Pentagonal pyramid

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Categories: Pyramids and bipyramids | Self-dual polyhedra | Prismatoid polyhedra | Johnson solids | Polyhedron stubs

Pentagonal pyramid

Type	Johnson J₁ - J₂ - J₃
Faces	5 triangles 1 pentagon
Edges	10
Vertices	6
Vertex configuration	5(3².5) (3⁵)
Symmetry group	C_5v
Dual polyhedron	self
Properties	convex
Image:Pentagonal pyramid flat.svg Net of Pentagonal pyramid

In geometry, a pentagonal pyramid is a pyramid with a pentagonal base upon which are erected five triangular faces that meet at a point (the vertex). Like any pyramid, it is self-dual.

The regular pentagonal pyramid has a base that is a regular pentagon and lateral faces that are equilateral triangles. It is one of the Johnson solids (J₂). It can be seen as the "lid" of an icosahedron; the rest of the icosahedron forms a gyroelongated pentagonal pyramid, J₁₁. The 92 Johnson solids were named and described by Norman Johnson in 1966.

More generally an order-2 vertex-uniform pentagonal pyramid can be defined with a regular pentagonal base and 5 isosceles triangle sides of any height.