Elongated bicupola

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

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

See also

• Bicupola
• Elongated cupola
• Gyroelongated bicupola

References

• 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.