Acronym ...
Name cyclo-hexagonally diminished ico,
tegum sum of 2 bi-dual (x,q)-triddips
Circumradius 1
Lace city
in approx. ASCII-art
   q3o   o3q   
               
o3q         q3o
               
   q3o   o3q   
    o3x     x3o    
                   
                   
x3o             o3x
                   
                   
    o3x     x3o    

This polychoron is obtained from a (unit) ico, when diminished at all 6 vertices of a vertex inscribed hexagon. As such it can also be considered as oct || cyclo-diminished co || oct.


Incidence matrix according to Dynkin symbol

xo3ox qo3oq&#zx   → height = 0
(tegum sum of 2 bi-dual (x,q)-triddips)

o.3o. o.3o.    | 9 * | 2 2  4 0 0 | 1 1  4  2  4  2 0 0 | 2 2 2 2
.o3.o .o3.o    | * 9 | 0 0  4 2 2 | 0 0  2  4  2  4 1 1 | 2 2 2 2
---------------+-----+------------+---------------------+--------
x. .. .. ..    | 2 0 | 9 *  * * * | 1 0  2  0  0  0 0 0 | 2 1 0 0  x
.. .. q. ..    | 2 0 | * 9  * * * | 0 1  0  0  2  0 0 0 | 0 0 1 2  q
oo3oo oo3oo&#x | 1 1 | * * 36 * * | 0 0  1  1  1  1 0 0 | 1 1 1 1  x
.. .x .. ..    | 0 2 | * *  * 9 * | 0 0  0  2  0  0 1 0 | 2 0 1 0  x
.. .. .. .q    | 0 2 | * *  * * 9 | 0 0  0  0  0  2 0 1 | 0 1 0 2  q
---------------+-----+------------+---------------------+--------
x.3o. .. ..    | 3 0 | 3 0  0 0 0 | 3 *  *  *  *  * * * | 2 0 0 0  (xxx)
.. .. q.3o.    | 3 0 | 0 3  0 0 0 | * 3  *  *  *  * * * | 0 0 0 2  (qqq)
xo .. .. ..&#x | 2 1 | 1 0  2 0 0 | * * 18  *  *  * * * | 1 1 0 0  (xxx)
.. ox .. ..&#x | 1 2 | 0 0  2 1 0 | * *  * 18  *  * * * | 1 0 1 0  (xxx)
.. .. qo ..&#x | 2 1 | 0 1  2 0 0 | * *  *  * 18  * * * | 0 0 1 1  (xxq)
.. .. .. oq&#x | 1 2 | 0 0  2 0 1 | * *  *  *  * 18 * * | 0 1 0 1  (xxq)
.o3.x .. ..    | 0 3 | 0 0  0 3 0 | * *  *  *  *  * 3 * | 2 0 0 0  (xxx)
.. .. .o3.q    | 0 3 | 0 0  0 0 3 | * *  *  *  *  * * 3 | 0 0 0 2  (qqq)
---------------+-----+------------+---------------------+--------
xo3ox .. ..&#x | 3 3 | 3 0  6 3 0 | 1 0  3  3  0  0 1 0 | 6 * * *  x-oct
xo .. .. oq&#x | 2 2 | 1 0  4 0 1 | 0 0  2  0  0  2 0 0 | * 9 * *  1/4 oct
.. ox qo ..&#x | 2 2 | 0 1  4 1 0 | 0 0  0  2  2  0 0 0 | * * 9 *  1/4 oct
.. .. qo3oq&#x | 3 3 | 0 3  6 0 3 | 0 1  0  0  3  3 0 1 | * * * 6  equ. cube segment

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