Acronym ... Name triaugmented trigonal mibdi-laced wedge ```centered at top line (layer a): © centered at bottom trip (layer d): ©``` Circumradius ... Lace cityin 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
```