Johnson Solids (Page 3)

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(J48) Gyroelongated Pentagonal Birotunda
Vertices:  40  ({10 * 2}[4] + {10 * 2}[5])
Faces:52  ({10 * 4} equilateral triangles + {10 + 2} regular pentagons)
Edges:90
Symmetry:  5-fold Dihedral  (D5)
(values below based on edge length = 1)
Volume:(45+17*sqrt(5)+5*sqrt(2    
    *(sqrt(10*(65+29*sqrt(5)))    
    −1−sqrt(5))))/6    
≈20.584813811796399002