Acronym  chopy, pt  cho 
Name  (degenerate) cubohemioctahedron pyramid 
Circumradius  ∞ i.e. flat in euclidean space 
Dihedral angles  
Confer 

It either can be thought of as a degenerate 4D segmentotope with zero height, or as a 3D euclidean decomposition of the larger base into smaller bits.
Incidence matrix according to Dynkin symbol
pt  cho → height = 0 1 * ♦ 12 0  24 0 0  6 4 0 * 12  1 4  4 2 2  2 2 1 +++ 1 1  12 *  4 0 0  2 2 0 0 2  * 24  1 1 1  1 1 1 +++ 1 2  2 1  24 * *  1 1 0 0 4  0 4  * 6 *  1 0 1 0 6  0 6  * * 4  0 1 1 +++ ♦ 1 4  4 4  4 1 0  6 * * ♦ 1 6  6 6  6 0 1  * 4 * ♦ 0 12  0 24  0 6 4  * * 1
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