * * * * * * * * * 10
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