Johnson Solids (Page 4)

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(J65) Augmented Truncated Tetrahedron
Vertices:  15  ({3 * 2}[3] + {6 + 3}[4])
Faces:14  ({3 * 2 + 1 * 2} equilateral triangles + 3 squares
    + 3 regular hexagons)
Edges:27
Symmetry:  3-fold Pyramidal  (C3v)
(values below based on edge length = 1)
Volume:11*sqrt(2)/4    ≈3.8890872965260113842