A triaugmented truncated dodecahedron is formed by attaching three pentagonal cupolas to mutually nonadjacent decagonal faces
of a truncated dodecahedron. Each pentagonal
cupola is oriented so that its quadrilateral faces meet the triangular faces
of the truncated dodecahedron.
The convex equilateral form with regular polygonal faces
is the Johnson solid 
.
It has 75 polyhedron vertices, 135 polyhedron edges, and 62 faces. The faces
consist of 35 equilateral triangles, 15 squares, 3 regular pentagons,
and 9 regular decagons (McCooey).
See also
Augmented Truncated Dodecahedron,
Pentagonal Cupola,
Truncated
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 Truncated Dodecahedron." https://dmccooey.com/polyhedra/TriaugmentedTruncatedDodecahedron.html.Referenced
on Wolfram|Alpha
Triaugmented Truncated
Dodecahedron
Cite this as:
Weisstein, Eric W. "Triaugmented Truncated Dodecahedron." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/TriaugmentedTruncatedDodecahedron.html
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