Acronym octhipdaw (alt.: traporhip)
Name (oct,hip)-disphenoid,
trigonal antiprism atop axis-orthogonal hexagonal prism
Circumradius sqrt[(183+64 sqrt(3))/222] = 1.150502
Lace hyper city
in approx. ASCII-art
x3o             
             o3x
                
            x3x 
                
                
 x3x            
(disphenoid in configuration space)
Confer
general polytopal classes:
segmentotera  

Incidence matrix according to Dynkin symbol

oxxx3xoxx&#x   → height(1,2) = height(1,3) = height(1,4) = height(2,3) = height(2,4) = sqrt(2/3) = 0.816497
                 height(2,4) = 1
                 height(12,34) = sqrt[(8 sqrt(3)-9)/12] = 0.636161
(3-ap || axis-ortho hip)

o...3o...    | 3 * * * | 2 2 2 2 0 0 0 0 0 0 0 0 | 1 1 2 2 2 1 2 2 1 2 0 0 0 0 0 0 0 0 0 0 | 1 1 2 2 1 2 1 1 2 1 0 0 0 0 0 | 1 1 2 1 1 0
.o..3.o..    | * 3 * * | 0 2 0 0 2 2 2 0 0 0 0 0 | 0 2 1 2 2 0 0 0 0 0 1 2 1 2 2 1 0 0 0 0 | 1 2 1 2 2 1 0 0 0 0 1 2 1 1 0 | 1 2 1 1 0 1
..o.3..o.    | * * 6 * | 0 0 1 0 0 1 0 1 1 1 0 0 | 0 0 0 1 0 1 1 1 0 0 0 1 1 1 0 0 1 1 1 0 | 0 1 1 1 0 0 1 1 1 0 1 1 1 0 1 | 1 1 1 0 1 1
...o3...o    | * * * 6 | 0 0 0 1 0 0 1 0 0 1 1 1 | 0 0 0 0 1 0 0 1 1 1 0 0 0 1 1 1 0 1 1 1 | 0 0 0 1 1 1 0 1 1 1 0 1 1 1 1 | 0 1 1 1 1 1
-------------+---------+-------------------------+-----------------------------------------+-------------------------------+------------
.... x...    | 2 0 0 0 | 3 * * * * * * * * * * * | 1 0 1 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 | 1 0 1 0 0 1 1 0 1 1 0 0 0 0 0 | 1 0 1 1 1 0
oo..3oo..&#x | 1 1 0 0 | * 6 * * * * * * * * * * | 0 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 | 1 1 1 1 0 0
o.o.3o.o.&#x | 1 0 1 0 | * * 6 * * * * * * * * * | 0 0 0 1 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 | 0 1 1 1 0 0 1 1 1 0 0 0 0 0 0 | 1 1 1 0 1 0
o..o3o..o&#x | 1 0 0 1 | * * * 6 * * * * * * * * | 0 0 0 0 1 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 | 0 0 0 1 1 1 0 1 1 1 0 0 0 0 0 | 0 1 1 1 1 0
.x.. ....    | 0 2 0 0 | * * * * 3 * * * * * * * | 0 1 0 0 0 0 0 0 0 0 1 1 0 0 1 0 0 0 0 0 | 1 1 0 0 1 0 0 0 0 0 1 1 0 1 0 | 1 1 0 1 0 1
.oo.3.oo.&#x | 0 1 1 0 | * * * * * 6 * * * * * * | 0 0 0 1 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 | 0 1 1 1 0 0 0 0 0 0 1 1 1 0 0 | 1 1 1 0 0 1
.o.o3.o.o&#x | 0 1 0 1 | * * * * * * 6 * * * * * | 0 0 0 0 1 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 | 0 0 0 1 1 1 0 0 0 0 0 1 1 1 0 | 0 1 1 1 0 1
