Acronym | ... |
Name | Ffxo xofo3ofox5xoxx&#zx |
Face vector | 360, 1470, 1608, 498 |
Confer |
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The relation to ex runs as follows: ex in axial icosahedral subsymmetry can be given as VFfxo2oxofo3oooox5ooxoo&#zx = oxofofoxo3ooooxoooo5ooxoooxoo&#xt (F = ff = f+x, V = uf = f+f). That will be transformed into VFfxo2oxofo3oofox5oo(-x)oo&#zx. Then a Stott expansion wrt. the third node produces oxofofoxo3oofoxofoo5xxoxxxoxx. This polychoron then will be the monostratic parabidiminishing therefrom.
Incidence matrix according to Dynkin symbol
xofofox3ofoxofo5xoxxxox&#xt → height(1,2) = height(3,4) = height(4,5) = height(7,8) = 1/2 height(2,3) = height(5,6) = (sqrt(5)-1)/4 = 0.309017 (srid || pseudo f-id || pseudo (f,x)-srid || pseudo tid || pseudo (f,x)-srid || pseudo f-id || srid) o......3o......5o...... & | 120 * * * | 2 2 2 1 0 0 0 0 0 0 0 | 1 2 1 2 2 2 2 0 0 0 0 0 0 0 0 0 | 1 1 2 1 2 0 0 0 0 .o.....3.o.....5.o..... & | * 60 * * | 0 0 4 0 4 2 0 0 0 0 0 | 0 0 0 2 2 0 4 2 1 4 0 0 0 0 0 0 | 0 2 1 0 2 2 0 0 0 ..o....3..o....5..o.... & | * * 120 * | 0 0 0 1 2 0 2 2 1 0 0 | 0 0 0 0 0 2 2 2 0 2 1 1 2 2 2 0 | 0 1 0 1 2 2 1 1 2 ...o...3...o...5...o... | * * * 60 | 0 0 0 0 0 2 0 4 0 2 1 | 0 0 0 0 0 0 0 0 2 4 0 4 4 0 2 1 | 0 2 0 0 0 4 0 2 2 ------------------------------+---------------+------------------------------------------+----------------------------------------------------------+---------------------------- x...... ....... ....... & | 2 0 0 0 | 120 * * * * * * * * * * | 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 | 1 1 1 0 0 0 0 0 0 ....... ....... x...... & | 2 0 0 0 | * 120 * * * * * * * * * | 0 1 1 0 1 1 0 0 0 0 0 0 0 0 0 0 | 1 0 1 1 1 0 0 0 0 oo.....3oo.....5oo.....&#x & | 1 1 0 0 | * * 240 * * * * * * * * | 0 0 0 1 1 0 1 0 0 0 0 0 0 0 0 0 | 0 1 1 0 1 0 0 0 0 o.o....3o.o....5o.o....&#x & | 1 0 1 0 | * * * 120 * * * * * * * | 0 0 0 0 0 2 2 0 0 0 0 0 0 0 0 0 | 0 1 0 1 2 0 0 0 0 .oo....3.oo....5.oo....&#x & | 0 1 1 0 | * * * * 240 * * * * * * | 0 0 0 0 0 0 1 1 0 1 0 0 0 0 0 0 | 0 1 0 0 1 1 0 0 0 .o.o...3.o.o...5.o.o...&#x & | 0 1 0 1 | * * * * * 120 * * * * * | 0 0 0 0 0 0 0 0 1 2 0 0 0 0 0 0 | 0 1 0 0 0 2 0 0 0 ....... ....... ..x.... & | 0 0 2 0 | * * * * * * 120 * * * * | 0 0 0 0 0 1 0 1 0 0 1 0 1 1 0 0 | 0 0 0 1 1 1 1 0 1 ..oo...3..oo...5..oo...