Elongated cupola

In geometry, the elongated cupolae are an infinite set of polyhedra, constructed by adjoining an n-gonal cupola to a 2n-gonal prism.

There are three elongated cupolae that are Johnson solids made from regular triangles, squares, and pentagons. Higher forms can be constructed with isosceles triangles. Adjoining a triangular prism to a cube also generates a polyhedron, but has two pairs of coplanar faces, so is not a Johnson solid. Higher forms can be constructed without regular faces.

Forms

See also

• Gyroelongated cupola
• Bicupola
• Elongated bicupola
• Gyroelongated bicupola
• Rotunda

References

• Norman W. Johnson, "Convex Solids with Regular Faces", Canadian Journal of Mathematics, 18, 1966, pages 169–200. Contains the original enumeration of the 92 solids and the conjecture that there are no others.
• The first proof that there are only 92 Johnson solids.