Acronym ... Name FAxoAFxoxx3FxAAoxFxox oxofofxFof3ooxofxfoFf&#zx Confer uniform relative: ex   general polytopal classes: expanded kaleido-facetings

The relation to ex runs as follows: ex in triangular duoprismatic subsymmetry can be given as fFoxffooxo 3 foFfxofxoo 2 oxofofxFof 3 ooxofxfoFf &#zx (F = ff = f+x). That will be transformed finally into fFo(-x)Ffo(-x)oo 3 foFF(-x)ofo(-x)o 2 oxofofxFof 3 ooxofxfoFf &#zx. Then a Stott expansion wrt. the first and second nodes produces this polychoron (A = F+x = f+2x).

Incidence matrix according to Dynkin symbol

```FAxoAFxoxx3FxAAoxFxox oxofofxFof3ooxofxfoFf&#zx   → all heights = 0 – but not all lacings exist

o.........3o......... o.........3o.........       | 6  *  *  *  *  * |  6  0  0  0  0  0  0  0  0  0  0  0  0 |  6  6  0  0  0  0  0  0  0  0  0  0  0  0  0 0  0  0 0 |  2  6 0  0  0  0  0  0  0
.o........3.o........ .o........3.o........     & | * 36  *  *  *  * |  1  1  2  2  2  0  0  0  0  0  0  0  0 |  2  2  2  1  2  2  2  1  2  0  0  0  0  0  0 0  0  0 0 |  1  3 1  2  1  2  0  0  0
...o......3...o...... ...o......3...o......     & | *  * 18  *  *  * |  0  0  0  4  0  4  0  0  0  0  0  0  0 |  0  0  0  0  2  2  0  0  4  2  2  0  0  0  0 0  0  0 0 |  0  2 0  1  0  2  1  0  0
.....o....3.....o.... .....o....3.....o....     & | *  *  * 72  *  * |  0  0  0  0  1  1  1  1  1  1  0  0  0 |  0  1  0  0  0  0  1  1  1  1  2  1  1  1  1 0  0  0 0 |  0  2 0  0  1  1  2  1  0
.......o..3.......o.. .......o..3.......o..     & | *  *  *  * 18  * |  0  0  0  0  0  0  0  0  0  0  2  4  0 |  0  0  0  0  0  0  0  0  0  0  0  0  0  2  0 1  2  4 0 |  0  0 0  0  0  0  1  2  2
.........o3.........o .........o3.........o       | *  *  *  *  * 36 |  0  0  0  0  0  0  0  0  0  2  0  2  2 |  0  0  0  0  0  0  0  0  0  0  0  0  2  2  1 0  2  2 1 |  0  0 0  0  0  0  2  2  2
--------------------------------------------------+------------------+----------------------------------------+--------------------------------------------------------+--------------------------
oo........3oo........ oo........3oo........&#x  & | 1  1  0  0  0  0 | 36  *  *  *  *  *  *  *  *  *  *  *  * |  2  2  0  0  0  0  0  0  0  0  0  0  0  0  0 0  0  0 0 |  1  3 0  0  0  0  0  0  0
.......... .x........ .......... ..........     & | 0  2  0  0  0  0 |  * 18  *  *  *  *  *  *  *  *  *  *  * |  0  0  2  0  2  0  2  0  0  0  0  0  0  0  0 0  0  0 0 |  0  0 1  2  1  2  0  0  0
.......... .......... .x........ ..........     & | 0  2  0  0  0  0 |  *  * 36  *  *  *  *  *  *  *  *  *  * |  1  0  1  1  0  1  0  0  0  0  0  0  0  0  0 0  0  0 0 |  1  1 1  1  0  0  0  0  0
.o..o.....3.o..o..... .o..o.....3.o..o.....&#x  & | 0  1  1  0  0  0 |  *  *  * 72  *  *  *  *  *  *  *  *  * |  0  0  0  0  1  1  0  0  1  0  0  0  0  0  0 0  0  0 0 |  0  1 0  1  0  1  0  0  0
.o...o....3.o...o.... .o...o....3.o...o....&#x  & | 0  1  0  1  0  0 |  *  *  *  * 72  *  *  *  *  *  *  *  * |  0  1  0  0  0  0  1  1  1  0  0  0  0  0  0 0  0  0 0 |  0  2 0  0  1  1  0  0  0
...o..o...3...o..o... ...o..o...3...o..o...&#x  & | 0  0  1  1  0  0 |  *  *  *  *  * 72  *  *  *  *  *  *  * |  0  1  0  0  0  0  0  0  1  1  1  0  0  0  0 0  0  0 0 |  0  1 0  0  0  1  1  0  0
.......... .....x.... .......... ..........     & | 0  0  0  2  0  0 |  *  *  *  *  *  * 36  *  *  *  *  *  * |  0  0  0  0  0  0  1  0  0  1  0  1  1  0  0 0  0  0 0 |  0  0 0  0  1  1  1  1  0
