x5o           x5o                 
                        x5x                        
                                                   
                                                   
     x5o                                   x5o     
                        F5o                        
                 x5f           x5f                 
                                                   
     x5x                                   x5x     
            F5o                     F5o            
                                                   
x5o                     o5F                     x5o
                                                   
            x5f                     x5f            
                                                   
                                                   
                 F5o           F5o                 
                        x5f                        
     x5o                                   x5o     
            x5x                     x5x            
                                                   
                                                   
                 x5o           x5o                 	where F = ff = f+x

This polychoron occurs as a icosipentadiminishing of oFxxox5Fofxfo oxofox5ooxofx&#zx. In fact, the 5th layer of that tegum sum representation is dropped, representing the vertex set of an inscribed f-pedip. The relation of that un-diminished one then 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.

Incidence matrix according to Dynkin symbol

oFxxx5Fofxo oxofx5ooxox&#zx   → all existing heights = 0

o....5o.... o....5o....     | 5  *  *  *  * ♦ 10  0   0  0  0  0   0  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
.o...5.o... .o...5.o...     | * 25  *  *  * |  0  2   4  2  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  2  2  2  0  0  0  0 0 0
..o..5..o.. ..o..5..o..     | *  * 50  *  * |  1  0   2  0  1  2   2  0  0   0  0  0  0 |  1  2 0  1  2  0   2  2  2  1  2  0  0  0  0  0  0 |  2  1  1  2  2  1  0  0 0 0
...o.5...o. ...o.5...o.     | *  *  * 50  * |  0  0   0  1  0  0   2  1  1   2  0  0  0 |  0  0 0  0  0  1   2  0  2  2  1  2  2  1  0  0  0 |  0  0  2  1  1  2  1  1 0 0
....o5....o ....o5....o     | *  *  *  * 50 |  0  0   0  0  0  0   0  0  0   2  2  1  1 |  0  0 0  0  0  0   0  0  0  2  0  2  1  2  1  2  2 |  0  0  1  0  0  2  2  1 1 1
----------------------------+---------------+-------------------------------------------+----------------------------------------------------+----------------------------
o.o..5o.o.. o.o..5o.o..&#x  | 1  0  1  0  0 | 50  *   *  *  *  *   *  *  *   *  *  *  * |  1  2 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
..... ..... .x... .....     | 0  2  0  0  0 |  * 25   *  *  *  *   *  *  *   *  *  *  * |  0  0 1  2  0  0   0  0  0  0  0  0  0  0  0  0  0 |  0  2  1  0  0  0  0  0 0 0
.oo..5.oo.. .oo..5.oo..&#x  | 0  1  1  0  0 |  *  * 100  *  *  *   *  *  *   *  *  *  * |  0  0 0  1  1  0   1  0  0  0  0  0  0  0  0  0  0 |  0  1  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  1   2  0  0  0  0  0  0  0  0  0  0 |  0  0  2  1  0  0  0  0 0 0
