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The tridiminished icosahedron is Johnson solid 
.
Interestingly, its skeleton has the same degree
sequence as the triangular cupola.
Tridiminished Icosahedron
See also
Diminished Polyhedron, Johnson Solid, Regular IcosahedronExplore with Wolfram|Alpha
Cite this as:
Weisstein, Eric W. "Tridiminished Icosahedron." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/TridiminishedIcosahedron.html