Johnson Solids (Page 1)

(box: x-ray)  (F: faces)  (slider: perspective)  (image: L=rotate R=zoom)  (M: metrics)

(J19) Elongated Square Cupola
Vertices:  20  (8[3] + {8 + 4}[4])
Faces:18  (4 equilateral triangles + {4 * 3 + 1} squares
    + 1 regular octagon)
Edges:36
Symmetry:  4-fold Pyramidal  (C4v)
(values below based on edge length = 1)
Volume:(9+8*sqrt(2))/3    ≈6.77123616632825346347