..x.. ..... ..... .....     | 0  0  2  0  0 |  *  *   *  * 25  *   *  *  *   *  *  *  * |  1  0 0  0  0  0   0  2  2  0  0  0  0  0  0  0  0 |  2  0  0  0  2  1  0  0 0 0
..... ..... ..... ..x..     | 0  0  2  0  0 |  *  *   *  *  * 50   *  *  *   *  *  *  * |  0  1 0  0  1  0   0  1  0  0  1  0  0  0  0  0  0 |  1  1  0  1  1  0  0  0 0 0
..oo.5..oo. ..oo.5..oo.&#x  | 0  0  1  1  0 |  *  *   *  *  *  * 100  *  *   *  *  *  * |  0  0 0  0  0  0   1  0  1  1  1  0  0  0  0  0  0 |  0  0  1  1  1  1  0  0 0 0
...x. ..... ..... .....     | 0  0  0  2  0 |  *  *   *  *  *  *   * 25  *   *  *  *  * |  0  0 0  0  0  0   0  0  2  0  0  2  0  0  0  0  0 |  0  0  0  0  1  2  1  0 0 0
..... ...x. ..... .....     | 0  0  0  2  0 |  *  *   *  *  *  *   *  * 25   *  *  *  * |  0  0 0  0  0  1   0  0  0  0  0  0  2  0  0  0  0 |  0  0  2  0  0  0  0  1 0 0
...oo5...oo ...oo5...oo&#x  | 0  0  0  1  1 |  *  *   *  *  *  *   *  *  * 100  *  *  * |  0  0 0  0  0  0   0  0  0  1  0  1  1  1  0  0  0 |  0  0  1  0  0  1  1  1 0 0
....x ..... ..... .....     | 0  0  0  0  2 |  *  *   *  *  *  *   *  *  *   * 50  *  * |  0  0 0  0  0  0   0  0  0  0  0  1  0  0  1  1  1 |  0  0  0  0  0  1  1  0 1 1
..... ..... ....x .....     | 0  0  0  0  2 |  *  *   *  *  *  *   *  *  *   *  * 25  * |  0  0 0  0  0  0   0  0  0  2  0  0  0  0  0  2  0 |  0  0  1  0  0  2  0  0 1 0
..... ..... ..... ....x     | 0  0  0  0  2 |  *  *   *  *  *  *   *  *  *   *  *  * 25 |  0  0 0  0  0  0   0  0  0  0  0  0  0  2  0  0  2 |  0  0  0  0  0  0  2  1 0 1
----------------------------+---------------+-------------------------------------------+----------------------------------------------------+----------------------------
o.x.. ..... ..... .....&#x  | 1  0  2  0  0 |  2  0   0  0  1  0   0  0  0   0  0  0  0 | 25  * *  *  *  *   *  *  *  *  *  *  *  *  *  *  * |  2  0  0  0  0  0  0  0 0 0
..... ..... ..... o.x..&#x  | 1  0  2  0  0 |  2  0   0  0  0  1   0  0  0   0  0  0  0 |  * 50 *  *  *  *   *  *  *  *  *  *  *  *  *  *  * |  1  1  0  0  0  0  0  0 0 0
..... ..... .x...5.o...     | 0  5  0  0  0 |  0  5   0  0  0  0   0  0  0   0  0  0  0 |  *  * 5  *  *  *   *  *  *  *  *  *  *  *  *  *  * |  0  2  0  0  0  0  0  0 0 0
..... ..... .xo.. .....&#x  | 0  2  1  0  0 |  0  1   2  0  0  0   0  0  0   0  0  0  0 |  *  * * 50  *  *   *  *  *  *  *  *  *  *  *  *  * |  0  1  1  0  0  0  0  0 0 0
..... ..... ..... .ox..&#x  | 0  1  2  0  0 |  0  0   2  0  0  1   0  0  0   0  0  0  0 |  *  * *  * 50  *   *  *  *  *  *  *  *  *  *  *  * |  0  1  0  1  0  0  0  0 0 0
..... .o.x. ..... .....&#x  | 0  1  0  2  0 |  0  0   0  2  0  0   0  0  1   0  0  0  0 |  *  * *  *  * 25   *  *  *  *  *  *  *  *  *  *  * |  0  0  2  0  0  0  0  0 0 0
.ooo.5.ooo. .ooo.5.ooo.&#x  | 0  1  1  1  0 |  0  0   1  1  0  0   1  0  0   0  0  0  0 |  *  * *  *  *  * 100  *  *  *  *  *  *  *  *  *  * |  0  0  1  1  0  0  0  0 0 0
..x.. ..... ..... ..x..     | 0  0  4  0  0 |  0  0   0  0  2  2   0  0  0   0  0  0  0 |  *  * *  *  *  *   * 25  *  *  *  *  *  *  *  *  * |  1  0  0  0  1  0  0  0 0 0
..xx. ..... ..... .....&#x  | 0  0  2  2  0 |  0  0   0  0  1  0   2  1  0   0  0  0  0 |  *  * *  *  *  *   *  * 50  *  *  *  *  *  *  *  * |  0  0  0  0  1  1  0  0 0 0
