Acronym ...
Name f3o3x,
variation of cuboctahedron
Circumradius sqrt[17+5 sqrt(5)]/4 = 1.327129
Coordinates 2/sqrt(8), τ2/sqrt(8), τ-1/sqrt(8))     & all even permutations, all changes of sign
where τ = (1+sqrt(5))/2
General of army (is itself convex)
Colonel of regiment (is itself locally convex)
Dihedral angles
  • between f3o and f . x:   arccos(-1/sqrt(3)) = 125.264390°
  • between o3x and f . x:   arccos(-1/sqrt(3)) = 125.264390°
Confer
uniform variant:
co  
variations:
a3b3c   q3o3x   u3o3x   v3o3x  

Incidence matrix according to Dynkin symbol

f3o3x

. . . | 12 |  2  2 | 1 2 1
------+----+-------+------
f . . |  2 | 12  * | 1 1 0
. . x |  2 |  * 12 | 0 1 1
------+----+-------+------
f3o . |  3 |  3  0 | 4 * *
f . x |  4 |  2  2 | * 6 *
. o3x |  3 |  0  3 | * * 4

f3/2o3/2x

.   .   . | 12 |  2  2 | 1 2 1
----------+----+-------+------
f   .   . |  2 | 12  * | 1 1 0
.   .   x |  2 |  * 12 | 0 1 1
----------+----+-------+------
f3/2o   . |  3 |  3  0 | 4 * *
f   .   x |  4 |  2  2 | * 6 *
.   o3/2x |  3 |  0  3 | * * 4

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