# Elongated pyramid

In geometry, the **elongated pyramids** are an infinite set of polyhedra, constructed by adjoining an n-gonal pyramid to an n-gonal prism. Along with the set of pyramids, these figures are topologically self-dual.

Set of elongated pyramids | |
---|---|

Example Pentagonal form | |

Faces | n triangles n squares 1 n-gon |

Edges | 4n |

Vertices | 2n+1 |

Symmetry group | C_{nv}, [n], (*nn) |

Rotational group | C_{n}, [n]^{+}, (nn) |

Dual polyhedron | self-dual |

Properties | convex |

There are three *elongated pyramids* that are Johnson solids made from regular triangles and square, and pentagons. Higher forms can be constructed with isosceles triangles.

## Forms

name | faces | |
---|---|---|

elongated triangular pyramid (J7) | 3+1 triangles, 3 squares | |

elongated square pyramid (J8) | 4 triangles, 4+1 squares | |

elongated pentagonal pyramid (J9) | 5 triangles, 5 squares, 1 pentagon |

## 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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