&#x & | 0 0 1 1 | * * * * * * * 240 * * * | 0 0 0 0 0 0 0 0 0 1 0 1 1 0 1 0 | 0 1 0 0 0 1 0 1 1 ..o.o..3..o.o..5..o.o..&#x | 0 0 2 0 | * * * * * * * * 60 * * | 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 0 | 0 0 0 0 0 0 1 1 2 ....... ...x... ....... | 0 0 0 2 | * * * * * * * * * 60 * | 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 1 | 0 2 0 0 0 0 0 1 0 ....... ....... ...x... | 0 0 0 2 | * * * * * * * * * * 30 | 0 0 0 0 0 0 0 0 2 0 0 0 4 0 0 0 | 0 0 0 0 0 4 0 0 2 ------------------------------+---------------+------------------------------------------+----------------------------------------------------------+---------------------------- x......3o...... ....... & | 3 0 0 0 | 3 0 0 0 0 0 0 0 0 0 0 | 40 * * * * * * * * * * * * * * * | 1 1 0 0 0 0 0 0 0 x...... ....... x...... & | 4 0 0 0 | 2 2 0 0 0 0 0 0 0 0 0 | * 60 * * * * * * * * * * * * * * | 1 0 1 0 0 0 0 0 0 ....... o......5x...... & | 5 0 0 0 | 0 5 0 0 0 0 0 0 0 0 0 | * * 24 * * * * * * * * * * * * * | 1 0 0 1 0 0 0 0 0 xo..... ....... .......&#x & | 2 1 0 0 | 1 0 2 0 0 0 0 0 0 0 0 | * * * 120 * * * * * * * * * * * * | 0 1 1 0 0 0 0 0 0 ....... ....... xo.....&#x & | 2 1 0 0 | 0 1 2 0 0 0 0 0 0 0 0 | * * * * 120 * * * * * * * * * * * | 0 0 1 0 1 0 0 0 0 ....... ....... x.x....&#x & | 2 0 2 0 | 0 1 0 2 0 0 1 0 0 0 0 | * * * * * 120 * * * * * * * * * * | 0 0 0 1 1 0 0 0 0 ooo....3ooo....5ooo....&#x & | 1 1 1 0 | 0 0 1 1 1 0 0 0 0 0 0 | * * * * * * 240 * * * * * * * * * | 0 1 0 0 1 0 0 0 0 ....... ....... .ox....&#x & | 0 1 2 0 | 0 0 0 0 2 0 1 0 0 0 0 | * * * * * * * 120 * * * * * * * * | 0 0 0 0 1 1 0 0 0 ....... ....... .o.x...&#x & | 0 1 0 2 | 0 0 0 0 0 2 0 0 0 0 1 | * * * * * * * * 60 * * * * * * * | 0 0 0 0 0 2 0 0 0 .ooo...3.ooo...5.ooo...&#x & | 0 1 1 1 | 0 0 0 0 1 1 0 1 0 0 0 | * * * * * * * * * 240 * * * * * * | 0 1 0 0 0 1 0 0 0 ....... ..o....5..x.... & | 0 0 5 0 | 0 0 0 0 0 0 5 0 0 0 0 | * * * * * * * * * * 24 * * * * * | 0 0 0 1 0 0 1 0 0 ....... ..ox... .......&#x & | 0 0 1 2 | 0 0 0 0 0 0 0 2 0 1 0 | * * * * * * * * * * * 120 * * * * | 0 1 0 0 0 0 0 1 0 ....... ....... ..xx...&#x & | 0 0 2 2 | 0 0 0 0 0 0 1 2 0 0 1 | * * * * * * * * * * * * 120 * * * | 0 0 0 0 0 1 0 0 1 ....... ....... ..x.x..