Acronym | ... |
Name | xxxFooAFxxAxxFx3oxFxxAxxxFooFxx3xfoxFoofFxxFoox&#xt |
Face vector | 246, 768, 696, 174 |
Confer |
|
The relation to ex runs as follows: ex in axial tetrahedral subsymmetry can be given as xoofoxFfoofxofo 3 oofoxfooofxofoo 3 ofoxfoofFxofoox &#xt (F = ff = f+x). There the first layer will be transformed according to: x3o3o → (-x)3x3o → o3(-x)3x, the fifth layer according to: o3x3f → x3(-x)3F → (-x)3o3F, the sixth layer according to: x3f3o → (-x)3F3o, the eleventh layer according to: f3x3o → F3(-x)3x, and the twelfth layer according to: x3o3f → (-x)3x3f → o3(-x)3F. This then results in the kaleido-faceting ooof(-x)(-x)FfooFoofo 3 (-x)ofooFooof(-x)(-x)foo 3 xfoxFoofFxxFoox &#xt. Then a (uniformly to all layers) applied Stott expansion wrt. the first and second node produces this polychoron (A = F+x = f+2x).
Incidence matrix according to Dynkin symbol
xxxFooAFxxAxxFx3oxFxxAxxxFooFxx3xfoxFoofFxxFoox&#xt → height(1,2) = height(3,4) = height(5,6) = height(7,8) = height(8,9) = height(10,11) = height(12,13) = height(14,15) = sqrt[3-sqrt(5)]/4 = 0.218508 height(2,3) = height(6,7) = height(9,10) = height(13,14) = sqrt[7-3 sqrt(5)]/4 = 0.135045 height(4,5) = height(11,12) = 1/sqrt(8) = 0.353553 (co || pseudo (x,x,f)-toe || pseudo (x,F,o)-tut || pseudo (F,x,x)-toe || pseudo (o,x,F)-tut || pseudo A-oct || pseudo (A,x,o)-tut || pseudo (F,x,f)-toe || pseudo (x,x,F)-toe || pseudo (x,F,x)-toe || pseudo (A,x)-co || pseudo (x,F)-co || pseudo (x,F,o)-tut || pseudo (F,x,o)-tut || toe) o..............3o..............3o.............. | 12 * * * * * * * * * * * * * * | 2 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 1 2 1 2 1 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 1 1 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 .o.............3.o.............3.o............. | * 24 * * * * * * * * * * * * * | 0 0 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 0 0 0 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 ..o............3..o............3..o............ | * * 12 * * * * * * * * * * * * | 0 0 0 0 0 2 0 0 1 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 0 0 0 0 0 1 0 2 0 0 0 2 0 1 1 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 0 0 1 1 0 2 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ...o...........3...o...........3...o........... | * * * 24 * * * * * * * * * * * | 0 0 0 0 0 0 1 0 0 1 0 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 0 0 0 0 0 0 0 0 1 0 0 1 1 1 0 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 0 0 0 1 0 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ....o..........3....o..........3....o.......... | * * * * 12 * * * * * * * * * * | 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 0 0 0 0 0 0 0 0 0 1 2 0 2 0 0 0 0 0 0 0 0 1 1 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 0 0 0 0 1 1 2 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 .....o.........3.....o.........3.....o......... | * * * * * 6 * * * * * * * * * | 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 4 0 0 0 0 0 0 0 0 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 0 0 0 0 0 2 0 2 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 ......o........3......o........3......o........ | * * * * * * 12 * * * * * * * * | 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 2 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 2 0 0 0 0 0 1 2 2 1 1 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 0 0 0 0 0 0 0 1 1 2 0 0 1 2 1 0 0 0 0 0 0 0 0 0 0 .......o.......3.......o.......3.......o....... | * * * * * * * 24 * * * * * * * | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 1 1 0 0 0 0 0 0 1 0 0 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 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 1 1 1 0 0 0 0 0 0 0 0 0 ........o......3........o......3........o...... | * * * * * * * * 24 * * * * * * | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 1 0 1 0 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 0 0 0 0 0 1 1 0 0 0 1 0 0 0 0 0 1 1 1 0 0 0 0 0 0 .........o.....3.........o.....3.........o..... | * * * * * * * * * 24 * * * * * | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 1 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 1 0 0 0 0 1 0 0 0 1 1 0 1 0 0 1 1 1 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0 0 0 0 0 0 2 0 0 0 0 2 0 2 1 0 0 0 0 0 0 2 1 2 0 0 0 0 0 0 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 2 0 2 1 0 0 1 1 0 0 .............o.3.............o.3.............o. | * * * * * * * * * * * * * 12 * | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 1 0 2 2 0 0 0 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 2 1 0 0 0 0 0 2 1 2 1 0 0 0 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 2 0 0 0 1 0 0 1 1 0 ..............o3..............o3..............o | * * * * * * * * * * * * * * 24 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 1 1 1 1 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 1 1 1 0 1 1 1 1 1 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 1 1 1 1 1 ----------------------------------------------------+---------------------------------------------+-----------------------------------------------------------------------------------------------------------------------------------+------------------------------------------------------------------------------------------------------------------------------------------------------------------+----------------------------------------------------------- x.............. ............... ............... | 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 12 * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * | 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 ............... ............... x.............. | 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | * 12 * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * | 0 1 1 0 0 1 0 0 0 0 0 0 0 0 0 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* 12 * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * | 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 0 0 0 0 0 2 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ............... ...x........... ............... | 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 | * * * * * * * * * * * 12 * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * | 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 0 0 0 1 0 0 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ............... ............... ...x........... | 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 | * * * * * * * * * * * * 12 * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 ...o..o........3...o..o........3...o..o........&#x | 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 | * * * * * * * * * * * * * 24 * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * | 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 ...o...o.......3...o...o.......3...o...o.......&#x | 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 | * * * * * * * * * * * * * * 24 * * * * * * * * * * * * * * * * * * * * * * * * * * * * * | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 ............... ....x.......... ............... | 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 | * * * * * * * * * * * * * * * 12 * * * * * * * * * * * * * * * * * * * * * * * * * * * * | 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 0 0 0 0 1 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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1 1 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 ......oo.......3......oo.......3......oo.......&#x | 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 | * * * * * * * * * * * * * * * * * * * 24 * * * * * * * * * * * * * * * * * * * * * * * * | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 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 0 0 0 0 0 0 0 0 0 0 0 | 0 0 0 0 0 0 0 1 0 1 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 ......o...o....3......o...o....3......o...o....&#x | 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 | * * * * * * * * * * * * * * * * * * * * 24 * * * * * * * * * * * * * * * * * * * * * * * | 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 ............... .......x....... ............... | 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 | * * * * * * * * * * * * * * * * * * * * * 12 * * * * * * * * * * * * * * * * * * * * * * | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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