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Parabigyrate Rhombicosidodecahedron


J73J73Net

The metabigyrate rhombicosidodecahedron is a convex equilateral solid obtained by rotating two of the pentagonal cupolas of a small rhombicosidodecahedron located in the "para" (in the chemical arene substitution pattern sense) by 1/10 of a turn each. It is Johnson solid J_(73).

The unit parabigyrate rhombicosidodecahedron has volume

 V=20+(29)/3sqrt(5)
(1)

and Dehn invariant

D=60<3>_5-30<5>_1
(2)
=30sin^(-1)((5-4sqrt(5))/(15)),
(3)

where the first expression uses the basis of Conway et al. (1999). It can be dissected into the gryrate rhombicosidodecahedron, parabigyrate rhombicosidodecahedron, small rhombicosidodecahedron, and trigyrate rhombicosidodecahedron (E. Weisstein, Aug. 17, 2023).


See also

Gyrate Rhombicosidodecahedron, Johnson Solid, Metabigyrate Rhombicosidodecahedron, Small Rhombicosidodecahedron, Trigyrate 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. "Parabigyrate Rhombicosidodecahedron." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/ParabigyrateRhombicosidodecahedron.html

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