.......... .......... .......... .....x....     & | 0  0  0  2  0  0 |  *  *  *  *  *  *  * 36  *  *  *  *  * |  0  0  0  0  0  0  0  1  0  0  1  1  0  1  0 0  0  0 0 |  0  1 0  0  1  0  1  1  0
.....oo...3.....oo... .....oo...3.....oo...&#x    | 0  0  0  2  0  0 |  *  *  *  *  *  *  *  * 36  *  *  *  * |  0  1  0  0  0  0  0  0  0  0  2  0  0  0  1 0  0  0 0 |  0  2 0  0  0  0  2  0  0
.....o...o3.....o...o .....o...o3.....o...o&#x  & | 0  0  0  1  0  1 |  *  *  *  *  *  *  *  *  * 72  *  *  * |  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  2  1  0
.......... .......x.. .......... ..........     & | 0  0  0  0  2  0 |  *  *  *  *  *  *  *  *  *  * 18  *  * |  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 1  0  2 0 |  0  0 0  0  0  0  0  1  2
.......o.o3.......o.o .......o.o3.......o.o&#x  & | 0  0  0  0  1  1 |  *  *  *  *  *  *  *  *  *  *  * 72  * |  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  1  1  1
.........x .......... .......... ..........     & | 0  0  0  0  0  2 |  *  *  *  *  *  *  *  *  *  *  *  * 36 |  0  0  0  0  0  0  0  0  0  0  0  0  1  0  0 0  1  1 1 |  0  0 0  0  0  0  1  1  2
--------------------------------------------------+------------------+----------------------------------------+--------------------------------------------------------+--------------------------
.......... .......... ox........ ..........&#x  & | 1  2  0  0  0  0 |  2  0  1  0  0  0  0  0  0  0  0  0  0 | 36  *  *  *  *  *  *  *  *  *  *  *  *  *  * *  *  * * |  1  1 0  0  0  0  0  0  0
ooo..oo...3ooo..oo... ooo..oo...3ooo..oo...&#xr   | 1  2  0  2  0  0 |  2  0  0  0  2  0  0  0  1  0  0  0  0 |  * 36  *  *  *  *  *  *  *  *  *  *  *  *  * *  *  * * |  0  2 0  0  0  0  0  0  0 cycle: (ABFGC)
.......... .x........ .x........ ..........     & | 0  4  0  0  0  0 |  0  2  2  0  0  0  0  0  0  0  0  0  0 |  *  * 18  *  *  *  *  *  *  *  *  *  *  *  * *  *  * * |  0  0 1  1  0  0  0  0  0
.......... .......... .x........3.o........     & | 0  3  0  0  0  0 |  0  0  3  0  0  0  0  0  0  0  0  0  0 |  *  *  * 12  *  *  *  *  *  *  *  *  *  *  * *  *  * * |  1  0 1  0  0  0  0  0  0
.......... .x..o..... .......... ..........&#x  & | 0  2  1  0  0  0 |  0  1  0  2  0  0  0  0  0  0  0  0  0 |  *  *  *  * 36  *  *  *  *  *  *  *  *  *  * *  *  * * |  0  0 0  1  0  1  0  0  0
.......... .......... .x..o..... ..........&#x  & | 0  2  1  0  0  0 |  0  0  1  2  0  0  0  0  0  0  0  0  0 |  *  *  *  *  * 36  *  *  *  *  *  *  *  *  * *  *  * * |  0  1 0  1  0  0  0  0  0
.......... .x...x.... .......... ..........&#x  & | 0  2  0  2  0  0 |  0  1  0  0  2  0  1  0  0  0  0  0  0 |  *  *  *  *  *  * 36  *  *  *  *  *  *  *  * *  *  * * |  0  0 0  0  1  1  0  0  0
.......... .......... .......... .o...x....&#x  & | 0  1  0  2  0  0 |  0  0  0  0  2  0  0  1  0  0  0  0  0 |  *  *  *  *  *  *  * 36  *  *  *  *  *  *  * *  *  * * |  0  1 0  0  1  0  0  0  0
.o..oo....3.o..oo.... .o..oo....3.o..oo....&#x  & | 0  1  1  1  0  0 |  0  0  0  1  1  1  0  0  0  0  0  0  0 |  *  *  *  *  *  *  *  * 72  *  *  *  *  *  * *  *  * * |  0  1 0  0  0  1  0  0  0
...o..x... .......... .......... ..........&#x  & | 0  0  1  2  0  0 |  0  0  0  0  0  2  1  0  0  0  0  0  0 |  *  *  *  *  *  *  *  *  * 36  *  *  *  *  * *  *  * * |  0  0 0  0  0  1  1  0  0
.......... .......... ....ofx... ..........&#xt & | 0  0  1  4  0  0 |  0  0  0  0  0  2  0  1  2  0  0  0  0 |  *  *  *  *  *  *  *  *  *  * 36  *  *  *  * *  *  * * |  0  1 0  0  0  0  1  0  0
