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Gyrate Bidiminished Rhombicosidodecahedron

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J82
J82Net

The gyrate bidiminished rhombicosidodecahedron is a convex equilateral solid that is Johnson solid J_(82).

The unit gyrate bidiminished rhombicosidodecahedron has volume

V=5/3(11+5sqrt(5))
(1)

and Dehn invariant

D=30<3>_5-25<5>_1
(2)
=5[3cot^(-1)(2/(sqrt(5)))-5tan^(-1)2],
(3)

where the first expression uses the basis of Conway et al. (1999). It can be dissected into the metabidiminished rhombicosidodecahedron and parabidiminished rhombicosidodecahedron, from which it differs only by the position at which the cupolas are removed.

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. "Gyrate Bidiminished Rhombicosidodecahedron." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/GyrateBidiminishedRhombicosidodecahedron.html

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