Acronym ...
Name dodeca-diminished equatorial tetrastratic segment of rox
Circumradius sqrt[5+2 sqrt(5)] = 3.077684
Lace city
in approx. ASCII-art
    x5o             x5o    
            o5f            
                           
x5x                     x5x
                           
            x5f            		F=ff=x+f=2x+v, 
    F5o             F5o    		V=F+v=2f=2x+2v,
o5F                     o5F		A=F+x=3x+v
                           
                           
    f5f             f5f    
                           
                           
o5V                     o5V
                           
            x5F            
    F5x             F5x    
                           
                           
x5F                     x5F
                           
           oA5Ao           
                           
F5x                     F5x
                           
                           
    x5F             x5F    
            F5x            
                           
V5o                     V5o
                           
                           
    f5f             f5f    
                           
                           
F5o                     F5o
    o5F             o5F    
            f5x            
                           
x5x                     x5x
                           
            f5o            
    o5x             o5x    
 o3x o3F   x3V   F3F B3x   V3F       F3V   x3B F3F   V3x   F3o x3o 
                                                                   
   f3x   F3f B3o   x3B      fC3Bo Bo3fC      B3x   o3B f3F   x3f   
                                                                   		F=ff=x+f=2x+v,
                                                                   		V=F+v=2f=2x+2v,
x3o   x3F   o3B A3f   F3V B3f         f3B V3F   f3A B3o   F3x   o3x		A=F+x=3x+v,
                                                                   		B=fff=A+v=3x+2v,
                                                                   		C=B+x=4x+2v=2F
   f3x   F3f B3o   x3B      fC3Bo Bo3fC      B3x   o3B f3F   x3f   
                                                                   
 o3x o3F   x3V   F3F B3x   V3F       F3V   x3B F3F   V3x   F3o x3o 
Confer
uniform variant:
rox  
related CRFs:
oo|ofxfo|oo-3-xo|xxoxx|ox-5-of|xofox|fo-&#xt   ox|ofxfo|xo-3-xx|xxoxx|xx-5-oo|xofox|oo-&#xt   ox|ofxfo|oo-3-xx|xxoxx|ox-5-oo|xofox|fo-&#xt   of(Vx)fo-3-xx(oo)xx-5-xo(of)ox-&#xt   hexastratic ike-first cap of rox  
related segmentochora:
pippy  

By means of either the pair of segmentochora idati and tiatid or alternatively the bistratic id-cap of rahi this polychoron can independantly continued on either side, then resulting in oo|ofxfo|oo-3-xo|xxoxx|ox-5-of|xofox|fo-&#xt, ox|ofxfo|xo-3-xx|xxoxx|xx-5-oo|xofox|oo-&#xt, or ox|ofxfo|oo-3-xx|xxoxx|ox-5-oo|xofox|fo-&#xt. All 3 in turn are different EKFs derived from ex.

The relation to rox runs as follows: that one in ike-first axial orientation can be given as DCBAVFfxoo-2-xoxFofofVx-3-oxoofoxxoo-5-ooxooxxoof-&#zx or xoxFofof(Vx)fofoFxox-3-oxoofoxx(oo)xxofooxo-5-ooxooxxo(of)oxxooxoo-&#xt. When applying a hexastratic diminishing on either side, i.e. removing xoxFofo-3-oxoofox-5-ooxooxx-&#xt on either side, one results with the equatorial tetrastratic segment of(Vx)fo-3-xx(oo)xx-5-xo(of)ox-&#xt. This polychoron then is the dodecadiminishing therefrom, deleting the vertex set of an inscribed V-scaled ike.


