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Elongated bicupola

From Wikipedia, the free encyclopedia
Set of elongated bicupolae
Example pentagonal ortho form
Faces2n triangles
4n squares
2 n-gon
Edges12n
Vertices6n
Symmetry groupOrtho: Dnh, [2,n], (*n22), order 4n
Gyro: Dnd, [2+,2n], (2*n), order 4n
Propertiesconvex

In geometry, the elongated bicupolae are two infinite sets of polyhedra, constructed by adjoining two n-gonal cupolas to an n-gonal prism. They have 2n triangles, 4n squares, and 2 n-gon. The ortho forms have the cupola aligned, while gyro forms are counter aligned.

3 4 5
Elongated orthobicupola
J35 Semiregular J38
Elongated triangular orthobicupola Elongated square orthobicupola
(rhombicuboctahedron)
Elongated pentagonal orthobicupola
Elongated gyrobicupola
J36 J37 J39
Elongated triangular gyrobicupola Elongated square gyrobicupola
(pseudorhombicuboctahedron)
Elongated pentagonal gyrobicupola

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.