Elongated bipyramid

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Set of elongated bipyramids
Hexagonal elongated bipyramid
Faces 2n triangles,
n squares
Edges 5n
Vertices 2n+2
Symmetry group Dnh, [n,2], (*n22)
Rotation group Dn, [n,2]+, (n22)
Dual polyhedron bifrustums
Properties convex

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).

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

Forms[edit]

Name J14 J15 J16 elongated
hexagonal
bipyramid
Type Equilateral Irregular
Image Elongated triangular dipyramid.png Elongated square dipyramid.png Elongated pentagonal dipyramid.png Elongated hexagonal dipyramid.png
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[edit]

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.