Johnson Solids (Page 5)

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(J92) Triangular Hebesphenorotunda
Vertices:  18  ({6 * 2 + 3 * 2}[4])
Faces:20  ({6 + 3 * 2 + 1} equilateral triangles + 3 squares
    + 3 regular pentagons + 1 regular hexagon)
Edges:36
Symmetry:  3-fold Pyramidal  (C3v)
(values below based on edge length = 1)
Volume:(15+7*sqrt(5))/6    ≈5.1087459737497546458