The diminished rhombicosidodecahedron is a convex equilateral solid that is Johnson solid .

This solid is the diminished polyhedron obtained by diminishing a small rhombicosidodecahedron
by one of its pentagonal cupolas .

The unit diminished rhombicosidodecahedron has volume

(1)

and Dehn invariant

where the first expression uses the basis of Conway et al. (1999). It can be dissected into the bigyrate
diminished rhombicosidodecahedron , metagyrate
diminished rhombicosidodecahedron , and paragyrate
diminished rhombicosidodecahedron , all of which differ only by rotation of one
or more pentagonal cupolas.

See also Diminished Polyhedron ,

Small Rhombicosidodecahedron
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References Conway, J. H.; Radin, C.; and Sadun, L. "On Angles Whose Squared Trigonometric Functions Are Rational." Discr. Computat. Geom. 22 ,
321-332, 1999. Johnson, N. W. "Convex Polyhedra with Regular
Faces." Canad. J. Math. 18 , 169-200, 1966.
Cite this as:
Weisstein, Eric W. "Diminished Rhombicosidodecahedron."
From MathWorld --A Wolfram Web Resource. https://mathworld.wolfram.com/DiminishedRhombicosidodecahedron.html

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