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). Its height H, from the midpoint of the pentagonal face to the apex, (as a function of a, where a is the side length), can be computed as:
Its surface area, A, can be computed as the area of pentagonal base plus five times the area of one triangle:
Its volume when an edge length is known can be figured out with this formula:
It can be seen as the "lid" of an icosahedron; the rest of the icosahedron forms a gyroelongated pentagonal pyramid, J11, one of the 92 Johnson solids 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.
Read more about Pentagonal Pyramid: Related Polyhedra
Famous quotes containing the word pyramid:
“So universal and widely related is any transcendent moral greatness, and so nearly identical with greatness everywhere and in every age,—as a pyramid contracts the nearer you approach its apex,—that, when I look over my commonplace-book of poetry, I find that the best of it is oftenest applicable, in part or wholly, to the case of Captain Brown.”
—Henry David Thoreau (1817–1862)