&#x | 0 0 4 0 | 0 0 0 0 0 0 2 0 2 0 0 | * * * * * * * * * * * * * 60 * * | 0 0 0 0 0 0 1 0 1 ..ooo..3..ooo..5..ooo..&#x | 0 0 2 1 | 0 0 0 0 0 0 0 2 1 0 0 | * * * * * * * * * * * * * * 120 * | 0 0 0 0 0 0 0 1 1 ...o...3...x... ....... | 0 0 0 3 | 0 0 0 0 0 0 0 0 0 3 0 | * * * * * * * * * * * * * * * 20 | 0 2 0 0 0 0 0 0 0 ------------------------------+---------------+------------------------------------------+----------------------------------------------------------+---------------------------- x......3o......5x...... & ♦ 60 0 0 0 | 60 60 0 0 0 0 0 0 0 0 0 | 20 30 12 0 0 0 0 0 0 0 0 0 0 0 0 0 | 2 * * * * * * * * xofo... ofox... .......&#xt & ♦ 3 3 3 3 | 3 0 6 3 6 3 0 6 0 3 0 | 1 0 0 3 0 0 6 0 0 6 0 3 0 0 0 1 | * 40 * * * * * * * xo..... ....... xo.....&#x & ♦ 4 1 0 0 | 2 2 4 0 0 0 0 0 0 0 0 | 0 1 0 2 2 0 0 0 0 0 0 0 0 0 0 0 | * * 60 * * * * * * ....... o.o....5x.x....&#x & ♦ 5 0 5 0 | 0 5 0 5 0 0 5 0 0 0 0 | 0 0 1 0 0 5 0 0 0 0 1 0 0 0 0 0 | * * * 24 * * * * * ....... ....... xox....&#x & ♦ 2 1 2 0 | 0 1 2 2 2 0 1 0 0 0 0 | 0 0 0 0 1 1 2 1 0 0 0 0 0 0 0 0 | * * * * 120 * * * * ....... ....... .oxx...&#x & ♦ 0 1 2 2 | 0 0 0 0 2 2 1 2 0 0 1 | 0 0 0 0 0 0 0 1 1 2 0 0 1 0 0 0 | * * * * * 120 * * * ....... ..o.o..5..x.x..&#x ♦ 0 0 10 0 | 0 0 0 0 0 0 10 0 5 0 0 | 0 0 0 0 0 0 0 0 0 0 2 0 0 5 0 0 | * * * * * * 12 * * ....... ..oxo.. .......&#x ♦ 0 0 2 2 | 0 0 0 0 0 0 0 4 1 1 0 | 0 0 0 0 0 0 0 0 0 0 0 2 0 0 2 0 | * * * * * * * 60 * ....... ....... ..xxx..&#x ♦ 0 0 4 2 | 0 0 0 0 0 0 2 4 2 0 1 | 0 0 0 0 0 0 0 0 0 0 0 0 2 1 2 0 | * * * * * * * * 60
Ffxo xofo3ofox5xoxx&#zx → heights = 0 o... o...3o...5o... | 120 * * * | 2 2 2 1 0 0 0 0 0 0 0 | 1 2 1 2 2 2 2 0 0 0 0 0 0 0 0 0 | 1 1 2 1 2 0 0 0 0 .o.. .o..3.o..5.o.. | * 60 * * | 0 0 4 0 4 2 0 0 0 0 0 | 0 0 0 2 2 0 4 2 1 4 0 0 0 0 0 0 | 0 2 1 0 2 2 0 0 0 ..o. ..o.3..o.5..o. | * * 120 * | 0 0 0 1 2 0 1 2 2 0 0 | 0 0 0 0 0 2 2 2 0 2 1 1 2 2 2 0 | 0 1 0 1 2 2 1 1 2 ...o ...o3...o5...o | * * * 60 | 0 0 0 0 0 2 0 0 4 2 1 | 0 0 0 0 0 0 0 0 2 4 0 4 4 0 2 1 | 0 2 0 0 0 4 0 2 2 ------------------------+---------------+------------------------------------------+----------------------------------------------------------+---------------------------- .... x... .... .... | 2 0 0 0 | 120 * * * * * * * * * * | 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 | 1 1 1 0 0 0 0 0 0 .... .... .... x... | 2 0 0 0 | * 120 * * * * * * * * * | 0 1 1 0 1 1 0 0 0 0 0 0 0 0 0 0 | 1 0 1 1 1 0 0 0 0 oo.. oo..3oo..5oo..