A triaugmented dodecahedron is formed by attaching pentagonal pyramids to three mutually nonadjacent faces of a regular dodecahedron.
The convex equilateral form with regular polygonal faces
is the Johnson solid 
.
It has 23 polyhedron vertices, 45 polyhedron edges, and 24 faces. The faces
consist of 15 equilateral triangles and 9
regular pentagons (McCooey).
See also
Augmentation,
Pentagonal
Pyramid,
Regular Dodecahedron
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References
Johnson, N. W. "Convex Polyhedra with Regular Faces." Canad. J. Math. 18, 169-200, 1966. https://doi.org/10.4153/CJM-1966-021-8.McCooey,
D. I. "Triaugmented Dodecahedron." https://dmccooey.com/polyhedra/TriaugmentedDodecahedron.html.Referenced
on Wolfram|Alpha
Triaugmented Dodecahedron
Cite this as:
Weisstein, Eric W. "Triaugmented Dodecahedron."
From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/TriaugmentedDodecahedron.html
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