# 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 | |
---|---|

Faces | 2n triangles, n squares |

Edges | 5n |

Vertices | 2n+2 |

Symmetry group | D_{nh}, [n,2], (*n22) |

Rotation group | D_{n}, [n,2]^{+}, (n22) |

Dual polyhedron | bifrustums |

Properties | convex |

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

## Forms

Name | J14 | J15 | 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 |

## 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.

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