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

This polychoron occurs as a triacontadiminishing of oFxxox5Fofxfo oxofox5ooxofx&#zx. In fact, both the 1st and 5th layer of that tegum sum representation are dropped, representing an inscribed F-{5} resp. 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. (The non-expanded version itself would be fooo5ofxo xofx5oxox&#zx.)

Incidence matrix according to Dynkin symbol

Fxxx5ofxo xofx5oxox&#zx   → all existing heights = 0

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