Johnson Solids (Page 3)

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(J45) Gyroelongated Square Bicupola
Vertices:  24  (8[4] + {8 * 2}[5])
Faces:34  ({8 * 3} equilateral triangles + {8 + 2} squares)
Edges:56
Symmetry:  4-fold Dihedral  (D4)
(values below based on edge length = 1)
Volume:2*(3+2*sqrt(2)+sqrt(2*(2+sqrt(2)    
    +sqrt(146+103*sqrt(2)))))/3    
≈8.15357483362126340253