Acronym ... Name Fxxox5ofxfo xofox5oxofx&#zx Lace cityin approx. ASCII-art ``` x5o x5o x5x o5f o5f x5o x5o F5o x5f x5f x5x x5x F5o F5o x5o x5o x5f x5f o5f o5f F5o F5o x5f x5o x5o x5x x5x o5f x5o x5o where F = ff = f+x ``` Confer uniform relative: ex   related CRFs: oFxxox5Fofxfo oxofox5ooxofx&#zx   oFxx.x5Fofx.o oxof.x5ooxo.x&#zx   .Fxx.x5F.fx.o .xof.x5.oxo.x&#zx   cydadex   general polytopal classes: expanded kaleido-facetings

This polychoron occurs as a triacontadiminishing of oFxxox5Fofxfo oxofox5ooxofx&#zx. In fact, the 1st layer of that tegum sum representation is dropped, representing the vertex set of an inscribed F-{5}. The relation of that un-diminished one to ex runs as follows: ex in pentagonal duoprismatic subsymmetry can be given as xfooxo5xofxoo oxofox5ooxofx&#zx. That will be transformed into (-x)fooxo5Fofxoo oxofox5ooxofx&#zx. And finally into (-x)foo(-x)o5Fofxfo oxofox5ooxofx&#zx. Then a Stott expansion wrt. the first node produces that un-diminished polychoron.

The relation of this polychoron to cydadex can be seen when displaying that one in this symmetry as fooxo5ofxoo xofox5oxofx&#zx, then rewriting the same vertex set as foo(-x)o5ofxfo xofox5oxofx&#zx and thereafter applying a Stott expansion to the first nodes each. – In fact, the diminishing, which obtains cydadex from ex or which obtains this polychoron from oFxxox5Fofxfo oxofox5ooxofx&#zx do commutate with the here resp. above described expanded kaleido-facetings.

Incidence matrix according to Dynkin symbol

```Fxxox5ofxfo xofox5oxofx&#zx   → all existing heights = 0

o....5o.... o....5o....     | 25  *  *  *  * |  2   4  2  0  0   0  0  0  0   0   0   0  0  0  0 | 1  4  2  1   4  0  0  0  0  0   0  0  0  0  0   0  0  0  0  0  0 |  2  2  2 0  0  0  0  0  0  0 0 0
.o...5.o... .o...5.o...     |  * 50  *  *  * |  0   2  0  1  2   2  1  0  0   0   0   0  0  0  0 | 0  1  2  0   2  2  1  2  2  1   2  0  0  0  0   0  0  0  0  0  0 |  1  1  2 1  2  2  0  0  0  0 0 0
..o..5..o.. ..o..5..o..     |  *  * 50  *  * |  0   0  1  0  0   2  0  1  1   2   2   0  0  0  0 | 0  0  0  1   2  0  0  2  1  0   2  2  2  2  1   2  0  0  0  0  0 |  0  2  1 0  1  2  2  1  1  0 0 0
...o.5...o. ...o.5...o.     |  *  *  * 25  * |  0   0  0  0  0   0  2  0  0   4   0   4  0  0  0 | 0  0  0  0   0  0  0  0  0  1   4  2  0  0  0   4  2  2  0  0  0 |  0  2  0 0  0  2  2  0  0  1 0 0
....o5....o ....o5....o     |  *  *  *  * 50 |  0   0  0  0  0   0  0  0  0   0   2   2  2  1  1 | 0  0  0  0   0  0  0  0  0  0   0  0  2  1  2   2  2  2  1  2  2 |  0  1  0 0  0  0  2  2  1  2 1 1
----------------------------+----------------+---------------------------------------------------+------------------------------------------------------------------+---------------------------------
..... ..... x.... .....     |  2  0  0  0  0 | 25   *  *  *  *   *  *  *  *   *   *   *  *  *  * | 1  2  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
oo...5oo... oo...5oo...&#x  |  1  1  0  0  0 |  * 100  *  *  *   *  *  *  *   *   *   *  *  *  * | 0  1  1  0   1  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
