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Bigyrate Diminished Rhombicosidodecahedron

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The bigyrate diminished rhombicosidodecahedron is a convex equilateral solid that is Johnson solid J_(79).

The unit bigyrate diminished rhombicosidodecahedron has volume

V=(115)/6+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 diminished rhombicosidodecahedron, metagyrate diminished rhombicosidodecahedron, and paragyrate 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. "Bigyrate Diminished Rhombicosidodecahedron." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/BigyrateDiminishedRhombicosidodecahedron.html

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