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Metabidiminished Icosahedron

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J62
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The metabidiminished icosahedron is a convex equilateral solid that is Johnson solid J_(62).

The unit metabidiminished icosahedron has volume

V=1/6(5+2sqrt(5))
(1)

and Dehn invariant

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

where the first expression uses the basis of Conway et al. (1999). It can be dissected into the pentagonal antiprism (E. Weisstein, Sep. 6, 2023).

See also

Diminished Polyhedron, Regular Icosahedron

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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 Icosahedron." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/MetabidiminishedIcosahedron.html

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