o.o..5o.o.. o.o..5o.o..&#x  |  1  0  1  0  0 |  *   * 50  *  *   *  *  *  *   *   *   *  *  *  * | 0  0  0  1   2  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
.x... ..... ..... .....     |  0  2  0  0  0 |  *   *  * 25  *   *  *  *  *   *   *   *  *  *  * | 0  0  0  0   0  2  0  2  0  1   0  0  0  0  0   0  0  0  0  0  0 |  0  0  0 1  2  2  0  0  0  0 0 0
..... ..... ..... .x...     |  0  2  0  0  0 |  *   *  *  * 50   *  *  *  *   *   *   *  *  *  * | 0  0  1  0   0  1  1  0  1  0   0  0  0  0  0   0  0  0  0  0  0 |  1  0  1 1  1  0  0  0  0  0 0 0
.oo..5.oo.. .oo..5.oo..&#x  |  0  1  1  0  0 |  *   *  *  *  * 100  *  *  *   *   *   *  *  *  * | 0  0  0  0   1  0  0  1  1  0   1  0  0  0  0   0  0  0  0  0  0 |  0  1  1 0  1  1  0  0  0  0 0 0
.o.o.5.o.o. .o.o.5.o.o.&#x  |  0  1  0  1  0 |  *   *  *  *  *   * 50  *  *   *   *   *  *  *  * | 0  0  0  0   0  0  0  0  0  1   2  0  0  0  0   0  0  0  0  0  0 |  0  1  0 0  0  2  0  0  0  0 0 0
..x.. ..... ..... .....     |  0  0  2  0  0 |  *   *  *  *  *   *  * 25  *   *   *   *  *  *  * | 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  1  2  2  1  0  0 0 0
..... ..x.. ..... .....     |  0  0  2  0  0 |  *   *  *  *  *   *  *  * 25   *   *   *  *  *  * | 0  0  0  1   0  0  0  0  0  0   0  0  0  2  0   0  0  0  0  0  0 |  0  2  0 0  0  0  0  0  1  0 0 0
..oo.5..oo. ..oo.5..oo.&#x  |  0  0  1  1  0 |  *   *  *  *  *   *  *  *  * 100   *   *  *  *  * | 0  0  0  0   0  0  0  0  0  0   1  1  0  0  0   1  0  0  0  0  0 |  0  1  0 0  0  1  1  0  0  0 0 0
..o.o5..o.o ..o.o5..o.o&#x  |  0  0  1  0  1 |  *   *  *  *  *   *  *  *  *   * 100   *  *  *  * | 0  0  0  0   0  0  0  0  0  0   0  0  1  1  1   1  0  0  0  0  0 |  0  1  0 0  0  0  1  1  1  0 0 0
...oo5...oo ...oo5...oo&#x  |  0  0  0  1  1 |  *   *  *  *  *   *  *  *  *   *   * 100  *  *  * | 0  0  0  0   0  0  0  0  0  0   0  0  0  0  0   1  1  1  0  0  0 |  0  1  0 0  0  0  1  0  0  1 0 0
....x ..... ..... .....     |  0  0  0  0  2 |  *   *  *  *  *   *  *  *  *   *   *   * 50  *  * | 0  0  0  0   0  0  0  0  0  0   0  0  1  0  0   0  1  0  1  1  1 |  0  0  0 0  0  0  1  1  0  1 1 1
..... ..... ....x .....     |  0  0  0  0  2 |  *   *  *  *  *   *  *  *  *   *   *   *  * 25  * | 0  0  0  0   0  0  0  0  0  0   0  0  0  0  0   0  0  2  0  2  0 |  0  1  0 0  0  0  0  0  0  2 1 0
..... ..... ..... ....x     |  0  0  0  0  2 |  *   *  *  *  *   *  *  *  *   *   *   *  *  * 25 | 0  0  0  0   0  0  0  0  0  0   0  0  0  0  2   0  0  0  0  0  2 |  0  0  0 0  0  0  0  2  1  0 0 1
----------------------------+----------------+---------------------------------------------------+------------------------------------------------------------------+---------------------------------
..... ..... x....5o....     |  5  0  0  0  0 |  5   0  0  0  0   0  0  0  0   0   0   0  0  0  0 | 5  *  *  *   *  *  *  *  *  *   *  *  *  *  *   *  *  *  *  *  * |  2  0  0 0  0  0  0  0  0  0 0 0
..... ..... xo... .....&#x  |  2  1  0  0  0 |  1   2  0  0  0   0  0  0  0   0   0   0  0  0  0 | * 50  *  *   *  *  *  *  *  *   *  *  *  *  *   *  *  *  *  *  * |  1  1  0 0  0  0  0  0  0  0 0 0