Incidence matrix according to Dynkin symbol

fxo ofx3xxo5xof&#zx   → all heights = 0

o.. o..3o..5o..     | 120   *  * |   2  1   2   2   0   0  0  0 |  1  2   2   2   1   2   2  0  0   0   0  0 | 1  2  1  1   2  0  0
.o. .o.3.o.5.o.     |   * 120  * |   0  0   2   0   2   2  1  0 |  0  0   2   1   0   0   2  1  2   2   2  0 | 0  1  0  1   2  1  2
..o ..o3..o5..o     |   *   * 60 |   0  0   0   4   0   4  0  2 |  0  0   0   0   4   2   4  0  0   2   2  1 | 0  0  2  2   2  0  1
--------------------+------------+------------------------------+--------------------------------------------+---------------------
... ... x.. ...     |   2   0  0 | 120  *   *   *   *   *  *  * |  1  1   1   0   0   1   0  0  0   0   0  0 | 1  1  1  0   1  0  0
... ... ... x..     |   2   0  0 |   * 60   *   *   *   *  *  * |  0  2   0   2   0   0   0  0  0   0   0  0 | 1  2  0  1   0  0  0
oo. oo.3oo.5oo.&#x  |   1   1  0 |   *  * 240   *   *   *  *  * |  0  0   1   1   0   0   1  0  0   0   0  0 | 0  1  0  1   1  0  0
o.o o.o3o.o5o.o&#x  |   1   0  1 |   *  *   * 240   *   *  *  * |  0  0   0   0   1   1   1  0  0   0   0  0 | 0  0  1  1   1  0  0
... ... .x. ...     |   0   2  0 |   *  *   *   * 120   *  *  * |  0  0   1   0   0   0   0  1  1   0   1  0 | 0  1  0  0   1  1  1
.oo .oo3.oo5.oo&#x  |   0   1  1 |   *  *   *   *   * 240  *  * |  0  0   0   0   0   0   1  0  0   1   1  0 | 0  0  0  1   1  0  1
.x. ... ... ...     |   0   2  0 |   *  *   *   *   *   * 60  * |  0  0   0   0   0   0   0  0  2   2   0  0 | 0  0  0  1   0  1  2
... ..x .. ..       |   0   0  2 |   *  *   *   *   *   *  * 60 |  0  0   0   0   2   0   0  0  0   0   0  1 | 0  0  2  1   0  0  0
--------------------+------------+------------------------------+--------------------------------------------+---------------------
... o..3x.. ...     |   3   0  0 |   3  0   0   0   0   0  0  0 | 40  *   *   *   *   *   *  *  *   *   *  * | 1  0  1  0   0  0  0
... ... x..5x..     |  10   0  0 |   5  5   0   0   0   0  0  0 |  * 24   *   *   *   *   *  *  *   *   *  * | 1  1  0  0   0  0  0
... ... xx. ...&#x  |   2   2  0 |   1  0   2   0   1   0  0  0 |  *  * 120   *   *   *   *  *  *   *   *  * | 0  1  0  0   1  0  0
... ... ... xo.&#x  |   2   1  0 |   0  1   2   0   0   0  0  0 |  *  *   * 120   *   *   *  *  *   *   *  * | 0  1  0  1   0  0  0
... o.x ... ...&#x  |   1   0  2 |   0  0   0   2   0   0  0  1 |  *  *   *   * 120   *   *  *  *   *   *  * | 0  0  1  1   0  0  0
... ... x.o ...&#x  |   2   0  1 |   1  0   0   2   0   0  0  0 |  *  *   *   *   * 120   *  *  *   *   *  * | 0  0  1  0   1  0  0
ooo ooo3ooo5ooo&#x  |   1   1  1 |   0  0   1   1   0   1  0  0 |  *  *   *   *   *   * 240  *  *   *   *  * | 0  0  0  1   1  0  0
... ... .x.5.o.     |   0   5  0 |   0  0   0   0   5   0  0  0 |  *  *   *   *   *   *   * 24  *   *   *  * | 0  1  0  0   0  1  0
.x. ... .x. ...     |   0   4  0 |   0  0   0   0   2   0  2  0 |  *  *   *   *   *   *   *  * 60   *   *  * | 0  0  0  0   0  1  1
.xo ... ... ...&#x  |   0   2  1 |   0  0   0   0   0   2  1  0 |  *  *   *   *   *   *   *  *  * 120   *  * | 0  0  0  1   0  0  1
... ... .xo ...&#x  |   0   2  1 |   0  0   0   0   1   2  0  0 |  *  *   *   *   *   *   *  *  *   * 120  * | 0  0  0  0   1  0  1
... ..x3..o ...     |   0   0  3 |   0  0   0   0   0   0  0  3 |  *  *   *   *   *   *   *  *  *   *   * 20 | 0  0  2  0   0  0  0
--------------------+------------+------------------------------+--------------------------------------------+---------------------
... o..3x..5x..       60   0  0 |  60 30   0   0   0   0  0  0 | 20 12   0   0   0   0   0  0  0   0   0  0 | 2  *  *  *   *  *  *
... ... xx.5xo.&#x    10   5  0 |   5  5  10   0   5   0  0  0 |  0  1   5   5   0   0   0  1  0   0   0  0 | * 24  *  *   *  *  *
... o.x3x.o ...&#x     3   0  3 |   3  0   0   6   0   0  0  3 |  1  0   0   0   3   3   0  0  0   0   0  1 | *  * 40  *   *  *  *
fxo ofx ... xof&#zx    4   4  4 |   0  2   8   8   0   8  2  2 |  0  0   0   4   4   0   8  0  0   4   0  0 | *  *  * 30   *  *  *
... ... xxo ...&#x     2   2  1 |   1  0   2   2   1   2  0  0 |  0  0   1   0   0   1   2  0  0   0   1  0 | *  *  *  * 120  *  *
.x. ... .x.5.o.        0  10  0 |   0  0   0   0  10   0  5  0 |  0  0   0   0   0   0   0  2  5   0   0  0 | *  *  *  *   * 12  *
.xo ... .xo ...&#x     0   4  1 |   0  0   0   0   2   4  2  0 |  0  0   0   0   0   0   0  0  1   2   2  0 | *  *  *  *   *  * 60