..x. ....    | 0 0 2 0 | * * * * * * * 3 * * * * | 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 1 1 0 0 | 0 1 0 0 0 0 1 1 0 0 1 1 0 0 1 | 1 1 0 0 1 1
.... ..x.    | 0 0 2 0 | * * * * * * * * 3 * * * | 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 1 0 1 0 | 0 0 1 0 0 0 1 0 1 0 1 0 1 0 1 | 1 0 1 0 1 1
..oo3..oo&#x | 0 0 1 1 | * * * * * * * * * 6 * * | 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 1 1 0 | 0 0 0 1 0 0 0 1 1 0 0 1 1 0 1 | 0 1 1 0 1 1
...x ....    | 0 0 0 2 | * * * * * * * * * * 3 * | 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 1 0 1 | 0 0 0 0 1 0 0 1 0 1 0 1 0 1 1 | 0 1 0 1 1 1
.... ...x    | 0 0 0 2 | * * * * * * * * * * * 3 | 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 1 1 | 0 0 0 0 0 1 0 0 1 1 0 0 1 1 1 | 0 0 1 1 1 1
-------------+---------+-------------------------+-----------------------------------------+-------------------------------+------------
o...3x...    | 3 0 0 0 | 3 0 0 0 0 0 0 0 0 0 0 0 | 1 * * * * * * * * * * * * * * * * * * * | 1 0 0 0 0 0 1 0 0 1 0 0 0 0 0 | 1 0 0 1 1 0
ox.. ....&#x | 1 2 0 0 | 0 2 0 0 1 0 0 0 0 0 0 0 | * 3 * * * * * * * * * * * * * * * * * * | 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 | 1 1 0 1 0 0
.... xo..&#x | 2 1 0 0 | 1 2 0 0 0 0 0 0 0 0 0 0 | * * 3 * * * * * * * * * * * * * * * * * | 1 0 1 0 0 1 0 0 0 0 0 0 0 0 0 | 1 0 1 1 0 0
ooo.3ooo.&#x | 1 1 1 0 | 0 1 1 0 0 1 0 0 0 0 0 0 | * * * 6 * * * * * * * * * * * * * * * * | 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 | 1 1 1 0 0 0
oo.o3oo.o&#x | 1 1 0 1 | 0 1 0 1 0 0 1 0 0 0 0 0 | * * * * 6 * * * * * * * * * * * * * * * | 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 | 0 1 1 1 0 0
o.x. ....&#x | 1 0 2 0 | 0 0 2 0 0 0 0 1 0 0 0 0 | * * * * * 3 * * * * * * * * * * * * * * | 0 1 0 0 0 0 1 1 0 0 0 0 0 0 0 | 1 1 0 0 1 0
.... x.x.&#x | 2 0 2 0 | 1 0 2 0 0 0 0 0 1 0 0 0 | * * * * * * 3 * * * * * * * * * * * * * | 0 0 1 0 0 0 1 0 1 0 0 0 0 0 0 | 1 0 1 0 1 0
o.oo3o.oo&#x | 1 0 1 1 | 0 0 1 1 0 0 0 0 0 1 0 0 | * * * * * * * 6 * * * * * * * * * * * * | 0 0 0 1 0 0 0 1 1 0 0 0 0 0 0 | 0 1 1 0 1 0
o..x ....&#x | 1 0 0 2 | 0 0 0 2 0 0 0 0 0 0 1 0 | * * * * * * * * 3 * * * * * * * * * * * | 0 0 0 0 1 0 0 1 0 1 0 0 0 0 0 | 0 1 0 1 1 0
.... x..x&#x | 2 0 0 2 | 1 0 0 2 0 0 0 0 0 0 0 1 | * * * * * * * * * 3 * * * * * * * * * * | 0 0 0 0 0 1 0 0 1 1 0 0 0 0 0 | 0 0 1 1 1 0
