Acronym ... Name xfofxxfoFxfxo3ooxxoFxFoxxoo3oxfxFofxxfofx&xt (F=ff=x+f) ` ©` Confer related CRFs: pretasto

If the equatorial vertex layer f3x3f would be replaced by 2 layers F3x3o and o3x3F, the thawroes get lost. And further 12 equatorial bilbiroes come in. Moreover the polychoron then gets full hex-symmetry! This is how pretasto is related to this polychoron.

Incidence matrix according to Dynkin symbol

```
xfofxxfoFxfxo3ooxxoFxFoxxoo3oxfxFofxxfofx&#xt   → height(1,2) = height(12,13) = sqrt[3+sqrt(5)]/4 = 0.572061
(F=ff=x+f)                                        height(2,3) = height(3,4) = height(4,5) = height(6,7) = height(7,8) = height(9,10) = height(10,11) = height(11,12) = 1/sqrt(8) = 0.353553
height(5,6) = height(8,9) = sqrt[3-sqrt(5)]/4 = 0.218508
(tet || pseudo (f,x)-co || inv. pseudo (f,x)-tut || pseudo (f,x,x)-toe || pseudo (x,F)-co || pseudo (x,F)-tut || pseudo (f,x,f)-toe || inv. pseudo (x,F)-tut || pseudo (F,x)-co || pseudo (x,x,f)-toe || pseudo (f,x)-tut || pseudo (x,f)-co || dual tet)

o............3o............3o............     & | 8  *  *  *  *  *  * |  3  3  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 | 3  6  3 0  0  0  0  0 0  0  0  0  0 0  0  0  0  0  0 0  0  0  0  0 | 1 3  3 1 0  0 0  0  0 0 0 tet lay
.o...........3.o...........3.o...........     & | * 24  *  *  *  *  * |  0  1  2  2  2  0  0  0  0  0  0  0  0  0  0  0  0  0  0 | 0  2  2 1  1  1  2  2 0  0  0  0  0 0  0  0  0  0  0 0  0  0  0  0 | 0 1  2 1 1  1 0  0  0 0 0 next tet base lay
..o..........3..o..........3..o..........     & | *  * 24  *  *  *  * |  0  0  0  2  0  2  2  2  0  0  0  0  0  0  0  0  0  0  0 | 0  1  0 0  2  0  0  2 1  1  2  2  1 0  0  0  0  0  0 0  0  0  0  0 | 0 1  1 0 0  2 1  1  0 0 0 teddi top lay
...o.........3...o.........3...o.........     & | *  *  * 48  *  *  * |  0  0  0  0  1  0  1  0  1  1  1  1  1  0  0  0  0  0  0 | 0  0  0 0  0  1  1  1 0  0  0  1  1 1  1  1  1  1  1 0  0  0  0  0 | 0 0  1 0 1  1 0  1  1 1 0 tricu base lay
....o........3....o........3....o........     & | *  *  *  * 24  *  * |  0  0  0  0  0  0  0  2  0  0  2  0  0  2  2  0  0  0  0 | 0  0  0 0  0  0  0  0 0  2  1  2  0 0  1  0  0  2  0 1  2  1  0  0 | 0 0  0 0 0  1 1  2  1 1 0 (cyan) 3ap base lay
.....o.......3.....o.......3.....o.......     & | *  *  *  *  * 24  * |  0  0  0  0  0  0  0  0  0  0  0  2  0  0  0  1  2  2  0 | 0  0  0 0  0  0  0  0 0  0  0  0  2 0  0  1  0  0  2 0  1  0  3  2 | 0 0  1 0 0  0 0  3  0 1 1 opp. bilbiro end lay / axial tet lay
......o......3......o......3......o......       | *  *  *  *  *  * 24 |  0  0  0  0  0  0  0  0  0  0  0  0  2  0  2  0  2  0  1 | 0  0  0 0  0  0  0  0 0  0  0  0  0 0  0  0  2  2  2 0  2  2  0  1 | 0 0  0 0 0  0 0  2  2 1 0 one of squippy's base sides: oct type edges of equatorial lay
------------------------------------------------+---------------------+----------------------------------------------------------+--------------------------------------------------------------------+--------------------------
