Elongated pyramid

Polyhedron formed by capping a prism with a pyramid From Wikipedia, the free encyclopedia

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.

Quick Facts Faces, Edges ...
Elongated pyramid
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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
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There are three elongated pyramids that are Johnson solids:

Higher forms can be constructed with isosceles triangles.

Forms

More information name, faces ...
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
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See also

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.
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