| Acronym | ... |
| Name | xooFxxFfooFoofo3xxFooFxxxFooFxx3ofooFoofFxxFoox&#xt |
| Face vector | 164, 588, 568, 144 |
| 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 fourth layer will be transformed according to: f3o3x → f3x3(-x) → F3(-x)3o, the fifth layer will be transformed according to: o3x3f → x3(-x)3F, 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 xooFxxFfooFoofo 3 oof(-x)(-x)fooof(-x)(-x)foo 3 ofooFoofFxxFoox &#xt. Then a (uniformly to all layers) applied Stott expansion wrt. the second node produces this polychoron.
There is an other axial EKF which re-uses one half of this polychoron, but then continues differently, still having the same vertex layers throughout: ooofxxFfooFoofo3oxFxoFxxxFooFxx3xfoxFoofFxxFoox&#xt.
Incidence matrix according to Dynkin symbol
xooFxxFfooFoofo3xxFooFxxxFooFxx3ofooFoofFxxFoox&#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
(tut || pseudo inv (f,x)-tut || pseudo F-oct || pseudo F-tet || pseudo (x,F)-co || pseudo (x,F)-tut || pseudo (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)
o..............3o..............3o.............. & | 24 * * * * * * * | 1 2 2 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 2 1 2 2 1 2 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 1 2 1 2 2 0 0 0 0 0 0
.o.............3.o.............3.o............. & | * 24 * * * * * * | 0 0 2 0 0 2 1 2 0 0 0 0 0 0 0 0 0 0 0 0 | 0 0 1 2 0 0 2 0 1 1 2 2 0 0 0 0 0 0 0 0 0 0 0 0 | 0 1 0 1 2 1 1 0 0 0 0
..o............3..o............3..o............ & | * * 12 * * * * * | 0 0 0 2 0 0 2 0 2 0 0 0 0 0 0 0 0 0 0 0 | 0 0 0 0 1 0 4 2 0 0 0 4 1 0 0 0 0 0 0 0 0 0 0 0 | 0 0 0 2 4 0 2 0 0 0 0
...o...........3...o...........3...o........... & | * * * 8 * * * * ♦ 0 0 0 0 3 0 0 0 0 3 0 0 0 0 0 0 0 0 0 0 | 0 0 0 0 0 3 0 3 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 0 | 0 0 1 0 3 0 0 1 0 0 0
....o..........3....o..........3....o.......... & | * * * * 24 * * * | 0 0 0 0 0 0 0 2 0 0 2 2 2 0 0 0 0 0 0 0 | 0 0 0 0 0 0 0 0 0 2 1 2 0 0 1 1 2 1 2 0 0 0 0 0 | 0 0 0 0 1 1 2 0 1 1 0
.....o.........3.....o.........3.....o......... & | * * * * * 24 * * | 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 2 2 0 0 0 | 0 0 0 0 0 0 0 1 0 0 0 2 1 0 0 0 0 0 0 3 2 2 0 0 | 0 0 0 0 2 0 3 0 0 0 1
......o........3......o........3......o........ & | * * * * * * 24 * | 0 0 0 0 0 0 0 0 0 1 0 0 2 0 1 0 0 2 2 0 | 0 0 0 0 0 0 0 1 0 0 0 0 0 2 0 0 1 2 2 0 2 0 1 2 | 0 0 0 0 2 0 1 1 2 1 0
.......o.......3.......o.......3.......o....... | * * * * * * * 24 | 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 2 0 0 2 1 | 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 2 0 0 2 0 2 1 0 2 | 0 0 0 0 2 0 2 0 2 0 0
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x.............. ............... ............... & | 2 0 0 0 0 0 0 0 | 12 * * * * * * * * * * * * * * * * * * * | 2 0 2 0 1 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
............... x.............. ............... & | 2 0 0 0 0 0 0 0 | * 24 * * * * * * * * * * * * * * * * * * | 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 1 0 1 0 0 0 0 0 0
oo.............3oo.............3oo.............&#x & | 1 1 0 0 0 0 0 0 | * * 48 * * * * * * * * * * * * * * * * * | 0 0 1 1 0 0 1 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
o.o............3o.o............3o.o............&#x & | 1 0 1 0 0 0 0 0 | * * * 24 * * * * * * * * * * * * * * * * | 0 0 0 0 1 0 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 0 0 0 2 2 0 0 0 0 0 0