x............ ............. .............     & | 2  0  0  0  0  0  0 | 12  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  * | 2  2  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 0 0  0 0  0  0 0 0
oo...........3oo...........3oo...........&#x  & | 1  1  0  0  0  0  0 |  * 24  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  * | 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 1  2 1 0  0 0  0  0 0 0
............. ............. .x...........     & | 0  2  0  0  0  0  0 |  *  * 24  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  * | 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 0  1 1 1  0 0  0  0 0 0
.oo..........3.oo..........3.oo..........&#x  & | 0  1  1  0  0  0  0 |  *  *  * 48  *  *  *  *  *  *  *  *  *  *  *  *  *  *  * | 0  1  0 0  1  0  0  1 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
.o.o.........3.o.o.........3.o.o.........&#x  & | 0  1  0  1  0  0  0 |  *  *  *  * 48  *  *  *  *  *  *  *  *  *  *  *  *  *  * | 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  1 0 1  1 0  0  0 0 0
............. ..x.......... .............     & | 0  0  2  0  0  0  0 |  *  *  *  *  * 24  *  *  *  *  *  *  *  *  *  *  *  *  * | 0  0  0 0  1  0  0  0 1  0  1  0  0 0  0  0  0  0  0 0  0  0  0  0 | 0 1  0 0 0  1 1  0  0 0 0
..oo.........3..oo.........3..oo.........&#x  & | 0  0  1  1  0  0  0 |  *  *  *  *  *  * 48  *  *  *  *  *  *  *  *  *  *  *  * | 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  1 0 0  1 0  1  0 0 0
..o.o........3..o.o........3..o.o........&#x  & | 0  0  1  0  1  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 0  1 1  1  0 0 0
............. ...x......... .............     & | 0  0  0  2  0  0  0 |  *  *  *  *  *  *  *  * 24  *  *  *  *  *  *  *  *  *  * | 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 1  1 0  0  1 1 0
............. ............. ...x.........     & | 0  0  0  2  0  0  0 |  *  *  *  *  *  *  *  *  * 24  *  *  *  *  *  *  *  *  * | 0  0  0 0  0  0  1  0 0  0  0  0  0 1  0  1  0  0  0 0  0  0  0  0 | 0 0  1 0 1  0 0  0  0 1 0
...oo........3...oo........3...oo........&#x  & | 0  0  0  1  1  0  0 |  *  *  *  *  *  *  *  *  *  * 48  *  *  *  *  *  *  *  * | 0  0  0 0  0  0  0  0 0  0  0  1  0 0  1  0  0  1  0 0  0  0  0  0 | 0 0  0 0 0  1 0  1  1 0 0
...o.o.......3...o.o.......3...o.o.......&#x  & | 0  0  0  1  0  1  0 |  *  *  *  *  *  *  *  *  *  *  * 48  *  *  *  *  *  *  * | 0  0  0 0  0  0  0  0 0  0  0  0  1 0  0  1  0  0  1 0  0  0  0  0 | 0 0  1 0 0  0 0  1  0 1 0
...o..o......3...o..o......3...o..o......&#x  & | 0  0  0  1  0  0  1 |  *  *  *  *  *  *  *  *  *  *  *  * 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 0  1  1 1 0
....x........ ............. .............     & | 0  0  0  0  2  0  0 |  *  *  *  *  *  *  *  *  *  *  *  *  * 24  *  *  *  *  * | 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 0 0  0 1  1  0 1 0
