| Acronym | ... |
| Name | BAVFfxoo xFofxFVo3xxFxooxo5xooxFfoV&#zx |
| Face vector | 980, 3120, 2780, 640 |
| Confer |
|
The relation to rox runs as follows: rox in icosahedral-prismatic subsymmetry can be given as DCBAVFfxoo 2 xoxFofofVx 3 oxoofoxxoo 5 ooxooxxoof &#zx. That will be transformed into DCBAVFfxoo 2 xoxFofofVx 3 o(-x)oofoxxoo 5 ooxooxxoof &#zx (faceting, same vertex set). This in turn will be transformed into DCBAVFfxoo 2 xoxFofxfVx 3 o(-x)oofo(-x)xoo 5 ooxooxFoof &#zx (other faceting, still same vertex set). Once more into DCBAVFfxoo 2 xoxFofxFVx 3 o(-x)oofo(-x)(-x)oo 5 ooxooxFfof &#zx and finally within the second of the central layers first into DCBAVFfxoo 2 xoxFofxFV(-x) 3 o(-x)oofo(-x)(-x)ox 5 ooxooxFfof &#zx and once agin into DCBAVFfxoo 2 xxxFofxFVo 3 o(-x)oofo(-x)(-x)o(-x) 5 ofxooxFfoV &#zx (still other faceting with same vertex set). Then a Stott expansion wrt. the third node produces DCBAVFfxoo xxxFofxFVo3xoxxFxooxo5ofxooxFfoV&#zx. This polychoron finally is the bistratic parabidiminishing therefrom wrt. its axial direction.
Alternatively these processes could be commutated here: starting from the accordingly parabidiminished version of rox the relevant part of that EKF construction could be applied thereon, which then reproduces this polychoron alike.
Here: F=f+x=ff, V=F+v=2f, A=F+x=f+2x, B=V+x=2f+x=fff, C=2F=2f+2x, D=F+V=3f+x.
Incidence matrix according to Dynkin symbol
BAVFfxoo xFofxFVo3xxFxooxo5xooxFfoV&#zx → all existing heights = 0 o....... o.......3o.......5o....... | 240 * * * * * * * | 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | 1 1 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 1 1 1 1 1 1 0 0 0 0 0 .o...... .o......3.o......5.o...... | * 120 * * * * * * | 0 0 0 2 0 0 2 2 0 0 0 0 0 0 0 0 0 0 0 | 0 0 1 2 1 0 0 0 2 0 1 2 1 0 0 0 0 0 0 0 0 0 0 0 0 | 0 1 0 0 2 1 1 0 0 0 0 ..o..... ..o.....3..o.....5..o..... | * * 60 * * * * * | 0 0 0 0 4 0 0 0 4 0 0 0 0 0 0 0 0 0 0 | 0 0 2 0 0 2 2 0 0 4 0 0 0 2 2 0 0 0 0 0 0 0 0 0 0 | 0 0 2 1 0 2 0 1 0 0 0 ...o.... ...o....3...o....5...o.... | * * * 240 * * * * | 0 0 0 0 0 1 0 1 1 1 1 1 1 0 0 0 0 0 0 | 0 0 0 0 0 0 0 1 1 1 0 1 1 1 1 1 1 1 1 0 0 0 0 0 0 | 0 0 1 0 1 1 1 1 1 0 0 ....o... ....o...3....o...5....o... | * * * * 120 * * * | 0 0 0 0 0 0 0 0 0 0 0 2 0 2 1 1 0 0 0 | 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 1 0 0 2 1 2 1 0 0 0 | 0 0 1 0 0 0 0 2 1 1 0 .....o.. .....o..3.....o..5.....o.. | * * * * * 120 * * | 0 0 0 0 0 0 0 0 0 0 0 0 2 0 1 0 1 2 0 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 2 2 0 0 1 2 1 0 | 0 0 0 0 0 0 1 2 1 0 1 ......o. ......o.3......o.5......o. | * * * * * * 60 * | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 2 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 2 4 1 | 0 0 0 0 0 0 2 1 0 0 2 .......o .......o3.......o5.......o | * * * * * * * 20 ♦ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6 0 0 0 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6 3 0 0 0 | 0 0 0 0 0 0 0 3 0 2 0 ----------------------------------------+------------------------------+---------------------------------------------------------------------------+----------------------------------------------------------------------------------------------+----------------------------------- ........ x....... ........ ........ | 2 0 0 0 0 0 0 0 | 120 * * * * * * * * * * * * * * * * * * | 1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 1 0 1 1 0 0 0 0 0 0 0 ........ ........ x....... ........ | 2 0 0 0 0 0 0 0 | * 120 * * * * * * * * * * * * * * * * * | 1 0 1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 1 1 1 0 1 0 0 0 0 0 0 ........ ........ ........ x....... | 2 0 0 0 0 0 0 0 | * * 120 * * * * * * * * * * * * * * * * | 0 1 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 1 1 0 1 0 1 0 0 0 0 0 oo...... oo......3oo......5oo......&#x | 1 1 0 0 0 0 0 0 | * * * 240 * * * * * * * * * * * * * * * | 0 0 0 1 1 0 0 0 1 0 0 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 o.o..... o.o.....3o.o.....5o.o.....&#x | 1 0 1 0 0 0 0 0 | * * * * 240 * * * * * * * * * * * * * * | 0 0 0 0 0 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 0 0 1 1 0 1 0 0 0 0 0 o..o.... o..o....3o..o....5o..o....&#x | 1 0 0 1 0 0 0 0 | * * * * * 240 * * * * * * * * * * * * * | 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 0 0 1 0 1 1 0 0 0 0 0 ........ ........ .x...... ........ | 0 2 0 0 0 0 0 0 | * * * * * * 120 * * * * * * * * * * * * | 0 0 0 1 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | 0 1 0 0 1 0 1 0 0 0 0 .o.o.... .o.o....3.o.o....5.o.o....&#x | 0 1 0 1 0 0 0 0 | * * * * * * * 240 * * * * * * * * * * * | 0 0 0 0 0 0 0 0 1 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 | 0 0 0 0 1 1 1 0 0 0 0 ..oo.... ..oo....3..oo....5..oo....&#x | 0 0 1 1 0 0 0 0 | * * * * * * * * 240 * * * * * * * * * * | 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 | 0 0 1 0 0 1 0 1 0 0 0 ........ ........ ...x.... ........ | 0 0 0 2 0 0 0 0 | * * * * * * * * * 120 * * * * * * * * * | 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 1 1 0 0 0 0 0 0 0 0 | 0 0 1 0 1 0 1 0 1 0 0 ........ ........ ........ ...x.... | 0 0 0 2 0 0 0 0 | * * * * * * * * * * 120 * * * * * * * * | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 1 0 0 0 0 0 0 0 | 0 0 0 0 0 1 1 1 0 0 0 ...oo... ...oo...3...oo...5...oo...&#x | 0 0 0 1 1 0 0 0 | * * * * * * * * * * * 240 * * * * * * * | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 1 0 0 0 0 0 0 | 0 0 1 0 0 0 0 1 1 0 0 ...o.o.. ...o.o..3...o.o..5...o.o..&#x | 0 0 0 1 0 1 0 0 | * * * * * * * * * * * * 240 * * * * * * | 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 0 0 0 1 1 1 0 0 ........ ....x... ........ ........ | 0 0 0 0 2 0 0 0 | * * * * * * * * * * * * * 120 * * * * * | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 1 0 0 0 0 | 0 0 1 0 0 0 0 1 0 1 0 ....oo.. ....oo..3....oo..5....oo..&#x | 0 0 0 0 1 1 0 0 | * * * * * * * * * * * * * * 120 * * * * | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 1 0 0 0 | 0 0 0 0 0 0 0 2 1 0 0 ....o..o ....o..o3....o..o5....o..o&#x | 0 0 0 0 1 0 0 1 | * * * * * * * * * * * * * * * 120 * * * | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 1 0 0 0 | 0 0 0 0 0 0 0 2 0 1 0 .....x.. ........ ........ ........ | 0 0 0 0 0 2 0 0 | * * * * * * * * * * * * * * * * 60 * * | 0 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 2 0 0 1 .....oo. .....oo.3.....oo.5.....oo.&#x | 0 0 0 0 0 1 1 0 | * * * * * * * * * * * * * * * * * 240 * | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 0 | 0 0 0 0 0 0 1 1 0 0 1 ........ ........ ......x. ........ | 0 0 0 0 0 0 2 0 | * * * * * * * * * * * * * * * * * * 60 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 1 | 0 0 0 0 0 0 2 0 0 0 1 ----------------------------------------+------------------------------+---------------------------------------------------------------------------+----------------------------------------------------------------------------------------------+----------------------------------- ........ x.......3x....... ........ | 6 0 0 0 0 0 0 0 | 3 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 40 * * * * * * * * * * * * * * * * * * * * * * * * | 1 0 1 0 0 0 0 0 0 0 0 ........ x....... ........ x....... | 4 0 0 0 0 0 0 0 | 2 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | * 60 * * * * * * * * * * * * * * * * * * * * * * * | 1 0 0 1 0 0 0 0 0 0 0 ........ ........ x.......5x....... | 0 5 5 0 0 0 0 0 | 0 5 5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | * * 24 * * * * * * * * * * * * * * * * * * * * * * | 1 1 0 0 0 0 0 0 0 0 0 ........ ........ xx...... ........&#x | 2 2 0 0 0 0 0 0 | 0 1 0 2 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 | * * * 120 * * * * * * * * * * * * * * * * * * * * * | 0 1 0 0 1 0 0 0 0 0 0 ........ ........ ........ xo......&#x | 2 1 0 0 0 0 0 0 | 0 0 1 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | * * * * 120 * * * * * * * * * * * * * * * * * * * * | 0 1 0 0 0 1 0 0 0 0 0 ........ x.o..... ........ ........&#x | 2 0 1 0 0 0 0 0 | 1 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | * * * * * 120 * * * * * * * * * * * * * * * * * * * | 0 0 1 1 0 0 0 0 0 0 0 ........ ........ ........ x.o.....&#x | 2 0 1 0 0 0 0 0 | 0 0 1 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | * * * * * * 120 * * * * * * * * * * * * * * * * * * | 0 0 0 1 0 1 0 0 0 0 0 ........ ........ x..x.... ........&#x | 2 0 0 2 0 0 0 0 | 0 1 0 0 0 2 0 0 0 1 0 0 0 0 0 0 0 0 0 | * * * * * * * 120 * * * * * * * * * * * * * * * * * | 0 0 1 0 1 0 0 0 0 0 0 oo.o.... oo.o....3oo.o....5oo.o....&#x | 1 1 0 1 0 0 0 0 | 0 0 0 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 | * * * * * * * * 240 * * * * * * * * * * * * * * * * | 0 0 0 0 1 1 0 0 0 0 0 o.oo.... o.oo....3o.oo....5o.oo....&#x | 1 0 1 1 0 0 0 0 | 0 0 0 0 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 | * * * * * * * * * 240 * * * * * * * * * * * * * * * | 0 0 1 0 0 1 0 0 0 0 0 ........ ........ .x......5.o...... | 0 5 0 0 0 0 0 0 | 0 0 0 0 0 0 5 0 0 0 0 0 0 0 0 0 0 0 0 | * * * * * * * * * * 24 * * * * * * * * * * * * * * | 0 1 0 0 0 0 1 0 0 0 0 ........ ........ .x.x.... ........&#x | 0 2 0 2 0 0 0 0 | 0 0 0 0 0 0 1 2 0 1 0 0 0 0 0 0 0 0 0 | * * * * * * * * * * * 120 * * * * * * * * * * * * * | 0 0 0 0 1 0 1 0 0 0 0 ........ ........ ........ .o.x....&#x | 0 1 0 2 0 0 0 0 | 0 0 0 0 0 0 0 2 0 0 1 0 0 0 0 0 0 0 0 | * * * * * * * * * * * * 120 * * * * * * * * * * * * | 0 0 0 0 0 1 1 0 0 0 0 ........ ..ofx... ........ ........&#xt | 0 0 1 2 2 0 0 0 | 0 0 0 0 0 0 0 0 2 0 0 2 0 1 0 0 0 0 0 | * * * * * * * * * * * * * 120 * * * * * * * * * * * | 0 0 1 0 0 0 0 1 0 0 0 ........ ........ ........ ..ox....&#x | 0 0 1 2 0 0 0 0 | 0 0 0 0 0 0 0 0 2 0 1 0 0 0 0 0 0 0 0 | * * * * * * * * * * * * * * 120 * * * * * * * * * * | 0 0 0 0 0 1 0 1 0 0 0 ........ ........ ...xo... ........&#x | 0 0 0 2 1 0 0 0 | 0 0 0 0 0 0 0 0 0 1 0 2 0 0 0 0 0 0 0 | * * * * * * * * * * * * * * * 120 * * * * * * * * * | 0 0 1 0 0 0 0 0 1 0 0 ........ ........ ...x.o.. ........&#x | 0 0 0 2 0 1 0 0 | 0 0 0 0 0 0 0 0 0 1 0 0 2 0 0 0 0 0 0 | * * * * * * * * * * * * * * * * 120 * * * * * * * * | 0 0 0 0 0 0 1 0 1 0 0 ........ ........ ........ ...x.fo.&#xt | 0 0 0 2 0 2 1 0 | 0 0 0 0 0 0 0 0 0 0 1 0 2 0 0 0 0 2 0 | * * * * * * * * * * * * * * * * * 120 * * * * * * * | 0 0 0 0 0 0 1 1 0 0 0 ...ooo.. ...ooo..3...ooo..5...ooo..&#x | 0 0 0 1 1 1 0 0 | 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 0 0 | * * * * * * * * * * * * * * * * * * 240 * * * * * * | 0 0 0 0 0 0 0 1 1 0 0 ........ ....x...3....o... ........ | 0 0 0 0 3 0 0 0 | 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 | * * * * * * * * * * * * * * * * * * * 40 * * * * * | 0 0 1 0 0 0 0 0 0 1 0 ........ ....x..o ........ ........&#x | 0 0 0 0 2 0 0 1 | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 2 0 0 0 | * * * * * * * * * * * * * * * * * * * * 120 * * * * | 0 0 0 0 0 0 0 1 0 1 0 ....fx.o ........ ........ ........&#xt | 0 0 0 0 2 2 0 1 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 1 0 0 | * * * * * * * * * * * * * * * * * * * * * 60 * * * | 0 0 0 0 0 0 0 2 0 0 0 tower: F-E-H .....xo. ........ ........ ........&#x | 0 0 0 0 0 2 1 0 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 2 0 | * * * * * * * * * * * * * * * * * * * * * * 120 * * | 0 0 0 0 0 0 0 1 0 0 1 ........ ........ .....ox. ........&#x | 0 0 0 0 0 1 2 0 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 1 | * * * * * * * * * * * * * * * * * * * * * * * 120 * | 0 0 0 0 0 0 1 0 0 0 1 ........ ........ ......x.5......o. | 0 0 0 0 0 0 5 0 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5 | * * * * * * * * * * * * * * * * * * * * * * * * 12 | 0 0 0 0 0 0 2 0 0 0 0 ----------------------------------------+------------------------------+---------------------------------------------------------------------------+----------------------------------------------------------------------------------------------+----------------------------------- ........ x.......3x.......5x....... ♦ 120 0 0 0 0 0 0 0 | 60 60 60 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 | 2 * * * * * * * * * * ........ ........ xx......5xo......&#xt ♦ 10 5 0 0 0 0 0 0 | 0 5 5 10 0 0 5 0 0 0 0 0 0 0 0 0 0 0 0 | 0 0 1 5 5 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | * 24 * * * * * * * * * ........ x.ofx...3x.Fxo... ........&#xt ♦ 6 0 3 6 3 0 0 0 | 3 3 0 0 6 6 0 0 6 3 0 6 0 3 0 0 0 0 0 | 1 0 0 0 0 3 0 3 0 6 0 0 0 3 0 3 0 0 0 1 0 0 0 0 0 | * * 40 * * * * * * * * ........ x.o..... ........ x.o.....&#x ♦ 4 0 1 0 0 0 0 0 | 2 0 2 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 0 1 0 0 0 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | * * * 60 * * * * * * * ........ ........ xx.x.... ........&#x ♦ 2 2 0 2 0 0 0 0 | 0 1 0 2 0 2 1 2 0 1 0 0 0 0 0 0 0 0 0 | 0 0 0 1 0 0 0 1 2 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | * * * * 120 * * * * * * ........ ........ ........ xoox....&#xr ♦ 2 1 1 2 0 0 0 0 | 0 0 1 2 2 2 0 2 2 0 1 0 0 0 0 0 0 0 0 | 0 0 0 0 1 0 1 0 2 2 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 | * * * * * 120 * * * * * cycle: (ABDC) ........ ........ .x.x.ox.5.o.x.fo.&#xt ♦ 0 5 0 10 0 5 5 0 | 0 0 0 0 0 0 5 10 0 5 5 0 10 0 0 0 0 10 5 | 0 0 0 0 0 0 0 0 0 0 1 5 5 0 0 0 5 5 0 0 0 0 0 5 1 | * * * * * * 24 * * * * ..VFfxoo ..ofxFVo ........ ..oxFfoV&#zx ♦ 0 0 2 8 8 8 2 2 | 0 0 0 0 0 0 0 0 8 0 4 8 8 4 8 8 4 8 0 | 0 0 0 0 0 0 0 0 0 0 0 0 0 4 4 0 0 4 8 0 4 4 4 0 0 | * * * * * * * 30 * * * ........ ........ ...xoo.. ........&#x ♦ 0 0 0 2 1 1 0 0 | 0 0 0 0 0 0 0 0 0 1 0 2 2 0 1 0 0 0 0 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 2 0 0 0 0 0 0 | * * * * * * * * 120 * * ........ ....x..o3....o..o ........&#x ♦ 0 0 0 0 3 0 0 1 | 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 3 0 0 0 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 3 0 0 0 0 | * * * * * * * * * 40 * .....xo. ........ .....ox. ........&#x ♦ 0 0 0 0 0 2 2 0 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 4 1 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 0 | * * * * * * * * * * 60
© 2004-2024 | top of page |