Elongated bipyramid

In geometry, the elongated bipyramids are an infinite set of polyhedra, constructed by elongating an n-gonal bipyramid (by inserting an n-gonal prism between its congruent halves).

Set of elongated bipyramids

Faces2n triangles,
n squares
Symmetry groupDnh, [n,2], (*n22)
Rotation groupDn, [n,2]+, (n22)
Dual polyhedronbifrustums

There are three elongated bipyramids that are Johnson solids made from regular triangles and squares. Higher forms can be constructed with isosceles triangles.


Name J14 J15 J16 elongated
Type Equilateral Irregular
Faces 6 triangles,
3 squares
8 triangles,
4 squares
10 triangles,
5 squares
12 triangles,
6 squares
Dual triangular bifrustum square bifrustum pentagonal bifrustum hexagonal bifrustum

See also


  • 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.
This article is issued from Wikipedia. The text is licensed under Creative Commons - Attribution - Sharealike. Additional terms may apply for the media files.