Acronym ... Name xxxFooAFxxAxxFx3oxFxxAxxxFooFxx3xfoxFoofFxxFoox&#xt Confer uniform relative: ex   general polytopal classes: expanded kaleido-facetings

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)3x3oo3(-x)3x, the fifth layer according to: o3x3fx3(-x)3F(-x)3o3F, the sixth layer according to: x3f3o(-x)3F3o, the eleventh layer according to: f3x3oF3(-x)3x, and the twelfth layer according to: x3o3f(-x)3x3fo3(-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  1 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  1  1 0  1 1 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  0  0  0  0  0  0  0  2  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 0  0  1  2  0  2  0  1  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 1  1  2  1 0  0 0 0 0 1  0 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  2  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  0  0  0  0  0  0 0  0  2  1  2 0  0  0 0  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  1 1  2 0 0 1 0  0 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  2  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  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  0 0  0  0  0  0 0  0  0  0  0 0  0  0  0  0  0  0  0  0  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 0  0  0  0 0  0 0 0 0  0  0  0 0  0 0 0 0 0  0 0 0
oo.............3oo.............3oo.............&#x  |  1  1  0  0  0 0  0  0  0  0  0  0  0  0  0 |  *  * 24  *  *  *  *  * *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  * *  *  *  *  *  *  *  * | 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  0  0  0  0  0  0  0  0 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
.x............. ............... ...............     |  0  2  0  0  0 0  0  0  0  0  0  0  0  0  0 |  *  *  * 12  *  *  *  * *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  * *  *  *  *  *  *  *  * | 0 0 0  1  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  0 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 0 0
............... .x............. ...............     |  0  2  0  0  0 0  0  0  0  0  0  0  0  0  0 |  *  *  *  * 12  *  *  * *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  * *  *  *  *  *  *  *  * | 0 0 0  0  1  0 1  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  0  0 0 0 0 | 0 1 0 1 1  0  1  0 0  0 0 0 0  0  0  0 0  0 0 0 0 0  0 0 0
.oo............3.oo............3.oo............&#x  |  0  1  1  0  0 0  0  0  0  0  0  0  0  0  0 |  *  *  *  *  * 24  *  * *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  * *  *  *  *  *  *  *  * | 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 0  0  0  0  0  0  0  0  0  0 0  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
.o.o...........3.o.o...........3.o.o...........&#x  |  0  1  0  1  0 0  0  0  0  0  0  0  0  0  0 |  *  *  *  *  *  * 24  * *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  * *  *  *  *  *  *  *  * | 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  0  0  0  0  0  0  0 0  0  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  0 0  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  1  0  0  1 0  0  0  0  0  0  0  0  0  0 |  *  *  *  *  *  *  * 24 *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  * *  *  *  *  *  *  *  * | 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 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
..x............ ............... ...............     |  0  0  2  0  0 0  0  0  0  0  0  0  0  0  0 |  *  *  *  *  *  *  *  * 6  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  * *  *  *  *  *  *  *  * | 0 0 0  0  0  0 0  2  0  0  0  0  0  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 1 0 0  2  0  0 0  0 0 0 0  0  0  0 0  0 0 0 0 0  0 0 0
..oo...........3..oo...........3..oo...........&#x  |  0  0  1  1  0 0  0  0  0  0  0  0  0  0  0 |  *  *  *  *  *  *  *  * * 24  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  * *  *  *  *  *  *  *  * | 0 0 0  0  0  0 0  0  0  0  0  1  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 | 0 0 0 1 0  1  0  1 0  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  1  0  0 1  0  0  0  0  0  0  0  0  0 |  *  *  *  *  *  *  *  * *  * 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
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............... ...x..x........ ...............&#x  |  0  0  0  2  0 0  2  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  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 | * * *  *  *  * *  *  *  *  *  *  *  * *  * * 12  *  *  * *  *  *  *  * *  *  *  *  *  *  *  *  *  * *  *  *  *  * *  *  * *  *  * *  *  *  *  *  * *  *  * * * * | 0 0 0 0 0  0  0  0 1  1 0 0 0  0  0  0 0  0 0 0 0 0  0 0 0
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...........x..x3...........o..x ...............&#x  ♦  0  0  0  0  0 0  0  0  0  0  0  3  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  0  0  0  0  0  0  0  0  0  0  0  3  6 0  0  0  0  0  3  3  0 | 0 0 0  0  0  0 0  0  0  0  0  0  0  0 0  0 0  0  0  0  0 0  0  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  3  3  0  0  0 0  0  0 1 0 0 | * * * * *  *  *  * *  * * * *  *  *  * *  * * * 4 *  * * *
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```

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