..... ..... ..... ox...&#x  |  1  2  0  0  0 |  0   2  0  0  1   0  0  0  0   0   0   0  0  0  0 | *  * 50  *   *  *  *  *  *  *   *  *  *  *  *   *  *  *  *  *  * |  1  0  1 0  0  0  0  0  0  0 0 0
..... o.x.. ..... .....&#x  |  1  0  2  0  0 |  0   0  2  0  0   0  0  0  1   0   0   0  0  0  0 | *  *  * 25   *  *  *  *  *  *   *  *  *  *  *   *  *  *  *  *  * |  0  2  0 0  0  0  0  0  0  0 0 0
ooo..5ooo.. ooo..5ooo..&#x  |  1  1  1  0  0 |  0   1  1  0  0   1  0  0  0   0   0   0  0  0  0 | *  *  *  * 100  *  *  *  *  *   *  *  *  *  *   *  *  *  *  *  * |  0  1  1 0  0  0  0  0  0  0 0 0
.x... ..... ..... .x...     |  0  4  0  0  0 |  0   0  0  2  2   0  0  0  0   0   0   0  0  0  0 | *  *  *  *   * 25  *  *  *  *   *  *  *  *  *   *  *  *  *  *  * |  0  0  0 1  1  0  0  0  0  0 0 0
..... ..... .o...5.x...     |  0  5  0  0  0 |  0   0  0  0  5   0  0  0  0   0   0   0  0  0  0 | *  *  *  *   *  * 10  *  *  *   *  *  *  *  *   *  *  *  *  *  * |  1  0  0 1  0  0  0  0  0  0 0 0
.xx.. ..... ..... .....&#x  |  0  2  2  0  0 |  0   0  0  1  0   2  0  1  0   0   0   0  0  0  0 | *  *  *  *   *  *  * 50  *  *   *  *  *  *  *   *  *  *  *  *  * |  0  0  0 0  1  1  0  0  0  0 0 0
..... ..... ..... .xo..&#x  |  0  2  1  0  0 |  0   0  0  0  1   2  0  0  0   0   0   0  0  0  0 | *  *  *  *   *  *  *  * 50  *   *  *  *  *  *   *  *  *  *  *  * |  0  0  1 0  1  0  0  0  0  0 0 0
.x.o. ..... ..... .....&#x  |  0  2  0  1  0 |  0   0  0  1  0   0  2  0  0   0   0   0  0  0  0 | *  *  *  *   *  *  *  *  * 25   *  *  *  *  *   *  *  *  *  *  * |  0  0  0 0  0  2  0  0  0  0 0 0
.ooo.5.ooo. .ooo.5.ooo.&#x  |  0  1  1  1  0 |  0   0  0  0  0   1  1  0  0   1   0   0  0  0  0 | *  *  *  *   *  *  *  *  *  * 100  *  *  *  *   *  *  *  *  *  * |  0  1  0 0  0  1  0  0  0  0 0 0
..xo. ..... ..... .....&#x  |  0  0  2  1  0 |  0   0  0  0  0   0  0  1  0   2   0   0  0  0  0 | *  *  *  *   *  *  *  *  *  *   * 50  *  *  *   *  *  *  *  *  * |  0  0  0 0  0  1  1  0  0  0 0 0
..x.x ..... ..... .....&#x  |  0  0  2  0  2 |  0   0  0  0  0   0  0  1  0   0   2   0  1  0  0 | *  *  *  *   *  *  *  *  *  *   *  * 50  *  *   *  *  *  *  *  * |  0  0  0 0  0  0  1  1  0  0 0 0
..... ..x.o ..... .....&#x  |  0  0  2  0  1 |  0   0  0  0  0   0  0  0  1   0   2   0  0  0  0 | *  *  *  *   *  *  *  *  *  *   *  *  * 50  *   *  *  *  *  *  * |  0  1  0 0  0  0  0  0  1  0 0 0
..... ..... ..... ..o.x&#x  |  0  0  1  0  2 |  0   0  0  0  0   0  0  0  0   0   2   0  0  0  1 | *  *  *  *   *  *  *  *  *  *   *  *  *  * 50   *  *  *  *  *  * |  0  0  0 0  0  0  0  1  1  0 0 0
..ooo5..ooo ..ooo5..ooo&#x  |  0  0  1  1  1 |  0   0  0  0  0   0  0  0  0   1   1   1  0  0  0 | *  *  *  *   *  *  *  *  *  *   *  *  *  *  * 100  *  *  *  *  * |  0  1  0 0  0  0  1  0  0  0 0 0
...ox ..... ..... .....&#x  |  0  0  0  1  2 |  0   0  0  0  0   0  0  0  0   0   0   2  1  0  0 | *  *  *  *   *  *  *  *  *  *   *  *  *  *  *   * 50  *  *  *  * |  0  0  0 0  0  0  1  0  0  1 0 0
..... ..... ...ox .....&#x  |  0  0  0  1  2 |  0   0  0  0  0   0  0  0  0   0   0   2  0  1  0 | *  *  *  *   *  *  *  *  *  *   *  *  *  *  *   *  * 50  *  *  * |  0  1  0 0  0  0  0  0  0  1 0 0
