Johnson Solids (Page 2)

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(J24) Gyroelongated Pentagonal Cupola
Vertices:  25  ({5 * 3}[4] + 10[5])
Faces:32  ({10 + 5 * 3} equilateral triangles + 5 squares
    + 1 regular pentagon + 1 regular decagon)
Edges:55
Symmetry:  5-fold Pyramidal  (C5v)
(values below based on edge length = 1)
Volume:(5+4*sqrt(5)+5*sqrt(2    
    *(sqrt(10*(65+29*sqrt(5)))    
    −1−sqrt(5))))/6    
≈9.0733331938801879931