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Elongated pyramid

From Wikipedia, the free encyclopedia
Elongated pyramid
Example: pentagonal form
Facesn triangles
n squares
1 n-gon
Edges4n
Vertices2n + 1
Symmetry groupCnv, [n], (*nn)
Rotation groupCn, [n]+, (nn)
Dual polyhedronself-dual
Propertiesconvex

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:

Higher forms can be constructed with isosceles triangles.

Forms

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name faces
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

See also

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References

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  • 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.