Acronym ...
Name triaugmented trigonal mibdi-laced wedge
 
centered at top line (layer a):
 ©
centered at bottom trip (layer d):
 ©
Circumradius ...
Lace city
in approx. ASCII-art
    o3o           o3o    
      a                  
           o3x           
x3o          b        x3o
  c                      
           f3o           
    o3x      d    o3x    
      e                  
Coordinates
    • (1/2, 0, 0, 0)                     & all changes of sign
    (layer x o3o in lace tower description resp. top one in lace city)
    • (0, 1/h, 0, sqrt(5)/2h)
    • (0, -1/2h, 1/2, sqrt(5)/2h)  & all changes of sign in 3rd coord.
    (layer o o3x in lace tower description resp. augmentation tips)
    • (f/2, 1/2h, 1/2, F/2h)         & all changes of sign in 1st and 3rd coord.
    • (f/2, -1/h, 0, F/2h)             & all changes of sign in 1st coord.
    (layer f x3o in lace tower description resp. medial one in lace city)
    • (0, f/2h, f/2, B/2h)             & all changes of sign in 3rd coord.
    • (0, -f/h, 0, B/2h)
    (layer o f3o in lace tower description resp. lower central one in lace city)
    • (1/2, 1/h, 0, F/h)               & all changes of sign in 1st coord.
    • (1/2, -1/2h, 1/2, F/h)         & all changes of sign in 1st and 3rd coord.
    (layer x o3x in lace tower description resp. bottom one in lace city)
where f=(1+sqrt(5))/2, h=sqrt(3), F=ff=f+x, B=fff=2f+x
General of army (is itself convex)
Colonel of regiment (is itself locally convex)
Confer
related CRFs:
xfox oxfo3ooox&#xt   mono-augmented 3-mibdi-wedge  
blend-components:
xfox oxfo3ooox&#xt   mibdipy  

This polychoron is obtained as triaugmentation of xfox oxfo3ooox&#xt, the trigonal mibdi-laced wedge. In fact it can be seen as the external blend of the latter with 3 mibdipies. The result still is CRF. (The individual augmentations are fully independant, similar ones with just one or two augmentation tips would exist too.)


Incidence matrix according to Dynkin symbol

xofox ooxfo3oxoox&#xt   → height(1,2) = sqrt(5/12) = 0.645497
                          height(2,3) = sqrt((7-3 sqrt(5))/24) = 0.110264
                          height(3,4) = sqrt[(3+sqrt(5))/24] = 0.467086
                          height(4,5) = sqrt(3)/6 = 1/sqrt(12) = 0.288675