ofxfo3xxoxx5xofox&#xt   → outer heights = (sqrt(5)-1)/4 = 0.309017
                          inner heights = 1/2
(tid || pseudo (f,x)-ti || pseudo (x,f)-srid || pseudo (f,x)-ti || tid)

o....3o....5o....     & | 120   *  * |   2  1   2   2   0   0  0  0 |  1  2   2   2   1   2   2  0   0  0   0  0 | 1  2  1  1   2  0  0
.o...3.o...5.o...     & |   * 120  * |   0  0   2   0   2   2  1  0 |  0  0   2   1   0   0   2  1   2  2   2  0 | 0  1  0  1   2  1  2
..o..3..o..5..o..       |   *   * 60 |   0  0   0   4   0   4  0  2 |  0  0   0   0   4   2   4  0   2  0   2  1 | 0  0  2  2   2  0  1
------------------------+------------+------------------------------+--------------------------------------------+---------------------
..... x.... .....     & |   2   0  0 | 120  *   *   *   *   *  *  * |  1  1   1   0   0   1   0  0   0  0   0  0 | 1  1  1  0   1  0  0
..... ..... x....     & |   2   0  0 |   * 60   *   *   *   *  *  * |  0  2   0   2   0   0   0  0   0  0   0  0 | 1  2  0  1   0  0  0
oo...3oo...5oo...&#x  & |   1   1  0 |   *  * 240   *   *   *  *  * |  0  0   1   1   0   0   1  0   0  0   0  0 | 0  1  0  1   1  0  0
o.o..3o.o..5o.o..&#x  & |   1   0  1 |   *  *   * 240   *   *  *  * |  0  0   0   0   1   1   1  0   0  0   0  0 | 0  0  1  1   1  0  0
..... .x... .....     & |   0   2  0 |   *  *   *   * 120   *  *  * |  0  0   1   0   0   0   0  1   1  1   0  0 | 0  1  0  0   1  1  1
.oo..3.oo..5.oo..&#x  & |   0   1  1 |   *  *   *   *   * 240  *  * |  0  0   0   0   0   0   1  0   1  0   1  0 | 0  0  0  1   1  0  1
.o.o.3.o.o.5.o.o.&#x    |   0   2  0 |   *  *   *   *   *   * 60  * |  0  0   0   0   0   0   0  0   0  2   2  0 | 0  0  0  1   0  1  2
..x.. ..... .....       |   0   0  2 |   *  *   *   *   *   *  * 60 |  0  0   0   0   2   0   0  0   0  0   0  1 | 0  0  2  1   0  0  0
------------------------+------------+------------------------------+--------------------------------------------+---------------------
o....3x.... .....     & |   3   0  0 |   3  0   0   0   0   0  0  0 | 40  *   *   *   *   *   *  *   *  *   *  * | 1  0  1  0   0  0  0
..... x....5x....     & |  10   0  0 |   5  5   0   0   0   0  0  0 |  * 24   *   *   *   *   *  *   *  *   *  * | 1  1  0  0   0  0  0
..... xx... .....&#x  & |   2   2  0 |   1  0   2   0   1   0  0  0 |  *  * 120   *   *   *   *  *   *  *   *  * | 0  1  0  0   1  0  0
