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Metabidiminished Rhombicosidodecahedron


J81J81Net

The metabidiminished rhombicosidodecahedron is a convex equilateral solid that is Johnson solid J_(81).

The unit metabidiminished 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 gyrate bidiminished 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. "Metabidiminished Rhombicosidodecahedron." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/MetabidiminishedRhombicosidodecahedron.html

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