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Metagyrate Diminished Rhombicosidodecahedron

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The metagyrate diminished rhombicosidodecahedron is a convex equilateral solid that is Johnson solid J_(78).

The unit metagyrate 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 bigyrate diminished rhombicosidodecahedron, 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. "Metagyrate Diminished Rhombicosidodecahedron." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/MetagyrateDiminishedRhombicosidodecahedron.html

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