..... ..... xo...&#x  & |   2   1  0 |   0  1   2   0   0   0  0  0 |  *  *   * 120   *   *   *  *   *  *   *  * | 0  1  0  1   0  0  0
o.x.. ..... .....&#x  & |   1   0  2 |   0  0   0   2   0   0  0  1 |  *  *   *   * 120   *   *  *   *  *   *  * | 0  0  1  1   0  0  0
..... x.o.. .....&#x  & |   2   0  1 |   1  0   0   2   0   0  0  0 |  *  *   *   *   * 120   *  *   *  *   *  * | 0  0  1  0   1  0  0
ooo..3ooo..5ooo..&#x  & |   1   1  1 |   0  0   1   1   0   1  0  0 |  *  *   *   *   *   * 240  *   *  *   *  * | 0  0  0  1   1  0  0
..... .x...5.o...     & |   0   5  0 |   0  0   0   0   5   0  0  0 |  *  *   *   *   *   *   * 24   *  *   *  * | 0  1  0  0   0  1  0
..... .xo.. .....&#x  & |   0   2  1 |   0  0   0   0   1   2  0  0 |  *  *   *   *   *   *   *  * 120  *   *  * | 0  0  0  0   1  0  1
..... .x.x. .....&#x    |   0   4  0 |   0  0   0   0   2   0  2  0 |  *  *   *   *   *   *   *  *   * 60   *  * | 0  0  0  0   0  1  1
.ooo.3.ooo.5.ooo.&#x    |   0   2  1 |   0  0   0   0   0   2  1  0 |  *  *   *   *   *   *   *  *   *  * 120  * | 0  0  0  1   0  0  1
..x..3..o.. .....       |   0   0  3 |   0  0   0   0   0   0  0  3 |  *  *   *   *   *   *   *  *   *  *   * 20 | 0  0  2  0   0  0  0
------------------------+------------+------------------------------+--------------------------------------------+---------------------
o....3x....5x....     &   60   0  0 |  60 30   0   0   0   0  0  0 | 20 12   0   0   0   0   0  0   0  0   0  0 | 2  *  *  *   *  *  *
..... xx...5xo...&#xt &   10   5  0 |   5  5  10   0   5   0  0  0 |  0  1   5   5   0   0   0  1   0  0   0  0 | * 24  *  *   *  *  *
o.x..3x.o.. .....&#x  &    3   0  3 |   3  0   0   6   0   0  0  3 |  1  0   0   0   3   3   0  0   0  0   0  1 | *  * 40  *   *  *  *
ofxfo ..... xofox&#xt      4   4  4 |   0  2   8   8   0   8  2  2 |  0  0   0   4   4   0   8  0   0  0   4  0 | *  *  * 30   *  *  *
..... xxo.. .....&#x  &    2   2  1 |   1  0   2   2   1   2  0  0 |  0  0   1   0   0   1   2  0   1  0   0  0 | *  *  *  * 120  *  *
..... .x.x.5.o.o.&#x       0  10  0 |   0  0   0   0  10   0  5  0 |  0  0   0   0   0   0   0  2   0  5   0  0 | *  *  *  *   * 12  *
..... .xox. .....&#x       0   4  1 |   0  0   0   0   2   4  2  0 |  0  0   0   0   0   0   0  0   2  1   2  0 | *  *  *  *   *  * 60

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