&#x | 1 1 0 0 | * * 240 * * * * * * * * | 0 0 0 1 1 0 1 0 0 0 0 0 0 0 0 0 | 0 1 1 0 1 0 0 0 0 o.o. o.o.3o.o.5o.o.&#x | 1 0 1 0 | * * * 120 * * * * * * * | 0 0 0 0 0 2 2 0 0 0 0 0 0 0 0 0 | 0 1 0 1 2 0 0 0 0 .oo. .oo.3.oo.5.oo.&#x | 0 1 1 0 | * * * * 240 * * * * * * | 0 0 0 0 0 0 1 1 0 1 0 0 0 0 0 0 | 0 1 0 0 1 1 0 0 0 .o.o .o.o3.o.o5.o.o&#x | 0 1 0 1 | * * * * * 120 * * * * * | 0 0 0 0 0 0 0 0 1 2 0 0 0 0 0 0 | 0 1 0 0 0 2 0 0 0 ..x. .... .... .... | 0 0 2 0 | * * * * * * 60 * * * * | 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 0 | 0 0 0 0 0 0 1 1 2 .... .... .... ..x. | 0 0 2 0 | * * * * * * * 120 * * * | 0 0 0 0 0 1 0 1 0 0 1 0 1 1 0 0 | 0 0 0 1 1 1 1 0 1 ..oo ..oo3..oo5..oo&#x | 0 0 1 1 | * * * * * * * * 240 * * | 0 0 0 0 0 0 0 0 0 1 0 1 1 0 1 0 | 0 1 0 0 0 1 0 1 1 .... .... ...x .... | 0 0 0 2 | * * * * * * * * * 60 * | 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 1 | 0 2 0 0 0 0 0 1 0 .... .... .... ...x | 0 0 0 2 | * * * * * * * * * * 30 | 0 0 0 0 0 0 0 0 2 0 0 0 4 0 0 0 | 0 0 0 0 0 4 0 0 2 ------------------------+---------------+------------------------------------------+----------------------------------------------------------+---------------------------- .... x...3o... .... | 3 0 0 0 | 3 0 0 0 0 0 0 0 0 0 0 | 40 * * * * * * * * * * * * * * * | 1 1 0 0 0 0 0 0 0 .... x... .... x... | 4 0 0 0 | 2 2 0 0 0 0 0 0 0 0 0 | * 60 * * * * * * * * * * * * * * | 1 0 1 0 0 0 0 0 0 .... .... o...5x... | 5 0 0 0 | 0 5 0 0 0 0 0 0 0 0 0 | * * 24 * * * * * * * * * * * * * | 1 0 0 1 0 0 0 0 0 .... xo.. .... ....&#x | 2 1 0 0 | 1 0 2 0 0 0 0 0 0 0 0 | * * * 120 * * * * * * * * * * * * | 0 1 1 0 0 0 0 0 0 .... .... .... xo..&#x | 2 1 0 0 | 0 1 2 0 0 0 0 0 0 0 0 | * * * * 120 * * * * * * * * * * * | 0 0 1 0 1 0 0 0 0 .... .... .... x.x.&#x | 2 0 2 0 | 0 1 0 2 0 0 0 1 0 0 0 | * * * * * 120 * * * * * * * * * * | 0 0 0 1 1 0 0 0 0 ooo. ooo.3ooo.5ooo.&#x | 1 1 1 0 | 0 0 1 1 1 0 0 0 0 0 0 | * * * * * * 240 * * * * * * * * * | 0 1 0 0 1 0 0 0 0 .... .... .... .ox.