..... ..... ..ofx .....&#xt | 0  0  1  2  2 |  0  0   0  0  0  0   2  0  0   2  0  1  0 |  *  * *  *  *  *   *  *  * 50  *  *  *  *  *  *  * |  0  0  1  0  0  1  0  0 0 0
..... ..... ..... ..xo.&#x  | 0  0  2  1  0 |  0  0   0  0  0  1   2  0  0   0  0  0  0 |  *  * *  *  *  *   *  *  *  * 50  *  *  *  *  *  * |  0  0  0  1  1  0  0  0 0 0
...xx ..... ..... .....&#x  | 0  0  0  2  2 |  0  0   0  0  0  0   0  1  0   2  1  0  0 |  *  * *  *  *  *   *  *  *  *  * 50  *  *  *  *  * |  0  0  0  0  0  1  1  0 0 0
..... ...xo ..... .....&#x  | 0  0  0  2  1 |  0  0   0  0  0  0   0  0  1   2  0  0  0 |  *  * *  *  *  *   *  *  *  *  *  * 50  *  *  *  * |  0  0  1  0  0  0  0  1 0 0
..... ..... ..... ...ox&#x  | 0  0  0  1  2 |  0  0   0  0  0  0   0  0  0   2  0  0  1 |  *  * *  *  *  *   *  *  *  *  *  *  * 50  *  *  * |  0  0  0  0  0  0  1  1 0 0
....x5....o ..... .....     | 0  0  0  0  5 |  0  0   0  0  0  0   0  0  0   0  5  0  0 |  *  * *  *  *  *   *  *  *  *  *  *  *  * 10  *  * |  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  2  2  0 |  *  * *  *  *  *   *  *  *  *  *  *  *  *  * 25  * |  0  0  0  0  0  1  0  0 1 0
....x ..... ..... ....x     | 0  0  0  0  4 |  0  0   0  0  0  0   0  0  0   0  2  0  2 |  *  * *  *  *  *   *  *  *  *  *  *  *  *  *  * 25 |  0  0  0  0  0  0  1  0 0 1
----------------------------+---------------+-------------------------------------------+----------------------------------------------------+----------------------------
o.x.. ..... ..... o.x..&#x  ♦ 1  0  4  0  0 |  4  0   0  0  2  2   0  0  0   0  0  0  0 |  2  2 0  0  0  0   0  1  0  0  0  0  0  0  0  0  0 | 25  *  *  *  *  *  *  * * *
..... ..... oxo..5oox..&#xt ♦ 1  5  5  0  0 |  5  5  10  0  0  5   0  0  0   0  0  0  0 |  0  5 1  5  5  0   0  0  0  0  0  0  0  0  0  0  0 |  * 10  *  *  *  *  *  * * * (tower: 132)
..... .ofxo .xofx .....&#xt ♦ 0  2  2  4  2 |  0  1   4  4  0  0   4  0  2   4  0  1  0 |  0  0 0  2  0  2   4  0  0  2  0  0  2  0  0  0  0 |  *  * 25  *  *  *  *  * * *
..... ..... ..... .oxo.&#x  ♦ 0  1  2  1  0 |  0  0   2  1  0  1   2  0  0   0  0  0  0 |  0  0 0  0  1  0   2  0  0  0  1  0  0  0  0  0  0 |  *  *  * 50  *  *  *  * * *
..xx. ..... ..... ..xo.&#x  ♦ 0  0  4  2  0 |  0  0   0  0  2  2   4  1  0   0  0  0  0 |  0  0 0  0  0  0   0  1  2  0  2  0  0  0  0  0  0 |  *  *  *  * 25  *  *  * * *
..xxx ..... ..ofx .....&#xt ♦ 0  0  2  4  4 |  0  0   0  0  1  0   4  2  0   4  2  2  0 |  0  0 0  0  0  0   0  0  2  2  0  2  0  0  0  1  0 |  *  *  *  *  * 25  *  * * *
...xx ..... ..... ...ox&#x  ♦ 0  0  0  2  4 |  0  0   0  0  0  0   0  1  0   4  2  0  2 |  0  0 0  0  0  0   0  0  0  0  0  2  0  2  0  0  1 |  *  *  *  *  *  * 25  * * *
..... ...xo ..... ...ox&#x  ♦ 0  0  0  2  2 |  0  0   0  0  0  0   0  0  1   4  0  0  1 |  0  0 0  0  0  0   0  0  0  0  0  0  2  2  0  0  0 |  *  *  *  *  *  *  * 25 * *
....x5....o ....x .....     ♦ 0  0  0  0 10 |  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  2  5  0 |  *  *  *  *  *  *  *  * 5 *
....x5....o ..... ....x     ♦ 0  0  0  0 10 |  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  2  0  5 |  *  *  *  *  *  *  *  * * 5