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Pentagonal Rotunda


J06J06Net

The pentagonal rotunda is a convex polyhedron consisting of half of an icosidodecahedron, with the base being filled in by a decagon. It has 10 triangular and five pentagonal faces separating a pentagonal ceiling and a decagonal floor. It is Johnson solid J_6 (and hence has all edge lengths equal), and the only true rotunda.

For a pentagonal rotunda with unit edge length, the height, surface area, and volume are given by

h=sqrt(1/5(5+2sqrt(5)))
(1)
S=5/2(sqrt(3)+sqrt(26+(58)/(sqrt(5))))
(2)
V=1/(12)(45+17sqrt(5)).
(3)

See also

Icosidodecahedron, Johnson Solid, Rotunda

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Cite this as:

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

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