Elongated pyramid

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Set of elongated pyramids
Elongated pentagonal pyramid.png
Example Pentagonal form
Faces n triangles
n squares
1 n-gon
Edges 4n
Vertices 2n+1
Symmetry group Cnv, [n], (*nn)
Rotational group Cn, [n]+, (nn)
Dual polyhedron self-dual
Properties convex

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.

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[edit]

name faces
Elongated triangular pyramid.png elongated triangular pyramid (J7) 3+1 triangles, 3 squares
Elongated square pyramid.png elongated square pyramid (J8) 4 triangles, 4+1 squares
Elongated pentagonal pyramid.png elongated pentagonal pyramid (J9) 5 triangles, 5 squares, 1 pentagon

See also[edit]

References[edit]

  • 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.