Elongated square pyramid

Elongated square pyramid
Type Johnson
J7 - J8 - J9
Faces 4 triangles
1+4 squares
Edges 16
Vertices 9
Vertex configuration 4(43)
1(34)
4(32.42)
Symmetry group C4v, [4], (*44)
Rotation group C4, [4]+, (44)
Dual polyhedron self
Properties convex
Net

In geometry, the elongated square pyramid is one of the Johnson solids (J8). As the name suggests, it can be constructed by elongating a square pyramid (J1) by attaching a cube to its square base. Like any elongated pyramid, it is topologically (but not geometrically) self-dual.

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.

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

Elongated square bipyramid

References

  1. ↑ 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.
  2. ↑ http://woodenpolyhedra.web.fc2.com/J8.html

External links

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