Acronym  ... 
Name  2cho (?) 
Circumradius  1 
Vertex figure  2[4/3,6,4,6] 
Coordinates  (1/sqrt(2), 1/sqrt(2), 0) & all permutations, all changes of sign 
General of army  co 
Colonel of regiment  co 
Confer 

Looks like a compound of 2 cubohemioctahedra (cho), and indeed vertices, edges, and faces all coincide by pairs.
Incidence matrix according to Dynkin symbol
o4/3x3x4*a . . .  24  2 2  1 2 1 +++ . x .  2  24 *  1 1 0 . . x  2  * 24  0 1 1 +++ o4/3x .  4  4 0  6 * * . x3x  6  3 3  * 8 * o . x4*a  4  0 4  * * 6
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