Set of elongated bicupolae

Example pentagonal ortho form

Faces| 2n triangles
4n squares
2 n-gon
Edges| 12n
Vertices| 6n
Symmetry group| Ortho: Dnh, [2,n], (*n22), order 4n
Gyro: Dnd, [2+,2n], (2*n), order 4n
Properties| convex

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

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Elongated orthobicupola
J35  | Semiregular  | J38
Elongated triangular orthobicupola | Elongated square orthobicupola
(rhombicuboctahedron)  | Elongated pentagonal orthobicupola
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Elongated gyrobicupola
J36  | J37  | J39
Elongated triangular gyrobicupola | Elongated square gyrobicupola
(pseudorhombicuboctahedron)  | Elongated pentagonal gyrobicupola
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## See also[edit]

* Bicupola
* Elongated cupola
* Gyroelongated bicupola

## 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.

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Convex polyhedra

Platonic solids (regular)|

* tetrahedron
* cube
* octahedron
* dodecahedron
* icosahedron

Archimedean solids
(semiregular or uniform)

* truncated tetrahedron
* cuboctahedron
* truncated cube
* truncated octahedron
* rhombicuboctahedron
* truncated cuboctahedron
* snub cube
* icosidodecahedron
* truncated dodecahedron
* truncated icosahedron
* rhombicosidodecahedron
* truncated icosidodecahedron
* snub dodecahedron

Catalan solids
(duals of Archimedean)

* triakis tetrahedron
* rhombic dodecahedron
* triakis octahedron
* tetrakis hexahedron
* deltoidal icositetrahedron
* disdyakis dodecahedron
* pentagonal icositetrahedron
* rhombic triacontahedron
* triakis icosahedron
* pentakis dodecahedron
* deltoidal hexecontahedron
* disdyakis triacontahedron
* pentagonal hexecontahedron

Dihedral regular|

* dihedron
* hosohedron

Dihedral uniform|

* prisms
* antiprisms

duals:|

* bipyramids
* trapezohedra

Dihedral others|

* pyramids
* truncated trapezohedra
* gyroelongated bipyramid
* cupola
* bicupola
* frustum
* bifrustum
* rotunda
* birotunda
* prismatoid
* scutoid

Degenerate polyhedra are in italics.

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