Johnson Solids (Page 1)

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

(J10) Gyroelongated Square Pyramid
Vertices:  9  ({4 + 1}[4] + 4[5])
Faces:13  ({4 * 3} equilateral triangles + 1 square)
Edges:20
Symmetry:  4-fold Pyramidal  (C4v)
(values below based on edge length = 1)
Volume:(sqrt(2)+2*sqrt(4+3*sqrt(2)))/6    ≈1.1927022422322325591