o.... o....3o....     | 2 * * * * | 1 3 3  0 0 0 0 0  0  0 0 0 | 3 3  6 3 0  0  0  0 0 0 0  0 0 0 0 0 0 | 6 3 1 0  0 0 0 0 0 0 a
.o... .o...3.o...     | * 3 * * * | 0 2 0  4 2 2 0 0  0  0 0 0 | 1 0  4 0 2  4  4  4 1 0 0  0 0 0 0 0 0 | 2 2 0 2  4 2 0 0 0 0 b
..o.. ..o..3..o..     | * * 6 * * | 0 0 1  2 0 0 2 1  2  0 0 0 | 0 1  2 2 2  2  2  0 0 1 2  2 1 0 0 0 0 | 2 2 1 2  2 0 1 1 0 0 c
...o. ...o.3...o.     | * * * 3 * | 0 0 0  0 2 0 0 2  0  4 0 0 | 0 1  0 0 0  4  0  4 0 0 0  4 0 2 2 0 0 | 2 0 0 0  4 2 0 2 1 0 d
....o ....o3....o     | * * * * 6 | 0 0 0  0 0 1 0 0  2  2 1 2 | 0 0  0 0 0  0  2  2 1 0 1  2 2 2 2 2 1 | 0 0 0 1  2 2 1 2 2 1 e
----------------------+-----------+----------------------------+----------------------------------------+---------------------
x.... ..... .....     | 2 0 0 0 0 | 1 * *  * * * * *  *  * * * | 3 3  0 0 0  0  0  0 0 0 0  0 0 0 0 0 0 | 6 0 0 0  0 0 0 0 0 0
oo... oo...3oo...&#x  | 1 1 0 0 0 | * 6 *  * * * * *  *  * * * | 1 0  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
o.o.. o.o..3o.o..&#x  | 1 0 1 0 0 | * * 6  * * * * *  *  * * * | 0 1  2 2 0  0  0  0 0 0 0  0 0 0 0 0 0 | 2 2 1 0  0 0 0 0 0 0
.oo.. .oo..3.oo..&#x  | 0 1 1 0 0 | * * * 12 * * * *  *  * * * | 0 0  1 0 1  1  1  0 0 0 0  0 0 0 0 0 0 | 1 1 0 1  1 0 0 0 0 0
.o.o. .o.o.3.o.o.&#x  | 0 1 0 1 0 | * * *  * 6 * * *  *  * * * | 0 0  0 0 0  2  0  2 0 0 0  0 0 0 0 0 0 | 1 0 0 0  2 1 0 0 0 0
.o..o .o..o3.o..o&#x  | 0 1 0 0 1 | * * *  * * 6 * *  *  * * * | 0 0  0 0 0  0  2  2 1 0 0  0 0 0 0 0 0 | 0 0 0 1  2 2 0 0 0 0
..... ..x.. .....     | 0 0 2 0 0 | * * *  * * * 6 *  *  * * * | 0 0  0 1 1  0  0  0 0 1 1  0 0 0 0 0 0 | 0 1 1 1  0 0 1 0 0 0
..oo. ..oo.3..oo.&#x  | 0 0 1 1 0 | * * *  * * * * 6  *  * * * | 0 1  0 0 0  2  0  0 0 0 0  2 0 0 0 0 0 | 2 0 0 0  2 0 0 1 0 0
..o.o ..o.o3..o.o&#x  | 0 0 1 0 1 | * * *  * * * * * 12  * * * | 0 0  0 0 0  0  1  0 0 0 1  1 1 0 0 0 0 | 0 0 0 1  1 0 1 1 0 0
...oo ...oo3...oo&#x  | 0 0 0 1 1 | * * *  * * * * *  * 12 * * | 0 0  0 0 0  0  0  1 0 0 0  1 0 1 1 0 0 | 0 0 0 0  1 1 0 1 1 0
....x ..... .....     | 0 0 0 0 2 | * * *  * * * * *  *  * 3 * | 0 0  0 0 0  0  0  0 1 0 0  0 0 2 0 2 0 | 0 0 0 0  0 2 0 0 2 1
..... ..... ....x     | 0 0 0 0 2 | * * *  * * * * *  *  * * 6 | 0 0  0 0 0  0  0  0 0 0 0  0 1 0 1 1 1 | 0 0 0 0  0 0 1 1 1 1
----------------------+-----------+----------------------------+----------------------------------------+---------------------
xo... ..... .....&#x  | 2 1 0 0 0 | 1 2 0  0 0 0 0 0  0  0 0 0 | 3 *  * * *  *  *  * * * *  * * * * * * | 2 0 0 0  0 0 0 0 0 0
x.fo. ..... .....&#xt | 2 0 2 1 0 | 1 0 2  0 0 0 0 2  0  0 0 0 | * 3  * * *  *  *  * * * *  * * * * * * | 2 0 0 0  0 0 0 0 0 0
ooo.. ooo..3ooo..&#x  | 1 1 1 0 0 | 0 1 1  1 0 0 0 0  0  0 0 0 | * * 12 * *  *  *  * * * *  * * * * * * | 1 1 0 0  0 0 0 0 0 0
..... o.x.. .....&#x  | 1 0 2 0 0 | 0 0 2  0 0 0 1 0  0  0 0 0 | * *  * 6 *  *  *  * * * *  * * * * * * | 0 1 1 0  0 0 0 0 0 0
..... .ox.. .....&#x  | 0 1 2 0 0 | 0 0 0  2 0 0 1 0  0  0 0 0 | * *  * * 6  *  *  * * * *  * * * * * * | 0 1 0 1  0 0 0 0 0 0
