Acronym ...
Name trigonal mibdi-laced wedge
 
centered at top line (layer a):
 ©
centered at bottom trip (layer d):
 ©
Circumradius 1
Lace city
in approx. ASCII-art
    o3o           o3o    
      a                  
                         
x3o                   x3o
  b                      
           f3o           
    o3x      c    o3x    
      d                  
Coordinates
    • (1/2, 0, 0, -3/2h)                      & all changes of sign
    (layer x o3o in lace tower description resp. top one in lace city)
    • (f/2, 1/2h, 1/2, (f-2)/2h)           & all changes of sign in 1st and 3rd coord.
    • (f/2, -1/h, 0, (f-2)/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, (f-1)/h)                 & all changes of sign in 3rd coord.
    • (0, -f/h, 0, (f-1)/h)
    (layer o f3o in lace tower description resp. lower central one in lace city)
    • (1/2, 1/h, 0, (2f-1)/2h)             & all changes of sign in 1st coord.
    • (1/2, -1/2h, 1/2, (2f-1)/2h)       & 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)   &   and circumcenter is at origin
General of army (is itself convex)
Colonel of regiment (is itself locally convex)
Confer
related CRFs:
xofox ooxfo3oxoox&#xt (tri-augmented 3-mibdi-wedge)   mono-augmented 3-mibdi-wedge   xfoxo oxfox5ooofx&#xt   tetu  
related segmentochora:
{3}||teddi  

The special edge with 3 incident mibdies of this polychoron (each being adjoined with their special wedge edge) also allows for a 5-fold counterpart: xfoxo oxfox5ooofx&#xt. (A 4-fold version does not exist, so.)

Any mibdi here allows for an independant augmentation by an appropriate pyramid. The corresponding triaugmentation then is xofox ooxfo3oxoox&#xt.

In the above lace city the lower diagonal from the left b via the medial c towards the right d provides a teddi sectioning facet. If dissected at that hyperplane the polychoron falls into {3}||teddi (at the lower left) and tetu (at the upper right).


Incidence matrix according to Dynkin symbol

xfox oxfo3ooox&#xt   → height(1,2) = sqrt[(7+3 sqrt(5))/24] = 0.755761
                       height(2,3) = sqrt[(3+sqrt(5))/24] = 0.467086
                       height(3,4) = sqrt(3)/6 = 1/sqrt(12) = 0.288675

o... o...3o...     | 2 * * * | 1 3 0 0  0  0 0 0 | 3 3 0  0 0 0 0 0 0 0 | 3 1 0 0 0 0	a
.o.. .o..3.o..     | * 6 * * | 0 1 2 1  2  0 0 0 | 1 2 1  2 2 1 0 0 0 0 | 2 1 1 1 0 0	b
..o. ..o.3..o.     | * * 3 * | 0 0 0 2  0  4 0 0 | 1 0 0  4 0 0 2 2 0 0 | 2 0 0 2 1 0	c
...o ...o3...o     | * * * 6 | 0 0 0 0  2  2 1 2 | 0 0 0  2 1 2 2 2 2 1 | 1 0 1 2 2 1	d
-------------------+---------+-------------------+----------------------+------------
x... .... ....     | 2 0 0 0 | 1 * * *  *  * * * | 3 0 0  0 0 0 0 0 0 0 | 3 0 0 0 0 0
oo.. oo..3oo..&#x  | 1 1 0 0 | * 6 * *  *  * * * | 1 2 0  0 0 0 0 0 0 0 | 2 1 0 0 0 0
.... .x.. ....     | 0 2 0 0 | * * 6 *  *  * * * | 0 1 1  0 1 0 0 0 0 0 | 1 1 1 0 0 0
.oo. .oo.3.oo.&#x  | 0 1 1 0 | * * * 6  *  * * * | 1 0 0  2 0 0 0 0 0 0 | 2 0 0 1 0 0
.o.o .o.o3.o.o&#x  | 0 1 0 1 | * * * * 12  * * * | 0 0 0  1 1 1 0 0 0 0 | 1 0 1 1 0 0
..oo ..oo3..oo&#x  | 0 0 1 1 | * * * *  * 12 * * | 0 0 0  1 0 0 1 1 0 0 | 1 0 0 1 1 0
...x .... ....     | 0 0 0 2 | * * * *  *  * 3 * | 0 0 0  0 0 0 2 0 2 0 | 1 0 0 0 2 1
.... .... ...x     | 0 0 0 2 | * * * *  *  * * 6 | 0 0 0  0 0 1 0 1 1 1 | 0 0 1 1 1 1
-------------------+---------+-------------------+----------------------+------------
xfo. .... ....&#xt | 2 2 1 0 | 1 2 0 2  0  0 0 0 | 3 * *  * * * * * * * | 2 0 0 0 0 0
.... ox.. ....&#x  | 1 2 0 0 | 0 2 1 0  0  0 0 0 | * 6 *  * * * * * * * | 1 1 0 0 0 0
.... .x..3.o..     | 0 3 0 0 | 0 0 3 0  0  0 0 0 | * * 2  * * * * * * * | 0 1 1 0 0 0
.ooo .ooo3.ooo&#x  | 0 1 1 1 | 0 0 0 1  1  1 0 0 | * * * 12 * * * * * * | 1 0 0 1 0 0
.... .x.o ....&#x  | 0 2 0 1 | 0 0 1 0  2  0 0 0 | * * *  * 6 * * * * * | 1 0 1 0 0 0
.... .... .o.x&#x  | 0 1 0 2 | 0 0 0 0  2  0 0 1 | * * *  * * 6 * * * * | 0 0 1 1 0 0
..ox .... ....&#x  | 0 0 1 2 | 0 0 0 0  0  2 1 0 | * * *  * * * 6 * * * | 1 0 0 0 1 0
.... .... ..ox&#x  | 0 0 1 2 | 0 0 0 0  0  2 0 1 | * * *  * * * * 6 * * | 0 0 0 1 1 0
...x .... ...x     | 0 0 0 4 | 0 0 0 0  0  0 2 2 | * * *  * * * * * 3 * | 0 0 0 0 1 1
.... ...o3...x     | 0 0 0 3 | 0 0 0 0  0  0 0 3 | * * *  * * * * * * 2 | 0 0 1 0 0 1
-------------------+---------+-------------------+----------------------+------------
xfox oxfo ....&#xt  2 4 2 2 | 1 4 2 4  4  4 1 0 | 2 2 0  4 2 0 2 0 0 0 | 3 * * * * *
.... ox..3oo..&#x   1 3 0 0 | 0 3 3 0  0  0 0 0 | 0 3 1  0 0 0 0 0 0 0 | * 2 * * * *
.... .x.o3.o.x&#x   0 3 0 3 | 0 0 3 0  6  0 0 3 | 0 0 1  0 3 3 0 0 0 1 | * * 2 * * *
.... .... .oox&#x   0 1 1 2 | 0 0 0 1  2  2 0 1 | 0 0 0  2 0 1 0 1 0 0 | * * * 6 * *
..ox .... ..ox&#x   0 0 1 4 | 0 0 0 0  0  4 2 2 | 0 0 0  0 0 0 2 2 1 0 | * * * * 3 *
...x ...o3...x      0 0 0 6 | 0 0 0 0  0  0 3 6 | 0 0 0  0 0 0 0 0 3 2 | * * * * * 1

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