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).

Elongated bipyramid
Example: elongated hexagonal 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

There are three elongated bipyramids that are Johnson solids:

• Elongated triangular bipyramid (J₁₄),
• Elongated square bipyramid (J₁₅), and
• Elongated pentagonal bipyramid (J₁₆).

Higher forms can be constructed with isosceles triangles.

Forms

Name	elongated triangular bipyramid J14	elongated square bipyramid J15	elongated pentagonal bipyramid J16	elongated hexagonal bipyramid
Type	Equilateral			Irregular
Image
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

Applications

Elongated bipyramids are sometimes used as dice, especially to make dice with atypical side count, such as 5 or 7. Such a die has numbers written on the square faces, which are usually heightened into rectangles for convenience in rolling. Whichever number comes face-up when the die is rolled is the side that is to be read.

See also

• Gyroelongated bipyramid
• Gyroelongated pyramid
• Elongated pyramid
• Diminished trapezohedron

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.