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 apex). Like any pyramid, it is self-dual.
| Pentagonal pyramid | |
|---|---|
| Type | Johnson J1 – J2 – J3 |
| Faces | 5 triangles 1 pentagon |
| Edges | 10 |
| Vertices | 6 |
| Vertex configuration | 5(32.5) (35) |
| Schläfli symbol | ( ) ∨ {5} |
| Symmetry group | C5v, [5], (*55) |
| Rotation group | C5, [5]+, (55) |
| Dual polyhedron | self |
| Properties | convex |
| Net | |
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.
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.
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