.x..3.o..    | 0 3 0 0 | 0 0 0 0 3 0 0 0 0 0 0 0 | * * * * * * * * * * 1 * * * * * * * * * | 1 0 0 0 0 0 0 0 0 0 1 0 0 1 0 | 1 0 0 1 0 1
.xx. ....&#x | 0 2 2 0 | 0 0 0 0 1 2 0 1 0 0 0 0 | * * * * * * * * * * * 3 * * * * * * * * | 0 1 0 0 0 0 0 0 0 0 1 1 0 0 0 | 1 1 0 0 0 1
.... .ox.&#x | 0 1 2 0 | 0 0 0 0 0 2 0 0 1 0 0 0 | * * * * * * * * * * * * 3 * * * * * * * | 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 | 1 0 1 0 0 1
.ooo3.ooo&#x | 0 1 1 1 | 0 0 0 0 0 1 1 0 0 1 0 0 | * * * * * * * * * * * * * 6 * * * * * * | 0 0 0 1 0 0 0 0 0 0 0 1 1 0 0 | 0 1 1 0 0 1
.x.x ....&#x | 0 2 0 2 | 0 0 0 0 1 0 2 0 0 0 1 0 | * * * * * * * * * * * * * * 3 * * * * * | 0 0 0 0 1 0 0 0 0 0 0 1 0 1 0 | 0 1 0 1 0 1
.... .o.x&#x | 0 1 0 2 | 0 0 0 0 0 0 2 0 0 0 0 1 | * * * * * * * * * * * * * * * 3 * * * * | 0 0 0 0 0 1 0 0 0 0 0 0 1 1 0 | 0 0 1 1 0 1
..x.3..x.    | 0 0 6 0 | 0 0 0 0 0 0 0 3 3 0 0 0 | * * * * * * * * * * * * * * * * 1 * * * | 0 0 0 0 0 0 1 0 0 0 1 0 0 0 1 | 1 0 0 0 1 1
..xx ....&#x | 0 0 2 2 | 0 0 0 0 0 0 0 1 0 2 1 0 | * * * * * * * * * * * * * * * * * 3 * * | 0 0 0 0 0 0 0 1 0 0 0 1 0 0 1 | 0 1 0 0 1 1
.... ..xx&#x | 0 0 2 2 | 0 0 0 0 0 0 0 0 1 2 0 1 | * * * * * * * * * * * * * * * * * * 3 * | 0 0 0 0 0 0 0 0 1 0 0 0 1 0 1 | 0 0 1 0 1 1
...x3...x    | 0 0 0 6 | 0 0 0 0 0 0 0 0 0 0 3 3 | * * * * * * * * * * * * * * * * * * * 1 | 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 | 0 0 0 1 1 1
-------------+---------+-------------------------+-----------------------------------------+-------------------------------+------------
ox..3xo..&#x  3 3 0 0 | 3 6 0 0 3 0 0 0 0 0 0 0 | 1 3 3 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 | 1 * * * * * * * * * * * * * * | 1 0 0 1 0 0
oxx. ....&#x  1 2 2 0 | 0 2 2 0 1 2 0 1 0 0 0 0 | 0 1 0 2 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 | * 3 * * * * * * * * * * * * * | 1 1 0 0 0 0
.... xox.&#x  2 1 2 0 | 1 2 2 0 0 2 0 0 1 0 0 0 | 0 0 1 2 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 | * * 3 * * * * * * * * * * * * | 1 0 1 0 0 0
oooo3oooo&#x  1 1 1 1 | 0 1 1 1 0 1 1 0 0 1 0 0 | 0 0 0 1 1 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 | * * * 6 * * * * * * * * * * * | 0 1 1 0 0 0
ox.x ....&#x  1 2 0 2 | 0 2 0 2 1 0 2 0 0 0 1 0 | 0 1 0 0 2 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 | * * * * 3 * * * * * * * * * * | 0 1 0 1 0 0
