Acronym ...
Name q3o3o4x,
variation of sidpith
Circumradius sqrt(3) = 1.732051
Lace city
in approx. ASCII-art 
    o4x o4x    		-- o3o4x
               
o4x q4x q4x o4x		-- q3o4x
               
o4x q4x q4x o4x		-- q3o4x
               
    o4x o4x    		-- o3o4x
Coordinates (3/2, 1/2, 1/2, 1/2)   & all permutations, all changes of sign
General of army (is itself convex)
Colonel of regiment (is itself locally convex)
Dihedral angles
  • at q-{3} between q-tet and x q3o:   150°
  • at (x,q)-{4} between q x4o and x q3o:   arccos[-sqrt(2/3)] = 144.735610°
  • at x-{4} between q x4o and x-cube:   135°
Face vector 64, 192, 208, 80
Confer
uniform variant:
sidpith  
related isogonals:
x3o3o4q   Q3o3o4x  

Incidence matrix according to Dynkin symbol

q3o3o4x

. . . . | 64 |  3  3 |  3  6  3 |  1  3  3 1
--------+----+-------+----------+-----------
q . . . |  2 | 96  * |  2  2  0 |  1  2  1 0  q
. . . x |  2 |  * 96 |  0  2  2 |  0  1  2 1  x
--------+----+-------+----------+-----------
q3o . . |  3 |  3  0 | 64  *  * |  1  1  0 0
q . . x |  4 |  2  2 |  * 96  * |  0  1  1 0
. . o4x |  4 |  0  4 |  *  * 48 |  0  0  1 1
--------+----+-------+----------+-----------
q3o3o . ♦  4 |  6  0 |  4  0  0 | 16  *  * *
q3o . x ♦  6 |  6  3 |  2  3  0 |  * 32  * *
q . o4x ♦  8 |  4  8 |  0  4  2 |  *  * 24 *
. o3o4x ♦  8 |  0 12 |  0  0  6 |  *  *  * 8

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