Johnson Solids (Page 4)

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(J63) Tridiminished Icosahedron
Vertices:  9  ({3 * 2}[3] + 3[4])
Faces:8  ({3 + 1 * 2} equilateral triangles + 3 regular pentagons)
Edges:15
Symmetry:  3-fold Pyramidal  (C3v)
(values below based on edge length = 1)
Volume:(15+7*sqrt(5))/24    ≈1.277186493437438661453