.......... .....x.... .......... .....x....     & | 0  0  0  4  0  0 |  0  0  0  0  0  0  2  2  0  0  0  0  0 |  *  *  *  *  *  *  *  *  *  *  * 18  *  *  * *  *  * * |  0  0 0  0  1  0  0  1  0
.......... .....x...x .......... ..........&#x  & | 0  0  0  2  0  2 |  0  0  0  0  0  0  1  0  0  2  0  0  1 |  *  *  *  *  *  *  *  *  *  *  *  * 36  *  * *  *  * * |  0  0 0  0  0  0  1  1  0
.......... .......... .......... .....x.o.f&#xt & | 0  0  0  2  1  2 |  0  0  0  0  0  0  0  1  0  2  0  2  0 |  *  *  *  *  *  *  *  *  *  *  *  *  * 36  * *  *  * * |  0  0 0  0  0  0  1  1  0 tower: F-J-H
.....oo..o3.....oo..o .....oo..o3.....oo..o&#x    | 0  0  0  2  0  1 |  0  0  0  0  0  0  0  0  1  2  0  0  0 |  *  *  *  *  *  *  *  *  *  *  *  *  *  * 36 *  *  * * |  0  0 0  0  0  0  2  0  0
.......o..3.......x.. .......... ..........     & | 0  0  0  0  3  0 |  0  0  0  0  0  0  0  0  0  0  3  0  0 |  *  *  *  *  *  *  *  *  *  *  *  *  *  *  * 6  *  * * |  0  0 0  0  0  0  0  0  2
.......o.x .......... .......... ..........&#x  & | 0  0  0  0  1  2 |  0  0  0  0  0  0  0  0  0  0  0  2  1 |  *  *  *  *  *  *  *  *  *  *  *  *  *  *  * * 36  * * |  0  0 0  0  0  0  1  0  1
.......... .......x.x .......... ..........&#x  & | 0  0  0  0  2  2 |  0  0  0  0  0  0  0  0  0  0  1  2  1 |  *  *  *  *  *  *  *  *  *  *  *  *  *  *  * *  * 36 * |  0  0 0  0  0  0  0  1  1
.........x3.........x .......... ..........       | 0  0  0  0  0  6 |  0  0  0  0  0  0  0  0  0  0  0  0  6 |  *  *  *  *  *  *  *  *  *  *  *  *  *  *  * *  *  * 6 |  0  0 0  0  0  0  0  0  2
--------------------------------------------------+------------------+----------------------------------------+--------------------------------------------------------+--------------------------
.......... .......... ox........3oo........&#x  & ♦ 1  3  0  0  0  0 |  3  0  3  0  0  0  0  0  0  0  0  0  0 |  3  0  0  1  0  0  0  0  0  0  0  0  0  0  0 0  0  0 0 | 12  * *  *  *  *  *  *  *
.......... .......... oxo.ofx... ..........&#xt & ♦ 1  3  1  4  0  0 |  3  0  1  2  4  2  0  1  2  0  0  0  0 |  1  2  0  0  0  1  0  1  2  0  1  0  0  0  0 0  0  0 0 |  * 36 *  *  *  *  *  *  *
.......... .x........ .x........3.o........     & ♦ 0  6  0  0  0  0 |  0  3  6  0  0  0  0  0  0  0  0  0  0 |  0  0  3  2  0  0  0  0  0  0  0  0  0  0  0 0  0  0 0 |  *  * 6  *  *  *  *  *  *
.......... .x..o..... .x..o..... ..........&#x  & ♦ 0  4  1  0  0  0 |  0  2  2  4  0  0  0  0  0  0  0  0  0 |  0  0  1  0  2  2  0  0  0  0  0  0  0  0  0 0  0  0 0 |  *  * * 18  *  *  *  *  *
.......... .x...x.... .......... .o...x....&#x  & ♦ 0  2  0  4  0  0 |  0  1  0  0  4  0  2  2  0  0  0  0  0 |  0  0  0  0  0  0  2  2  0  0  0  1  0  0  0 0  0  0 0 |  *  * *  * 18  *  *  *  *
.......... .x..ox.... .......... ..........&#x  & ♦ 0  2  1  2  0  0 |  0  1  0  2  2  2  1  0  0  0  0  0  0 |  0  0  0  0  1  0  1  0  2  1  0  0  0  0  0 0  0  0 0 |  *  * *  *  * 36  *  *  *
...o.Fxo.x .......... .......... ...o.xfo.f&#xt & ♦ 0  0  1  8  1  4 |  0  0  0  0  0  4  2  2  4  8  0  4  2 |  0  0  0  0  0  0  0  0  0  2  2  0  2  2  4 0  2  0 0 |  *  * *  *  *  * 18  *  * tower: D-G-F-J-H
.......... .....x.x.x .......... .....x.o.f&#xt & ♦ 0  0  0  4  2  4 |  0  0  0  0  0  0  2  2  0  4  1  4  2 |  0  0  0  0  0  0  0  0  0  0  0  1  2  2  0 0  0  2 0 |  *  * *  *  *  *  * 18  * tower: F-J-H
.......o.x3.......x.x .......... ..........&#x  & ♦ 0  0  0  0  3  6 |  0  0  0  0  0  0  0  0  0  0  3  6  6 |  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 1  3  3 1 |  *  * *  *  *  *  *  * 12
```