o..o...........3o..o...........3o..o...........&#x & | 1 0 0 1 0 0 0 0 | * * * * 24 * * * * * * * * * * * * * * * | 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 0 1 0 2 0 0 0 0 0 0
............... .x............. ............... & | 0 2 0 0 0 0 0 0 | * * * * * 24 * * * * * * * * * * * * * * | 0 0 0 1 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | 0 1 0 0 1 1 0 0 0 0 0
.oo............3.oo............3.oo............&#x & | 0 1 1 0 0 0 0 0 | * * * * * * 24 * * * * * * * * * * * * * | 0 0 0 0 0 0 2 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 | 0 0 0 1 2 0 1 0 0 0 0
.o..o..........3.o..o..........3.o..o..........&#x & | 0 1 0 0 1 0 0 0 | * * * * * * * 48 * * * * * * * * * * * * | 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 1 1 1 0 0 0 0
..o..o.........3..o..o.........3..o..o.........&#x & | 0 0 1 0 0 1 0 0 | * * * * * * * * 24 * * * * * * * * * * * | 0 0 0 0 0 0 0 1 0 0 0 2 1 0 0 0 0 0 0 0 0 0 0 0 | 0 0 0 0 2 0 2 0 0 0 0
...o..o........3...o..o........3...o..o........&#x & | 0 0 0 1 0 0 1 0 | * * * * * * * * * 24 * * * * * * * * * * | 0 0 0 0 0 0 0 1 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 | 0 0 0 0 2 0 0 1 0 0 0
....x.......... ............... ............... & | 0 0 0 0 2 0 0 0 | * * * * * * * * * * 24 * * * * * * * * * | 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 1 0 0 0 0 0 0 0 | 0 0 0 0 0 1 1 0 0 1 0
....o..o.......3....o..o.......3....o..o.......&#x & | 0 0 0 0 1 0 0 1 | * * * * * * * * * * * 48 * * * * * * * * | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 1 0 0 0 0 0 | 0 0 0 0 1 0 1 0 1 0 0
....o...o......3....o...o......3....o...o......&#x & | 0 0 0 0 1 0 1 0 | * * * * * * * * * * * * 48 * * * * * * * | 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 1 0 1 1 0
.....x......... ............... ............... & | 0 0 0 0 0 2 0 0 | * * * * * * * * * * * * * 12 * * * * * * | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 2 0 0 0 0 | 0 0 0 0 0 0 2 0 0 0 1
.....oo........3.....oo........3.....oo........&#x & | 0 0 0 0 0 1 1 0 | * * * * * * * * * * * * * * 24 * * * * * | 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 2 0 0 0 | 0 0 0 0 2 0 1 1 0 0 0
.....o.o.......3.....o.o.......3.....o.o.......&#x & | 0 0 0 0 0 1 0 1 | * * * * * * * * * * * * * * * 48 * * * * | 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 0 0 1 0 2 0 0 0 0
.....o...o.....3.....o...o.....3.....o...o.....&#x | 0 0 0 0 0 2 0 0 | * * * * * * * * * * * * * * * * 24 * * * | 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 2 0 0 0 1
............... ......x........ ............... & | 0 0 0 0 0 0 2 0 | * * * * * * * * * * * * * * * * * 24 * * | 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 1 0 0 0 1 1 0
......oo.......3......oo.......3......oo.......&#x & | 0 0 0 0 0 0 1 1 | * * * * * * * * * * * * * * * * * * 48 * | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 1 | 0 0 0 0 1 0 1 0 1 0 0
............... .......x....... ............... | 0 0 0 0 0 0 0 2 | * * * * * * * * * * * * * * * * * * * 12 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 2 | 0 0 0 0 2 0 0 0 2 0 0
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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 0 | 8 * * * * * * * * * * * * * * * * * * * * * * * | 1 1 0 0 0 0 0 0 0 0 0
