Johnson Solids (Page 4)

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

(J64) Augmented Tridiminished Icosahedron
Vertices:  10  ({3 + 1}[3] + {3 * 2}[4])
Faces:10  ({3 * 2 + 1} equilateral triangles + 3 regular pentagons)
Edges:18
Symmetry:  3-fold Pyramidal  (C3v)
(values below based on edge length = 1)
Volume:(15+2*sqrt(2)+7*sqrt(5))/24    ≈1.3950376236351965822