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Paragyrate Diminished Rhombicosidodecahedron

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J77
J77Net

The paragyrate diminished rhombicosidodecahedron is a convex equilateral solid that is Johnson solid J_(77).

The unit paragyrate diminished rhombicosidodecahedron has volume

V=2(116)/9+9sqrt(5)
(1)

and Dehn invariant

D=45<3>_5-(55)/2<5>_1
(2)
=5/2[9cot^(-1)(2/(sqrt(5)))-11tan^(-1)2],
(3)

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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