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Elongated Triangular Orthobicupola

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J35
J35Net

The elongated triangular orthobicupola is a convex equilateral solid that is Johnson solid J_(35).

The unit longated triangular orthobicupola has volume

V=5/3sqrt(2)+3/2sqrt(3)
(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 elongated triangular gyrobicupola, from which it differs only by relative rotation of the top and bottom cupolas.

See also

Johnson Solid, Triangular Orthobicupola

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

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