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Square Orthobicupola

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J28
J28Net

The square orthobicupola is a convex equilateral solid that is Johnson solid J_(28).

The unit square orthobicupola has volume

V=2+4/3sqrt(2)
(1)

and Dehn invariant

D=24<3>_2
(2)
=24tan^(-1)(sqrt(2)),
(3)

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

See also

Johnson Solid, Square Gyrobicupola

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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. "Square Orthobicupola." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/SquareOrthobicupola.html

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