............... x..............3o.............. & | 3 0 0 0 0 0 0 0 | 0 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | * 8 * * * * * * * * * * * * * * * * * * * * * * | 1 0 1 0 0 0 0 0 0 0 0
xo............. ............... ...............&#x & | 2 1 0 0 0 0 0 0 | 1 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | * * 24 * * * * * * * * * * * * * * * * * * * * * | 0 1 0 1 0 0 0 0 0 0 0
............... xx............. ...............&#x & | 2 2 0 0 0 0 0 0 | 0 1 2 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | * * * 24 * * * * * * * * * * * * * * * * * * * * | 0 1 0 0 1 0 0 0 0 0 0
x.o............ ............... ...............&#x & | 2 0 1 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 | * * * * 12 * * * * * * * * * * * * * * * * * * * | 0 0 0 2 0 0 0 0 0 0 0
............... x..o........... ...............&#x & | 2 0 0 1 0 0 0 0 | 0 1 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | * * * * * 24 * * * * * * * * * * * * * * * * * * | 0 0 1 0 1 0 0 0 0 0 0
ooo............3ooo............3ooo............&#x & | 1 1 1 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 | * * * * * * 48 * * * * * * * * * * * * * * * * * | 0 0 0 1 1 0 0 0 0 0 0
o.oo.oo........3o.oo.oo........3o.oo.oo........&#xr & | 1 0 1 1 0 1 1 0 | 0 0 0 1 1 0 0 0 1 1 0 0 0 0 1 0 0 0 0 0 | * * * * * * * 24 * * * * * * * * * * * * * * * * | 0 0 0 0 2 0 0 0 0 0 0 cycle: (ACFGD)
.o.............3.x............. ............... & | 0 3 0 0 0 0 0 0 | 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | * * * * * * * * 8 * * * * * * * * * * * * * * * | 0 1 0 0 0 1 0 0 0 0 0
.o..x.......... ............... ...............&#x & | 0 1 0 0 2 0 0 0 | 0 0 0 0 0 0 0 2 0 0 1 0 0 0 0 0 0 0 0 0 | * * * * * * * * * 24 * * * * * * * * * * * * * * | 0 0 0 0 0 1 1 0 0 0 0
............... .x..o.......... ...............&#x & | 0 2 0 0 1 0 0 0 | 0 0 0 0 0 1 0 2 0 0 0 0 0 0 0 0 0 0 0 0 | * * * * * * * * * * 24 * * * * * * * * * * * * * | 0 0 0 0 1 1 0 0 0 0 0
.oo.oo.o.......3.oo.oo.o.......3.oo.oo.o.......&#xr & | 0 1 1 0 1 1 0 1 | 0 0 0 0 0 0 1 1 1 0 0 1 0 0 0 1 0 0 0 0 | * * * * * * * * * * * 48 * * * * * * * * * * * * | 0 0 0 0 1 0 1 0 0 0 0 cycle: (BCFHE)
..o..x......... ............... ...............&#x & | 0 0 1 0 0 2 0 0 | 0 0 0 0 0 0 0 0 2 0 0 0 0 1 0 0 0 0 0 0 | * * * * * * * * * * * * 12 * * * * * * * * * * * | 0 0 0 0 0 0 2 0 0 0 0
............... ...o..x........ ...............&#x & | 0 0 0 1 0 0 2 0 | 0 0 0 0 0 0 0 0 0 2 0 0 0 0 1 0 0 0 0 0 | * * * * * * * * * * * * * 24 * * * * * * * * * * | 0 0 0 0 1 0 0 1 0 0 0
....x..........3....o.......... ............... & | 0 0 0 0 3 0 0 0 | 0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 | * * * * * * * * * * * * * * 8 * * * * * * * * * | 0 0 0 0 0 1 0 0 0 1 0
............... ....o..x....... ...............&#x & | 0 0 0 0 1 0 0 2 | 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 1 | * * * * * * * * * * * * * * * 24 * * * * * * * * | 0 0 0 0 1 0 0 0 1 0 0
....x...o...... ............... ...............&#x & | 0 0 0 0 2 0 1 0 | 0 0 0 0 0 0 0 0 0 0 1 0 2 0 0 0 0 0 0 0 | * * * * * * * * * * * * * * * * 24 * * * * * * * | 0 0 0 0 0 0 1 0 0 1 0
............... ....o...x...... ...............&#x & | 0 0 0 0 1 0 2 0 | 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 1 0 0 | * * * * * * * * * * * * * * * * * 24 * * * * * * | 0 0 0 0 0 0 0 0 1 1 0
....o..oo......3....o..oo......3....o..oo......&#x & | 0 0 0 0 1 0 1 1 | 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 1 0 | * * * * * * * * * * * * * * * * * * 48 * * * * * | 0 0 0 0 0 0 1 0 1 0 0
