Pentagonal pyramid

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Pentagonal pyramid

In geometry

Geometry

Geometry arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers....
, a pentagonal pyramid is a pyramid

Pyramid (geometry)

In geometry, a pyramid is a polyhedron formed by connecting a polygonal base and a point, called the apex . Each base edge and apex form a triangle....
with a pentagon

Pentagon

In geometry, a pentagon is any five-sided polygon. A pentagon may be simple or self-intersecting. The internal angles in a simple pentagon total 540?....
al base upon which are erected five triangular

Triangle

A triangle is one of the basic shapes of geometry: a polygon with three corners or wikt:vertex and three sides or edges which are line segments....
faces that meet at a point (the vertex). Like any pyramid

Pyramid

A pyramid is a building where the outer surfaces are triangular and converge at a point. The base of pyramids are usually quadrilateral or trilateral , meaning that a pyramid usually has four or five faces....
, it is self-dual

Dual polyhedron

In geometry, polyhedron are associated into pairs called duals, where the wikt:vertex of one correspond to the face s of the other. The dual of the dual is the original polyhedron....
.

The regular pentagonal pyramid has a base that is a regular pentagon and lateral faces that are equilateral triangle

Equilateral triangle

In geometry, an equilateral triangle is a triangle in which all three sides are equal. In traditional or Euclidean geometry, equilateral triangles are also Equiangular polygon; that is, all three internal angles are also congruent to each other and are each 60?....
s. It is one of the Johnson solid

Johnson solid

In geometry, a Johnson solid is a strictly convex set polyhedron, each face of which is a regular polygon, but which is not uniform polyhedron, i.e., not a Platonic solid, Archimedean solid, prism or antiprism....
s (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:
, while its surface area, A, can be computed as: It can be seen as the "lid" of an icosahedron

Icosahedron

In geometry, an icosahedron isany polyhedron having 20 faces, but usually a regular icosahedron is implied, which has equilateral triangle s as faces....
; the rest of the icosahedron forms a gyroelongated pentagonal pyramid

Gyroelongated pentagonal pyramid

In geometry, the gyroelongated pentagonal pyramid is one of the Johnson solids . As its name suggests, it is formed by taking a pentagonal pyramid and "gyroelongating" it, which in this case involves joining a pentagonal antiprism to its base....
, J₁₁.

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