....x5....o ..... .....     |  0  0  0  0  5 |  0   0  0  0  0   0  0  0  0   0   0   0  5  0  0 | *  *  *  *   *  *  *  *  *  *   *  *  *  *  *   *  *  * 10  *  * |  0  0  0 0  0  0  0  0  0  0 1 1
....x ..... ....x .....     |  0  0  0  0  4 |  0   0  0  0  0   0  0  0  0   0   0   0  2  2  0 | *  *  *  *   *  *  *  *  *  *   *  *  *  *  *   *  *  *  * 25  * |  0  0  0 0  0  0  0  0  0  1 1 0
....x ..... ..... ....x     |  0  0  0  0  4 |  0   0  0  0  0   0  0  0  0   0   0   0  2  0  2 | *  *  *  *   *  *  *  *  *  *   *  *  *  *  *   *  *  *  *  * 25 |  0  0  0 0  0  0  0  1  0  0 0 1
----------------------------+----------------+---------------------------------------------------+------------------------------------------------------------------+---------------------------------
..... ..... xo...5ox...&#x  ♦  5  5  0  0  0 |  5  10  0  0  5   0  0  0  0   0   0   0  0  0  0 | 1  5  5  0   0  0  1  0  0  0   0  0  0  0  0   0  0  0  0  0  0 | 10  *  * *  *  *  *  *  *  * * *
..... ofxfo xofox .....&#xt ♦  2  2  4  2  2 |  1   4  4  0  0   4  2  0  2   4   4   4  0  1  0 | 0  2  0  2   4  0  0  0  0  0   4  0  0  2  0   4  0  2  0  0  0 |  * 25  * *  *  *  *  *  *  * * *
..... ..... ..... oxo..&#x  ♦  1  2  1  0  0 |  0   2  1  0  1   2  0  0  0   0   0   0  0  0  0 | 0  0  1  0   2  0  0  0  1  0   0  0  0  0  0   0  0  0  0  0  0 |  *  * 50 *  *  *  *  *  *  * * *
.x... ..... .o...5.x...     ♦  0 10  0  0  0 |  0   0  0  5 10   0  0  0  0   0   0   0  0  0  0 | 0  0  0  0   0  5  2  0  0  0   0  0  0  0  0   0  0  0  0  0  0 |  *  *  * 5  *  *  *  *  *  * * *
.xx.. ..... ..... .xo..&#x  ♦  0  4  2  0  0 |  0   0  0  2  2   4  0  1  0   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 |  *  *  * * 25  *  *  *  *  * * *
.xxo. ..... ..... .....&#x  ♦  0  2  2  1  0 |  0   0  0  1  0   2  2  1  0   2   0   0  0  0  0 | 0  0  0  0   0  0  0  1  0  1   2  1  0  0  0   0  0  0  0  0  0 |  *  *  * *  * 50  *  *  *  * * *
..xox ..... ..... .....&#x  ♦  0  0  2  1  2 |  0   0  0  0  0   0  0  1  0   2   2   2  1  0  0 | 0  0  0  0   0  0  0  0  0  0   0  1  1  0  0   2  1  0  0  0  0 |  *  *  * *  *  * 50  *  *  * * *
..x.x ..... ..... ..o.x&#x  ♦  0  0  2  0  4 |  0   0  0  0  0   0  0  1  0   0   4   0  2  0  2 | 0  0  0  0   0  0  0  0  0  0   0  0  2  0  2   0  0  0  0  0  1 |  *  *  * *  *  *  * 25  *  * * *
..... ..x.o ..... ..o.x&#x  ♦  0  0  2  0  2 |  0   0  0  0  0   0  0  0  1   0   4   0  0  0  1 | 0  0  0  0   0  0  0  0  0  0   0  0  0  2  2   0  0  0  0  0  0 |  *  *  * *  *  *  *  * 25  * * *
...ox ..... ...ox .....&#x  ♦  0  0  0  1  4 |  0   0  0  0  0   0  0  0  0   0   0   4  2  2  0 | 0  0  0  0   0  0  0  0  0  0   0  0  0  0  0   0  2  2  0  1  0 |  *  *  * *  *  *  *  *  * 25 * *
....x5....o ....x .....     ♦  0  0  0  0 10 |  0   0  0  0  0   0  0  0  0   0   0   0 10  5  0 | 0  0  0  0   0  0  0  0  0  0   0  0  0  0  0   0  0  0  2  5  0 |  *  *  * *  *  *  *  *  *  * 5 *
....x5....o ..... ....x     ♦  0  0  0  0 10 |  0   0  0  0  0   0  0  0  0   0   0   0 10  0  5 | 0  0  0  0   0  0  0  0  0  0   0  0  0  0  0   0  0  0  2  0  5 |  *  *  * *  *  *  *  *  *  * * 5
```

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