....o.o......3....o.o......3....o.o......&#x  & | 0  0  0  0  1  0  1 |  *  *  *  *  *  *  *  *  *  *  *  *  *  * 48  *  *  *  * | 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  1  1 1 0
.....x....... ............. .............     & | 0  0  0  0  0  2  0 |  *  *  *  *  *  *  *  *  *  *  *  *  *  *  * 12  *  *  * | 0  0  0 0  0  0  0  0 0  0  0  0  2 0  0  0  0  0  0 0  0  0  2  0 | 0 0  1 0 0  0 0  2  0 0 1
.....oo......3.....oo......3.....oo......&#x  & | 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 0  0 0  2  0 1 0
.....o.o.....3.....o.o.....3.....o.o.....&#x    | 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  0  0 0  0  0  2  1 | 0 0  0 0 0  0 0  2  0 0 1
............. ......x...... .............       | 0  0  0  0  0  0  2 |  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  * 12 | 0  0  0 0  0  0  0  0 0  0  0  0  0 0  0  0  2  0  0 0  0  2  0  0 | 0 0  0 0 0  0 0  0  2 2 0
------------------------------------------------+---------------------+----------------------------------------------------------+--------------------------------------------------------------------+--------------------------
x............3o............ .............     & | 3  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 1  0 0 0  0 0  0  0 0 0
xfo.......... ............. .............&#xt & | 2  2  1  0  0  0  0 |  1  2  0  2  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 | * 24  * *  *  *  *  * *  *  *  *  * *  *  *  *  *  * *  *  *  *  * | 0 1  1 0 0  0 0  0  0 0 0
............. ............. ox...........&#x  & | 1  2  0  0  0  0  0 |  0  2  1  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 | *  * 24 *  *  *  *  * *  *  *  *  * *  *  *  *  *  * *  *  *  *  * | 0 0  1 1 0  0 0  0  0 0 0
............. .o...........3.x...........     & | 0  3  0  0  0  0  0 |  0  0  3  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 | *  *  * 8  *  *  *  * *  *  *  *  * *  *  *  *  *  * *  *  *  *  * | 0 0  0 1 1  0 0  0  0 0 0
............. .ox.......... .............&#x  & | 0  1  2  0  0  0  0 |  0  0  0  2  0  1  0  0  0  0  0  0  0  0  0  0  0  0  0 | *  *  * * 24  *  *  * *  *  *  *  * *  *  *  *  *  * *  *  *  *  * | 0 1  0 0 0  1 0  0  0 0 0
............. .o.x......... .............&#x  & | 0  1  0  2  0  0  0 |  0  0  0  0  2  0  0  0  1  0  0  0  0  0  0  0  0  0  0 | *  *  * *  * 24  *  * *  *  *  *  * *  *  *  *  *  * *  *  *  *  * | 0 0  0 0 1  1 0  0  0 0 0
............. ............. .x.x.........&#x  & | 0  2  0  2  0  0  0 |  0  0  1  0  2  0  0  0  0  1  0  0  0  0  0  0  0  0  0 | *  *  * *  *  * 24  * *  *  *  *  * *  *  *  *  *  * *  *  *  *  * | 0 0  1 0 1  0 0  0  0 0 0
.ooo.........3.ooo.........3.ooo.........&#x  & | 0  1  1  1  0  0  0 |  0  0  0  1  1  0  1  0  0  0  0  0  0  0  0  0  0  0  0 | *  *  * *  *  *  * 48 *  *  *  *  * *  *  *  *  *  * *  *  *  *  * | 0 0  1 0 0  1 0  0  0 0 0
..o..........3..x.......... .............     & | 0  0  3  0  0  0  0 |  0  0  0  0  0  3  0  0  0  0  0  0  0  0  0  0  0  0  0 | *  *  * *  *  *  *  * 8  *  *  *  * *  *  *  *  *  * *  *  *  *  * | 0 1  0 0 0  0 1  0  0 0 0
