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