Acronym  ... 
Name  2thah (?) 
Circumradius  1/sqrt(2) = 0.707107 
Vertex figure  2[3/2,4,3,4]/0 
General of army  oct 
Colonel of regiment  oct 
Confer 

Looks like a compound of 2 tetrahemihexahedra (thah), and indeed vertices, edges, and faces all coincide by pairs. Each individual vertex figure is the same as the vertex figure of thah, a crossed square.
Incidence matrix according to Dynkin symbol
x3/2o3x . . .  12  2 2  1 2 1 +++ x . .  2  12 *  1 1 0 . . x  2  * 12  0 1 1 +++ x3/2o .  3  3 0  4 * * x . x  4  2 2  * 6 * o3x  3  0 3  * * 4 snubbed forms: β3/2o3x, x3/2o3β, β3/2o3β
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