.ooo. .ooo.3.ooo.&#x  | 0 1 1 1 0 | 0 0 0  1 1 0 0 1  0  0 0 0 | * *  * * * 12  *  * * * *  * * * * * * | 1 0 0 0  1 0 0 0 0 0
.oo.o .oo.o3.oo.o&#x  | 0 1 1 0 1 | 0 0 0  1 0 1 0 0  1  0 0 0 | * *  * * *  * 12  * * * *  * * * * * * | 0 0 0 1  1 0 0 0 0 0
.o.oo .o.oo3.o.oo&#x  | 0 1 0 1 1 | 0 0 0  0 1 1 0 0  0  1 0 0 | * *  * * *  *  * 12 * * *  * * * * * * | 0 0 0 0  1 1 0 0 0 0
.o..x ..... .....&#x  | 0 1 0 0 2 | 0 0 0  0 0 2 0 0  0  0 1 0 | * *  * * *  *  *  * 3 * *  * * * * * * | 0 0 0 0  0 2 0 0 0 0
..... ..x..3..o..     | 0 0 3 0 0 | 0 0 0  0 0 0 3 0  0  0 0 0 | * *  * * *  *  *  * * 2 *  * * * * * * | 0 0 1 0  0 0 1 0 0 0
..... ..x.o .....&#x  | 0 0 2 0 1 | 0 0 0  0 0 0 1 0  2  0 0 0 | * *  * * *  *  *  * * * 6  * * * * * * | 0 0 0 1  0 0 1 0 0 0
..ooo ..ooo3..ooo&#x  | 0 0 1 1 1 | 0 0 0  0 0 0 0 1  1  1 0 0 | * *  * * *  *  *  * * * * 12 * * * * * | 0 0 0 0  1 0 0 1 0 0
..... ..... ..o.x&#x  | 0 0 1 0 2 | 0 0 0  0 0 0 0 0  2  0 0 1 | * *  * * *  *  *  * * * *  * 6 * * * * | 0 0 0 0  0 0 1 1 0 0
...ox ..... .....&#x  | 0 0 0 1 2 | 0 0 0  0 0 0 0 0  0  2 1 0 | * *  * * *  *  *  * * * *  * * 6 * * * | 0 0 0 0  0 1 0 0 1 0
..... ..... ...ox&#x  | 0 0 0 1 2 | 0 0 0  0 0 0 0 0  0  2 0 1 | * *  * * *  *  *  * * * *  * * * 6 * * | 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 2 2 | * *  * * *  *  *  * * * *  * * * * 3 * | 0 0 0 0  0 0 0 0 1 1
..... ....o3....x     | 0 0 0 0 3 | 0 0 0  0 0 0 0 0  0  0 0 3 | * *  * * *  *  *  * * * *  * * * * * 2 | 0 0 0 0  0 0 1 0 0 1
----------------------+-----------+----------------------------+----------------------------------------+---------------------
xofo. ..... .....&#xr  2 1 2 1 0 | 1 2 2  2 1 0 0 2  0  0 0 0 | 1 1  2 0 0  2  0  0 0 0 0  0 0 0 0 0 0 | 6 * * *  * * * * * * cycle: (1342)
..... oox.. .....&#x   1 1 2 0 0 | 0 1 2  2 0 0 1 0  0  0 0 0 | 0 0  2 1 1  0  0  0 0 0 0  0 0 0 0 0 0 | * 6 * *  * * * * * *
..... o.x..3o.o..&#x   1 0 3 0 0 | 0 0 3  0 0 0 3 0  0  0 0 0 | 0 0  0 3 0  0  0  0 0 1 0  0 0 0 0 0 0 | * * 2 *  * * * * * *
..... .ox.o .....&#x   0 1 2 0 1 | 0 0 0  2 0 1 1 0  2  0 0 0 | 0 0  0 0 1  0  2  0 0 0 1  0 0 0 0 0 0 | * * * 6  * * * * * *
.oooo .oooo3.oooo&#x   0 1 1 1 1 | 0 0 0  1 1 1 0 1  1  1 0 0 | 0 0  0 0 0  1  1  1 0 0 0  1 0 0 0 0 0 | * * * * 12 * * * * *
.o.ox ..... .....&#x   0 1 0 1 2 | 0 0 0  0 1 2 0 0  0  2 1 0 | 0 0  0 0 0  0  0  2 1 0 0  0 0 1 0 0 0 | * * * *  * 6 * * * *
..... ..x.o3..o.x&#x   0 0 3 0 3 | 0 0 0  0 0 0 3 0  6  0 0 3 | 0 0  0 0 0  0  0  0 0 1 3  0 3 0 0 0 1 | * * * *  * * 2 * * *
..... ..... ..oox&#x   0 0 1 1 2 | 0 0 0  0 0 0 0 1  2  2 0 1 | 0 0  0 0 0  0  0  0 0 0 0  2 1 0 1 0 0 | * * * *  * * * 6 * *
...ox ..... ...ox&#x   0 0 0 1 4 | 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 2 2 1 0 | * * * *  * * * * 3 *
....x ....o3....x      0 0 0 0 6 | 0 0 0  0 0 0 0 0  0  0 3 6 | 0 0  0 0 0  0  0  0 0 0 0  0 0 0 0 3 2 | * * * *  * * * * * 1

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