TOPICS
Search

Pentagonal Orthobicupola

DOWNLOAD Mathematica NotebookDownload Wolfram Notebook
J30
J30Net

The pentagonal orthobicupola is a convex equilateral orthobicupola having regular pentagonal upper and lower faces. It is Johnson solid J_(30).

The unit pentagonal orthobicupola has volume

V=1/3(5+4sqrt(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 gyrobicupola, from which it differs only by the relative rotation of the top and bottom cupolas.

See also

Bicupola, Johnson Solid, Orthobicupola

Explore with Wolfram|Alpha

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

Subject classifications