&#x | 0 1 2 0 | 0 0 0 0 2 0 0 1 0 0 0 | * * * * * * * 120 * * * * * * * * | 0 0 0 0 1 1 0 0 0 .... .... .... .o.x&#x | 0 1 0 2 | 0 0 0 0 0 2 0 0 0 0 1 | * * * * * * * * 60 * * * * * * * | 0 0 0 0 0 2 0 0 0 .ooo .ooo3.ooo5.ooo&#x | 0 1 1 1 | 0 0 0 0 1 1 0 0 1 0 0 | * * * * * * * * * 240 * * * * * * | 0 1 0 0 0 1 0 0 0 .... .... ..o.5..x. | 0 0 5 0 | 0 0 0 0 0 0 0 5 0 0 0 | * * * * * * * * * * 24 * * * * * | 0 0 0 1 0 0 1 0 0 .... .... ..ox ....&#x | 0 0 1 2 | 0 0 0 0 0 0 0 0 2 1 0 | * * * * * * * * * * * 120 * * * * | 0 1 0 0 0 0 0 1 0 .... .... .... ..xx&#x | 0 0 2 2 | 0 0 0 0 0 0 0 1 2 0 1 | * * * * * * * * * * * * 120 * * * | 0 0 0 0 0 1 0 0 1 ..x. .... .... ..x. | 0 0 4 0 | 0 0 0 0 0 0 2 2 0 0 0 | * * * * * * * * * * * * * 60 * * | 0 0 0 0 0 0 1 0 1 ..xo .... .... ....&#x | 0 0 2 1 | 0 0 0 0 0 0 1 0 2 0 0 | * * * * * * * * * * * * * * 120 * | 0 0 0 0 0 0 0 1 1 .... ...o3...x .... | 0 0 0 3 | 0 0 0 0 0 0 0 0 0 3 0 | * * * * * * * * * * * * * * * 20 | 0 2 0 0 0 0 0 0 0 ------------------------+---------------+------------------------------------------+----------------------------------------------------------+---------------------------- .... x...3o...5x... ♦ 60 0 0 0 | 60 60 0 0 0 0 0 0 0 0 0 | 20 30 12 0 0 0 0 0 0 0 0 0 0 0 0 0 | 2 * * * * * * * * .... xofo ofox ....&#xt ♦ 3 3 3 3 | 3 0 6 3 6 3 0 0 6 3 0 | 1 0 0 3 0 0 6 0 0 6 0 3 0 0 0 1 | * 40 * * * * * * * .... xo.. .... xo..&#x ♦ 4 1 0 0 | 2 2 4 0 0 0 0 0 0 0 0 | 0 1 0 2 2 0 0 0 0 0 0 0 0 0 0 0 | * * 60 * * * * * * .... .... o.o.5x.x.&#x ♦ 5 0 5 0 | 0 5 0 5 0 0 0 5 0 0 0 | 0 0 1 0 0 5 0 0 0 0 1 0 0 0 0 0 | * * * 24 * * * * * .... .... .... xox.&#x ♦ 2 1 2 0 | 0 1 2 2 2 0 0 1 0 0 0 | 0 0 0 0 1 1 2 1 0 0 0 0 0 0 0 0 | * * * * 120 * * * * .... .... .... .oxx&#x ♦ 0 1 2 2 | 0 0 0 0 2 2 0 1 2 0 1 | 0 0 0 0 0 0 0 1 1 2 0 0 1 0 0 0 | * * * * * 120 * * * ..x. .... ..o.5..x.&#x ♦ 0 0 10 0 | 0 0 0 0 0 0 5 10 0 0 0 | 0 0 0 0 0 0 0 0 0 0 2 0 0 5 0 0 | * * * * * * 12 * * ..xo .... ..ox ....&#x ♦ 0 0 2 2 | 0 0 0 0 0 0 1 0 4 1 0 | 0 0 0 0 0 0 0 0 0 0 0 2 0 0 2 0 | * * * * * * * 60 * ..xo .... .... ..xx&#x ♦ 0 0 4 2 | 0 0 0 0 0 0 2 2 4 0 1 | 0 0 0 0 0 0 0 0 0 0 0 0 2 1 2 0 | * * * * * * * * 60
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