Acronym | ... |
Name | oxqw wxwx3ooxx4qwox&#zx |
Face vector | 216, 600, 488, 104 |
Confer |
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The relation to spic runs as follows: spic in demitessic subsymmetry can be given as oxqwQ 2 qowxx 3 xxooo 4 oxoxo &#zx. That will be transformed into oxqwQ 2 wowxx 3 (-x)xooo 4 qxoxo &#zx (faceting, same vertex set). This in turn will be transformed into oxqwQ 2 wxwxx 3 (-x)(-x)ooo 4 qwoxo &#zx (other faceting, still same vertex set). Then a Stott expansion wrt. the third node produces oxqwQ wxwxx3ooxxx4qwoxo&#zx. This polychoron then is the monostratic parabidiminishing therefrom wrt. its axial direction.
Alternatively these processes could be commutated here: starting from the accordingly parabidiminished version of spic the relevant part of that EKF construction could be applied thereon, which then reproduces this polychoron alike.
Here: Q=w+x=q+u.
Incidence matrix according to Dynkin symbol
oxqw wxwx3ooxx4qwox&#zx → all existing heights = 0 o... o...3o...4o... | 24 * * * | 2 4 0 0 0 0 0 0 0 0 | 1 2 2 4 0 0 0 0 0 0 0 0 0 0 | 2 1 2 0 0 0 0 .o.. .o..3.o..4.o.. | * 48 * * | 1 0 1 2 2 0 0 0 0 0 | 1 0 0 2 2 1 2 1 0 0 0 0 0 0 | 2 0 1 1 1 0 0 ..o. ..o.3..o.4..o. | * * 48 * | 0 2 0 0 0 2 2 0 0 0 | 0 2 1 2 0 0 0 0 1 2 1 0 0 0 | 1 1 2 0 0 1 0 ...o ...o3...o4...o | * * * 96 | 0 0 0 0 1 0 1 1 1 1 | 0 0 0 1 0 0 1 1 0 1 1 1 1 1 | 1 0 1 0 1 1 1 ------------------------+-------------+-------------------------------+-------------------------------------------+------------------ oo.. oo..3oo..4oo..&#x | 1 1 0 0 | 48 * * * * * * * * * | 1 0 0 2 0 0 0 0 0 0 0 0 0 0 | 2 0 1 0 0 0 0 o.o. o.o.3o.o.4o.o.&#x | 1 0 1 0 | * 96 * * * * * * * * | 0 1 1 1 0 0 0 0 0 0 0 0 0 0 | 1 1 1 0 0 0 0 .x.. .... .... .... | 0 2 0 0 | * * 24 * * * * * * * | 1 0 0 0 2 0 0 0 0 0 0 0 0 0 | 2 0 0 1 0 0 0 .... .x.. .... .... | 0 2 0 0 | * * * 48 * * * * * * | 0 0 0 0 1 1 1 0 0 0 0 0 0 0 | 1 0 0 1 1 0 0 .o.o .o.o3.o.o4.o.o&#x | 0 1 0 1 | * * * * 96 * * * * * | 0 0 0 1 0 0 1 1 0 0 0 0 0 0 | 1 0 1 0 1 0 0 .... .... ..x. .... | 0 0 2 0 | * * * * * 48 * * * * | 0 1 0 0 0 0 0 0 1 1 0 0 0 0 | 0 1 1 0 0 1 0 ..oo ..oo3..oo4..oo&#x | 0 0 1 1 | * * * * * * 96 * * * | 0 0 0 1 0 0 0 0 0 1 1 0 0 0 | 1 0 1 0 0 1 0 .... ...x .... .... | 0 0 0 2 | * * * * * * * 48 * * | 0 0 0 0 0 0 1 0 0 0 0 1 1 0 | 1 0 0 0 1 0 1 .... .... ...x .... | 0 0 0 2 | * * * * * * * * 48 * | 0 0 0 0 0 0 0 1 0 1 0 1 0 1 | 0 0 1 0 1 1 1 .... .... .... ...x | 0 0 0 2 | * * * * * * * * * 48 | 0 0 0 0 0 0 0 0 0 0 1 0 1 1 | 1 0 0 0 0 1 1 ------------------------+-------------+-------------------------------+-------------------------------------------+------------------ ox.. .... .... ....