Acronym ... Name ooofxxFfooFoofo3oxFxoFxxxFooFxx3xfoxFoofFxxFoox&#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 will be transformed according to: o3x3fx3(-x)3F, 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 ooofxxFfooFoofo 3 (-x)ofo(-x)fooof(-x)(-x)foo 3 xfoxFoofFxxFoox &#xt. Then a (uniformly to all layers) applied Stott expansion wrt. the second node produces this polychoron.

There are 2 other axial EKFs which re-use one half each of this polychoron, but then continue differently, still having the same vertex layers throughout: ooofxxFfooFxofx3oxFxoFxxxFoxFxo3xfoxFoofFxxfooo&#xt resp. xooFxxFfooFoofo3xxFooFxxxFooFxx3ofooFoofFxxFoox&#xt. As such this polychoron is just an asymmetric hemiglomal combination of those.

Incidence matrix according to Dynkin symbol

```ooofxxFfooFxofo 3 oxFxoFxxxFoxFxx 3 xfoxFoofFxxfoox &#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
(tet || pseudo (f,x)-tut || pseudo F-oct || pseudo (x,x,f)-toe || pseudo (F,x)-co || pseudo inv (x,F)-tut || pseudo inv (F,x)-tut || pseudo (f,x,f)-toe || pseudo inv (F,x)-tut || pseudo inv (x,F)-tut || pseudo (F,x)-co || pseudo dual F-tet || pseudo F-oct || pseudo (f,x)-tut || inv tut)

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.o............. 3 .o............. 3 .o.............      | * 12 *  *  *  *  *  *  *  *  * * *  *  * | 0  1  2  1  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  2 1 1  2  1  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 0  0  0 0 0 | 0 1 2 1  2  1  0 0  0  0  0  0  0 0 0  0 0  0  0 0 0 0  0 0 0  B
..o............ 3 ..o............ 3 ..o............      | *  * 6  *  *  *  *  *  *  *  * * *  *  * | 0  0  0  2  0  0  4  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 0  0  0  0  4  0  2 1  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  0 0 0 | 0 0 2 0  0  2  2 0  0  0  0  0  0 0 0  0 0  0  0 0 0 0  0 0 0  C
...o........... 3 ...o........... 3 ...o...........      | *  * * 24  *  *  *  *  *  *  * * *  *  * | 0  0  0  0  1  0  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  1  0  0  1  1  1 0  1 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 1 0  1  1  1 1  1  1  1  1  0 0 0  0 0  0  0 0 0 0  0 0 0  D
....o.......... 3 ....o.......... 3 ....o..........      | *  * *  * 12  *  *  *  *  *  * * *  *  * | 0  0  0  0  0  2  0  0  0  0  2  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  2  1  0  2  0 0  0 0  1  0  0  0  0  2  0  0  0 1  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 1  1  2  0 0  1  0  0  0  1 1 0  0 0  0  0 0 0 0  0 0 0  E
.....o......... 3 .....o......... 3 .....o.........      | *  * *  *  * 12  *  *  *  *  * * *  *  * | 0  0  0  0  0  0  0  1  0  0  0  2  0  0  0  0  0 1  1  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 1  2 0  0  1  0  0  0  0  2  2  0 0  0  0  0  0  2  1  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  2  1 0  0  1  0  2  0 0 1  1 0  0  0 0 0 0  0 0 0  F
......o........ 3 ......o........ 3 ......o........      | *  * *  *  *  * 12  *  *  *  * * *  *  * | 0  0  0  0  0  0  0  0  0  0  0  0  2  0  0  0  0 0  1  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  2  1  0  0  2  0  2 0  0  0  0  0  0  0  2  0 1  2  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 1  0  1  2  2  0 0 0  1 1  2  0 0 0 0  0 0 0  G
.......o....... 3 .......o....... 3 .......o.......      | *  * *  *  *  *  * 24  *  *  * * *  *  * | 0  0  0  0  0  0  0  0  0  0  0  0  0  1  0  1  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  1  1  0  1  1 0  1  0  0  1  0  0  1  1 0  1  0  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  1  0 0  1  0  1  1  1 0 0  1 0  1  1 0 0 0  0 0 0  H
........o...... 3 ........o...... 3 ........o......      | *  * *  *  *  *  *  * 12  *  * * *  *  * | 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  2  0  0  2  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  1  2  2  0  0  0  0 0  0  0  0  0  2  0  2  0 1  2  1 0 0  0  0  0  0 0 0  0  0 0 0 | 0 0 0 0  0  1  0 0  0  0  0  0  2 1 0  0 0  0  2 1 0 0  0 0 0  I
.........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  0  0  2  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 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  2  2 0  0  1 1 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  2 0  0  2 0 0 0  0 0 0  J
..........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  2  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  1  2  2  0  1  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  2 1  1  1 0 1 0  0 0 0  K
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............o.. 3 ............o.. 3 ............o..      | *  * *  *  *  *  *  *  *  *  * * 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  2  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  4 0  0  2 1 0  0  0  0  4 1 0  0  0 0 0 | 0 0 0 0  0  0  0 0  0  0  0  0  0 0 0  2 0  0  4 0 0 0  2 0 0  M
.............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  0  2  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  0  0  0  2 0  0  0 0 0  2  1  0  2 0 1  2  1 0 0 | 0 0 0 0  0  0  0 0  0  0  0  0  0 0 0  1 0  0  2 0 1 0  1 1 0  N
..............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  0  0  1  0  1  0  2  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  0  0 0  0  1 0 0  0  0  2  2 1 0  2  2 1 2 | 0 0 0 0  0  0  0 0  0  0  0  0  0 0 0  0 0  0  2 0 0 1  2 2 1  O
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oo............. 3 oo............. 3 oo............. &#x  | 1  1 0  0  0  0  0  0  0  0  0 0 0  0  0 | * 12  *  *  *  *  *  *  *  *  *  *  *  *  *  *  * *  *  *  *  *  *  *  *  *  *  *  *  *  * *  *  *  *  *  *  *  *  *  * * | 0  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  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  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  1 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 1 1 1  1  0  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  1 1  0  0  0  0  0  0  0  0 0 0  0  0 | *  *  * 12  *  *  *  *  *  *  *  *  *  *  *  *  * *  *  *  *  *  *  *  *  *  *  *  *  *  * *  *  *  *  *  *  *  *  *  * * | 0  0 1 0  0  0  0  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 2 0  0  1  0 0  0  0  0  0  0 0 0  0 0  0  0 0 0 0  0 0 0
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.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  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 1  1  1  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  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 1 0  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  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 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  1 0  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  1  0  0  0  0  0 0  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  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 1  1  0  1  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  1 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 1 0  0  0  1 1  0  1  0  0  0 0 0  0 0  0  0 0 0 0  0 0 0
...oo.......... 3 ...oo.......... 3 ...oo.......... &#x  | 0  0 0  1  1  0  0  0  0  0  0 0 0  0  0 | *  *  *  *  *  *  *  *  *  * 24  *  *  *  *  *  * *  *  *  *  *  *  *  *  *  *  *  *  *  * *  *  *  *  *  *  *  *  *  * * | 0  0 0 0  0  0  0  0  1  0 0  0 0  1  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  1  1  0 0  1  0  0  0  0 0 0  0 0  0  0 0 0 0  0 0 0
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