# Elongated pyramid

In geometry, the elongated pyramids are an infinite set of polyhedra, constructed by adjoining an n-gonal pyramid to an n-gonal prism. Along with the set of pyramids, these figures are topologically self-dual.

Set of elongated pyramids

Example Pentagonal form
Facesn triangles
n squares
1 n-gon
Edges4n
Vertices2n+1
Symmetry groupCnv, [n], (*nn)
Rotational groupCn, [n]+, (nn)
Dual polyhedronself-dual
Propertiesconvex

There are three elongated pyramids that are Johnson solids made from regular triangles and square, and pentagons. Higher forms can be constructed with isosceles triangles.

## Forms

namefaces
elongated triangular pyramid (J7)3+1 triangles, 3 squares
elongated square pyramid (J8)4 triangles, 4+1 squares
elongated pentagonal pyramid (J9)5 triangles, 5 squares, 1 pentagon

## References

• Norman W. Johnson, "Convex Solids with Regular Faces", Canadian Journal of Mathematics, 18, 1966, pages 169200. 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.