Johnson Solids (Page 3)

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(J41) Elongated Pentagonal Gyrocupolarotunda
Vertices:  35  ({10 * 2 + 5 * 3}[4])
Faces:37  ({5 * 3} equilateral triangles + {5 * 3} squares
    + {5 + 1 * 2} regular pentagons)
Edges:70
Symmetry:  5-fold Pyramidal  (C5v)
(values below based on edge length = 1)
Volume:5*(11+5*sqrt(5)    
    +6*sqrt(5+2*sqrt(5)))/12    
≈16.936017129396028707