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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 
(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
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(1)
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(2)
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(3)
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