.....x...o..... ............... ...............&#x & | 0 0 0 0 0 3 0 0 | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 2 0 0 0 | * * * * * * * * * * * * * * * * * * * 24 * * * * | 0 0 0 0 0 0 1 0 0 0 1
.....ooo.......3.....ooo.......3.....ooo.......&#x & | 0 0 0 0 0 1 1 1 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 0 | * * * * * * * * * * * * * * * * * * * * 48 * * * | 0 0 0 0 1 0 1 0 0 0 0
.....o.o.o.....3.....o.o.o.....3.....o.o.o.....&#x | 0 0 0 0 0 2 0 1 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 1 0 0 0 | * * * * * * * * * * * * * * * * * * * * * 24 * * | 0 0 0 0 0 0 2 0 0 0 0
............... ......x........3......o........ & | 0 0 0 0 0 0 3 0 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0 | * * * * * * * * * * * * * * * * * * * * * * 8 * | 0 0 0 0 0 0 0 1 0 1 0
............... ......xx....... ...............&#x & | 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 1 2 1 | * * * * * * * * * * * * * * * * * * * * * * * 24 | 0 0 0 0 1 0 0 0 1 0 0
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x..............3x..............3o.............. & ♦ 12 0 0 0 0 0 0 0 | 6 12 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 4 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 2 * * * * * * * * * *
xo.............3xx............. ...............&#x & ♦ 6 3 0 0 0 0 0 0 | 3 3 6 0 0 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 1 0 3 3 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | * 8 * * * * * * * * *
............... x..o...........3o..o...........&#x & ♦ 3 0 0 1 0 0 0 0 | 0 3 0 0 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 0 1 0 0 0 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | * * 8 * * * * * * * *
xoo............ ............... ...............&#x & ♦ 2 1 1 0 0 0 0 0 | 1 0 2 2 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | 0 0 1 0 1 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | * * * 24 * * * * * * *
............... xxFooFxx....... ...............&#xt & ♦ 2 2 2 1 1 2 2 2 | 0 1 2 2 2 1 2 2 2 2 0 2 0 0 2 2 0 1 2 1 | 0 0 0 1 0 1 2 2 0 0 1 2 0 1 0 1 0 0 0 0 2 0 0 1 | * * * * 24 * * * * * *
.o..x..........3.x..o.......... ...............&#x & ♦ 0 3 0 0 3 0 0 0 | 0 0 0 0 0 3 0 6 0 0 3 0 0 0 0 0 0 0 0 0 | 0 0 0 0 0 0 0 0 1 3 3 0 0 0 1 0 0 0 0 0 0 0 0 0 | * * * * * 8 * * * * *
.oo.xx.foo..... ............... ...............&#xt & ♦ 0 1 1 0 2 3 1 2 | 0 0 0 0 0 0 1 2 2 0 1 2 2 1 1 4 2 0 2 0 | 0 0 0 0 0 0 0 0 0 1 0 2 1 0 0 0 1 0 2 1 2 2 0 0 | * * * * * * 24 * * * *
............... ...o..x........3...o..o........&#x & ♦ 0 0 0 1 0 0 3 0 | 0 0 0 0 0 0 0 0 0 3 0 0 0 0 3 0 0 0 0 0 | 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 1 0 | * * * * * * * 8 * * *
............... ....o..xx...... ...............&#x & ♦ 0 0 0 0 1 0 2 2 | 0 0 0 0 0 0 0 0 0 0 0 2 2 0 0 0 0 1 2 1 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 2 0 0 0 0 1 | * * * * * * * * 24 * *
....x...o......3....o...x...... ...............&#x & ♦ 0 0 0 0 3 0 3 0 | 0 0 0 0 0 0 0 0 0 0 3 0 6 0 0 0 0 3 0 0 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 3 3 0 0 0 0 1 0 | * * * * * * * * * 8 *
.....x...o..... ............... .....o...x.....&#x ♦ 0 0 0 0 0 4 0 0 | 0 0 0 0 0 0 0 0 0 0 0 0 0 2 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 4 0 0 0 0 | * * * * * * * * * * 6
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