# Elongated square pyramid

In geometry, the **elongated square pyramid** is one of the Johnson solids (*J*_{8}). As the name suggests, it can be constructed by elongating a square pyramid (*J*_{1}) by attaching a cube to its square base. Like any elongated pyramid, it is topologically (but not geometrically) self-dual.

Elongated square pyramid | |
---|---|

Type | Johnson J _{7} - J - J_{8}_{9} |

Faces | 4 triangles 1+4 squares |

Edges | 16 |

Vertices | 9 |

Vertex configuration | 4(4^{3})1(3 ^{4})4(3 ^{2}.4^{2}) |

Symmetry group | C_{4v}, [4], (*44) |

Rotation group | C_{4}, [4]^{+}, (44) |

Dual polyhedron | self |

Properties | convex |

Net | |

A Johnson solid is one of 92 strictly convex polyhedra that have regular faces but are not uniform (that is, they are not Platonic solids, Archimedean solids, prisms, or antiprisms). They were named by Norman Johnson, who first listed these polyhedra in 1966.[1]

## Dual polyhedron

The dual of the elongated square pyramid has 9 faces: 4 triangular, 1 square and 4 trapezoidal. It is topologically identical to the Johnson solid.

Dual elongated square pyramid | Net of dual |
---|---|

## Related polyhedra and honeycombs

The elongated square pyramid can form a tessellation of space with tetrahedra,[2] similar to a modified tetrahedral-octahedral honeycomb.

## See also

## References

- Johnson, Norman W. (1966), "Convex polyhedra with regular faces",
*Canadian Journal of Mathematics*,**18**: 169–200, doi:10.4153/cjm-1966-021-8, MR 0185507, Zbl 0132.14603. - http://woodenpolyhedra.web.fc2.com/J8.html