&#x | 1 2 0 0 | 2 0 1 0 0 0 0 0 0 0 | 24 * * * * * * * * * * * * * | 2 0 0 0 0 0 0 .... .... o.x. ....&#x | 1 0 2 0 | 0 2 0 0 0 1 0 0 0 0 | * 48 * * * * * * * * * * * * | 0 1 1 0 0 0 0 o.q. .... .... q.o.&#zx | 2 0 2 0 | 0 4 0 0 0 0 0 0 0 0 | * * 24 * * * * * * * * * * * | 1 1 0 0 0 0 0 oooo oooo3oooo4oooo&#xr | 1 1 1 1 | 1 1 0 0 1 0 1 0 0 0 | * * * 96 * * * * * * * * * * | 1 0 1 0 0 0 0 cycle: (ABDC) .x.. .x.. .... .... | 0 4 0 0 | 0 0 2 2 0 0 0 0 0 0 | * * * * 24 * * * * * * * * * | 1 0 0 1 0 0 0 .... .x..3.o.. .... | 0 3 0 0 | 0 0 0 3 0 0 0 0 0 0 | * * * * * 16 * * * * * * * * | 0 0 0 1 1 0 0 .... .x.x .... ....&#x | 0 2 0 2 | 0 0 0 1 2 0 0 1 0 0 | * * * * * * 48 * * * * * * * | 1 0 0 0 1 0 0 .... .... .o.x ....&#x | 0 1 0 2 | 0 0 0 0 2 0 0 0 1 0 | * * * * * * * 48 * * * * * * | 0 0 1 0 1 0 0 .... .... ..x.4..o. | 0 0 4 0 | 0 0 0 0 0 4 0 0 0 0 | * * * * * * * * 12 * * * * * | 0 1 0 0 0 1 0 .... .... ..xx ....&#x | 0 0 2 2 | 0 0 0 0 0 1 2 0 1 0 | * * * * * * * * * 48 * * * * | 0 0 1 0 0 1 0 .... .... .... ..ox&#x | 0 0 1 2 | 0 0 0 0 0 0 2 0 0 1 | * * * * * * * * * * 48 * * * | 1 0 0 0 0 1 0 .... ...x3...x .... | 0 0 0 6 | 0 0 0 0 0 0 0 3 3 0 | * * * * * * * * * * * 16 * * | 0 0 0 0 1 0 1 .... ...x .... ...x | 0 0 0 4 | 0 0 0 0 0 0 0 2 0 2 | * * * * * * * * * * * * 24 * | 1 0 0 0 0 0 1 .... .... ...x4...x | 0 0 0 8 | 0 0 0 0 0 0 0 0 4 4 | * * * * * * * * * * * * * 12 | 0 0 0 0 0 1 1 ------------------------+-------------+-------------------------------+-------------------------------------------+------------------ oxqw wxwx .... qwox&#zx ♦ 4 8 4 8 | 8 8 4 4 8 0 8 4 0 4 | 4 0 2 8 2 0 4 0 0 0 4 0 2 0 | 12 * * * * * * o.q. .... o.x.4q.o.&#zx ♦ 4 0 8 0 | 0 16 0 0 0 8 0 0 0 0 | 0 8 4 0 0 0 0 0 2 0 0 0 0 0 | * 6 * * * * * .... .... ooxx ....&#xr ♦ 1 1 2 2 | 1 2 0 0 2 1 2 0 1 0 | 0 1 0 2 0 0 0 1 0 1 0 0 0 0 | * * 48 * * * * cycle: (ABDC) .x.. .x..3.o.. .... ♦ 0 6 0 0 | 0 0 3 6 0 0 0 0 0 0 | 0 0 0 0 3 2 0 0 0 0 0 0 0 0 | * * * 8 * * * .... .x.x3.o.x ....&#x ♦ 0 3 0 6 | 0 0 0 3 6 0 0 3 3 0 | 0 0 0 0 0 1 3 3 0 0 0 1 0 0 | * * * * 16 * * .... .... ..xx4..ox&#x ♦ 0 0 4 8 | 0 0 0 0 0 4 8 0 4 4 | 0 0 0 0 0 0 0 0 1 4 4 0 0 1 | * * * * * 12 * .... ...x3...x4...x ♦ 0 0 0 48 | 0 0 0 0 0 0 0 24 24 24 | 0 0 0 0 0 0 0 0 0 0 0 8 12 6 | * * * * * * 2
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