..o.x........ ............. .............&#x  & | 0  0  1  0  2  0  0 |  0  0  0  0  0  0  0  2  0  0  0  0  0  1  0  0  0  0  0 | *  *  * *  *  *  *  * * 24  *  *  * *  *  *  *  *  * *  *  *  *  * | 0 0  0 0 0  0 1  1  0 0 0
............. ..x.o........ .............&#x  & | 0  0  2  0  1  0  0 |  0  0  0  0  0  1  0  2  0  0  0  0  0  0  0  0  0  0  0 | *  *  * *  *  *  *  * *  * 24  *  * *  *  *  *  *  * *  *  *  *  * | 0 0  0 0 0  1 1  0  0 0 0
..ooo........3..ooo........3..ooo........&#x  & | 0  0  1  1  1  0  0 |  0  0  0  0  0  0  1  1  0  0  1  0  0  0  0  0  0  0  0 | *  *  * *  *  *  *  * *  *  * 48  * *  *  *  *  *  * *  *  *  *  * | 0 0  0 0 0  1 0  1  0 0 0
..of.x....... ............. .............&#xt & | 0  0  1  2  0  2  0 |  0  0  0  0  0  0  2  0  0  0  0  2  0  0  0  1  0  0  0 | *  *  * *  *  *  *  * *  *  *  * 24 *  *  *  *  *  * *  *  *  *  * | 0 0  1 0 0  0 0  1  0 0 0
............. ...x.........3...x.........     & | 0  0  0  6  0  0  0 |  0  0  0  0  0  0  0  0  3  3  0  0  0  0  0  0  0  0  0 | *  *  * *  *  *  *  * *  *  *  *  * 8  *  *  *  *  * *  *  *  *  * | 0 0  0 0 1  0 0  0  0 1 0
............. ...xo........ .............&#x  & | 0  0  0  2  1  0  0 |  0  0  0  0  0  0  0  0  1  0  2  0  0  0  0  0  0  0  0 | *  *  * *  *  *  *  * *  *  *  *  * * 24  *  *  *  * *  *  *  *  * | 0 0  0 0 0  1 0  0  1 0 0
............. ............. ...x.o.......&#x  & | 0  0  0  2  0  1  0 |  0  0  0  0  0  0  0  0  0  1  0  2  0  0  0  0  0  0  0 | *  *  * *  *  *  *  * *  *  *  *  * *  * 24  *  *  * *  *  *  *  * | 0 0  1 0 0  0 0  0  0 1 0
............. ...x..x...... .............&#x  & | 0  0  0  2  0  0  2 |  0  0  0  0  0  0  0  0  1  0  0  0  2  0  0  0  0  0  1 | *  *  * *  *  *  *  * *  *  *  *  * *  *  * 24  *  * *  *  *  *  * | 0 0  0 0 0  0 0  0  1 1 0
...oo.o......3...oo.o......3...oo.o......&#x  & | 0  0  0  1  1  0  1 |  0  0  0  0  0  0  0  0  0  0  1  0  1  0  1  0  0  0  0 | *  *  * *  *  *  *  * *  *  *  *  * *  *  *  * 48  * *  *  *  *  * | 0 0  0 0 0  0 0  1  1 0 0
...o.oo......3...o.oo......3...o.oo......&#x  & | 0  0  0  1  0  1  1 |  0  0  0  0  0  0  0  0  0  0  0  1  1  0  0  0  1  0  0 | *  *  * *  *  *  *  * *  *  *  *  * *  *  *  *  * 48 *  *  *  *  * | 0 0  0 0 0  0 0  1  0 1 0
....x........3....o........ .............     & | 0  0  0  0  3  0  0 |  0  0  0  0  0  0  0  0  0  0  0  0  0  3  0  0  0  0  0 | *  *  * *  *  *  *  * *  *  *  *  * *  *  *  *  *  * 8  *  *  *  * | 0 0  0 0 0  0 1  0  0 1 0
....x.fo..... ............. .............&#xt & | 0  0  0  0  2  1  2 |  0  0  0  0  0  0  0  0  0  0  0  0  0  1  2  0  2  0  0 | *  *  * *  *  *  *  * *  *  *  *  * *  *  *  *  *  * * 24  *  *  * | 0 0  0 0 0  0 0  1  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  0  2  0  0  0  1 | *  *  * *  *  *  *  * *  *  *  *  * *  *  *  *  *  * *  * 24  *  * | 0 0  0 0 0  0 0  0  1 1 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  0  1  0  2  0 | *  *  * *  *  *  *  * *  *  *  *  * *  *  *  *  *  * *  *  * 24  * | 0 0  0 0 0  0 0  1  0 0 1
