Johnson Solids (Page 3)

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(J53) Biaugmented Pentagonal Prism
Vertices:  12  (2[3] + {4 * 2 + 2}[4])
Faces:13  ({4 + 2 * 2} equilateral triangles + {2 + 1} squares
    + 2 regular pentagons)
Edges:23
Symmetry:  2-fold Pyramidal  (C2v)
(values below based on edge length = 1)
Volume:sqrt(257+90*sqrt(5)    
    +24*sqrt(10*(5+2*sqrt(5))))/12    
≈2.1918819213799986057