.... xo.x&#x  2 1 0 2 | 1 2 0 2 0 0 2 0 0 0 0 1 | 0 0 1 0 2 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 | * * * * * 3 * * * * * * * * * | 0 0 1 1 0 0
o.x.3x.x.&#x  3 0 6 0 | 3 0 6 0 0 0 0 3 3 0 0 0 | 1 0 0 0 0 3 3 0 0 0 0 0 0 0 0 0 1 0 0 0 | * * * * * * 1 * * * * * * * * | 1 0 0 0 1 0
o.xx ....&#x  1 0 2 2 | 0 0 2 2 0 0 0 1 0 2 1 0 | 0 0 0 0 0 1 0 2 1 0 0 0 0 0 0 0 0 1 0 0 | * * * * * * * 3 * * * * * * * | 0 1 0 0 1 0
.... x.xx&#x  2 0 2 2 | 1 0 2 2 0 0 0 0 1 2 0 1 | 0 0 0 0 0 0 1 2 0 1 0 0 0 0 0 0 0 0 1 0 | * * * * * * * * 3 * * * * * * | 0 0 1 0 1 0
o..x3x..x&#x  3 0 0 6 | 3 0 0 6 0 0 0 0 0 0 3 3 | 1 0 0 0 0 0 0 0 3 3 0 0 0 0 0 0 0 0 0 1 | * * * * * * * * * 1 * * * * * | 0 0 0 1 1 0
.xx.3.ox.&#x  0 3 6 0 | 0 0 0 0 3 6 0 3 3 0 0 0 | 0 0 0 0 0 0 0 0 0 0 1 3 3 0 0 0 1 0 0 0 | * * * * * * * * * * 1 * * * * | 1 0 0 0 0 1
.xxx ....&#x  0 2 2 2 | 0 0 0 0 1 2 2 1 0 2 1 0 | 0 0 0 0 0 0 0 0 0 0 0 1 0 2 1 0 0 1 0 0 | * * * * * * * * * * * 3 * * * | 0 1 0 0 0 1
.... .oxx&#x  0 1 2 2 | 0 0 0 0 0 2 2 0 1 2 0 1 | 0 0 0 0 0 0 0 0 0 0 0 0 1 2 0 1 0 0 1 0 | * * * * * * * * * * * * 3 * * | 0 0 1 0 0 1
.x.x3.o.x&#x  0 3 0 6 | 0 0 0 0 3 0 6 0 0 0 3 3 | 0 0 0 0 0 0 0 0 0 0 1 0 0 0 3 3 0 0 0 1 | * * * * * * * * * * * * * 1 * | 0 0 0 1 0 1
..xx3..xx&#x  0 0 6 6 | 0 0 0 0 0 0 0 3 3 6 3 3 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 3 3 1 | * * * * * * * * * * * * * * 1 | 0 0 0 0 1 1
-------------+---------+-------------------------+-----------------------------------------+-------------------------------+------------
oxx.3xox.&#x  3 3 6 0 | 3 6 6 0 3 6 0 3 3 0 0 0 | 1 3 3 6 0 3 3 0 0 0 1 3 3 0 0 0 1 0 0 0 | 1 3 3 0 0 0 1 0 0 0 1 0 0 0 0 | 1 * * * * *
oxxx ....&#x  1 2 2 2 | 0 2 2 2 1 2 2 1 0 2 1 0 | 0 1 0 2 2 1 0 2 1 0 0 1 0 2 1 0 0 1 0 0 | 0 1 0 2 1 0 0 1 0 0 0 1 0 0 0 | * 3 * * * *
.... xoxx&#x  2 1 2 2 | 1 2 2 2 0 2 2 0 1 2 0 1 | 0 0 1 2 2 0 1 2 0 1 0 0 1 2 0 1 0 0 1 0 | 0 0 1 2 0 1 0 0 1 0 0 0 1 0 0 | * * 3 * * *
ox.x3xo.x&#x  3 3 0 6 | 3 6 0 6 3 0 6 0 0 0 3 3 | 1 3 3 0 6 0 0 0 3 3 1 0 0 0 3 3 0 0 0 1 | 1 0 0 0 3 3 0 0 0 1 0 0 0 1 0 | * * * 1 * *
o.xx3x.xx&#x  3 0 6 6 | 3 0 6 6 0 0 0 3 3 6 3 3 | 1 0 0 0 0 3 3 6 3 3 0 0 0 0 0 0 1 3 3 1 | 0 0 0 0 0 0 1 3 3 1 0 0 0 0 1 | * * * * 1 *
.xxx3.oxx&#x  0 3 6 6 | 0 0 0 0 3 6 6 3 3 6 3 3 | 0 0 0 0 0 0 0 0 0 0 1 3 3 6 3 3 1 3 3 1 | 0 0 0 0 0 0 0 0 0 0 1 3 3 1 1 | * * * * * 1

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