|Set of elongated cupolae|
Example pentagonal form
|Symmetry group||Cnv, [n], (*nn)|
|Rotational group||Cn, [n]+, (nn)|
There are three elongated cupolae that are Johnson solids made from regular triangles and square, and pentagons. Higher forms can be constructed with isosceles triangles. Adjoining a triangular prism to a cube also generates a polyhedron, but has adjacent parallel faces, so is not a Johnson solid. Higher forms can be constructed without regular faces.
|elongated triangular prism||2 triangles, 6+1 squares|
|elongated triangular cupola (J18)||3+1 triangles, 9 squares, 1 hexagon|
|elongated square cupola (J19)||4 triangles, 12+1 squares, 1 octagon|
|elongated pentagonal cupola (J20)||5 triangles, 15 squares, 1 pentagon, 1 decagon|
|elongated hexagonal cupola||6 triangles, 18 squares, 1 hexagon, 1 dodecagon|
- 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.
- Victor A. Zalgaller (1969). Convex Polyhedra with Regular Faces. Consultants Bureau. No ISBN. The first proof that there are only 92 Johnson solids.
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