Pentagonal Orthobirotunda

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The pentagonal orthobirotunda is a convex equilateral orthobirotunda having regular pentagonal upper and lower faces arranged symmetrically about the midplane. It is Johnson solid 👁 J_(30)
.

The unit pentagonal orthobirotunda has volume

and Dehn invariant

where the first expression uses the basis of Conway et al. (1999). It can be dissected into the regular icosidodecahedron, from which it differs only by the relative rotation of the top and bottom rotundas.

See also

Bicupola, Johnson Solid

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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.

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Pentagonal Orthobirotunda

Cite this as:

Weisstein, Eric W. "Pentagonal Orthobirotunda." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/PentagonalOrthobirotunda.html

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