Cupola (geometry)

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For other uses, see cupola (disambiguation).

Pentagonal cupola

Type	Set of cupolas
Faces	n triangles, n squares 1 n-agon, 1 2n-agon
Edges	5n
Vertices	3n
Symmetry group	C_nv
Dual polyhedron	?
Properties	convex

In geometry, a cupola is a solid formed by joining two polygons, one (the base) with twice as many edges as the other, by an alternating band of triangles and rectangles. The triangular, square, and pentagonal cupolae all count among the Johnson solids, and can be formed by taking sections of the cuboctahedron, rhombicuboctahedron, and rhombicosidodecahedron, respectively.

A cupola can be seen as a prism where one of the polygons has been collapsed in half by merging alternate vertices.

Cupolae are a subclass of the prismatoids.

Examples

The digonal cupola (wedge)	The triangular cupola with regular faces (J3)
The square cupola with regular faces (J4)	The pentagonal cupola with regular faces (J5)

Plane "hexagonal cupolas" in one of the 8 semiregular tessellations

The above-mentioned three polyhedra are the only non-trivial cupolae with regular faces: The "hexagonal cupola" is a plane figure, and the triangular prism might be considered a "cupola" of degree 2 (the cupola of a line segment and a square). However, cupolae of higher-degree polygons may be constructed with irregular triangular and rectangular faces.

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