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

The unit paragyrate 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 , diminished
rhombicosidodecahedron , and metagyrate
diminished rhombicosidodecahedron , from which it differs only by the relative
positions of the two removed 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. "Paragyrate Diminished Rhombicosidodecahedron."
From MathWorld --A Wolfram Web Resource. https://mathworld.wolfram.com/ParagyrateDiminishedRhombicosidodecahedron.html

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