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Elongated Pentagonal Orthobicupola

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J38
J38Net

The elongated pentagonal orthobicupola is a convex equilateral solid that is Johnson solid J_(38).

The unit elongated pentagonal orthobicupola has volume

V=1/6(10+8sqrt(5)+15sqrt(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 elongated pentagonal gyrobicupola, from which it differs only by relative rotation of the top and bottom 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. "Elongated Pentagonal Orthobicupola." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/ElongatedPentagonalOrthobicupola.html

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