.....ooo.....3.....ooo.....3.....ooo.....&#x    | 0  0  0  0  0  2  1 |  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  2  1  0 | *  *  * *  *  *  *  * *  *  *  *  * *  *  *  *  *  * *  *  *  * 24 | 0 0  0 0 0  0 0  2  0 0 0
------------------------------------------------+---------------------+----------------------------------------------------------+--------------------------------------------------------------------+--------------------------
x............3o............3o............     & ♦ 4  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 | 4  0  0 0  0  0  0  0 0  0  0  0  0 0  0  0  0  0  0 0  0  0  0  0 | 2 *  * * *  * *  *  * * *
xfo..........3oox.......... .............&#xt & ♦ 3  3  3  0  0  0  0 |  3  3  0  6  0  3  0  0  0  0  0  0  0  0  0  0  0  0  0 | 1  3  0 0  3  0  0  0 1  0  0  0  0 0  0  0  0  0  0 0  0  0  0  0 | * 8  * * *  * *  *  * * *
xfof.x....... ............. oxfx.o.......&#xt & ♦ 2  4  2  4  0  2  0 |  1  4  2  4  4  0  4  0  0  2  0  4  0  0  0  1  0  0  0 | 0  2  2 0  0  0  2  4 0  0  0  0  2 0  0  2  0  0  0 0  0  0  0  0 | * * 12 * *  * *  *  * * *
............. oo...........3ox...........&#x  & ♦ 1  3  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  3 1  0  0  0  0 0  0  0  0  0 0  0  0  0  0  0 0  0  0  0  0 | * *  * 8 *  * *  *  * * *
............. .o.x.........3.x.x.........&#x  & ♦ 0  3  0  6  0  0  0 |  0  0  3  0  6  0  0  0  3  3  0  0  0  0  0  0  0  0  0 | 0  0  0 1  0  3  3  0 0  0  0  0  0 1  0  0  0  0  0 0  0  0  0  0 | * *  * * 8  * *  *  * * *
............. .oxxo........ .............&#xr & ♦ 0  1  2  2  1  0  0 |  0  0  0  2  2  1  2  2  1  0  2  0  0  0  0  0  0  0  0 | 0  0  0 0  1  1  0  2 0  0  1  2  0 0  1  0  0  0  0 0  0  0  0  0 | * *  * * * 24 *  *  * * *
..o.x........3..x.o........ .............&#x  & ♦ 0  0  3  0  3  0  0 |  0  0  0  0  0  3  0  6  0  0  0  0  0  3  0  0  0  0  0 | 0  0  0 0  0  0  0  0 1  3  3  0  0 0  0  0  0  0  0 1  0  0  0  0 | * *  * * *  * 8  *  * * *
..ofxxfo..... ............. .............&#xr & ♦ 0  0  1  2  2  3  2 |  0  0  0  0  0  0  2  2  0  0  2  2  2  1  2  1  4  2  0 | 0  0  0 0  0  0  0  0 0  1  0  2  1 0  0  0  0  2  2 0  1  0  1  2 | * *  * * *  * * 24  * * *
............. ...xo.x...... .............&#xr & ♦ 0  0  0  2  1  0  2 |  0  0  0  0  0  0  0  0  1  0  2  0  2  0  2  0  0  0  1 | 0  0  0 0  0  0  0  0 0  0  0  0  0 0  1  0  1  2  0 0  0  1  0  0 | * *  * * *  * *  * 24 * *
............. ...x.Fx.o....3...x.of.x....&#xt & ♦ 0  0  0  6  3  3  3 |  0  0  0  0  0  0  0  0  3  3  0  6  6  3  6  0  6  0  3 | 0  0  0 0  0  0  0  0 0  0  0  0  0 1  0  3  3  0  6 1  3  3  0  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  0  2  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  4  0 | * *  * * *  * *  *  * * 6
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