geometry Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is c ...

, the elongated pentagonal pyramid is one of the

Johnson solid In geometry, a Johnson solid is a strictly convex polyhedron each face of which is a regular polygon. There is no requirement that each face must be the same polygon, or that the same polygons join around each vertex. An example of a Johns ...

s (). As the name suggests, it can be constructed by elongating a

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. The ''regular'' pentagonal pyramid has a base that is a reg ...

() by attaching a

pentagonal prism In geometry, the pentagonal prism is a prism with a pentagonal base. It is a type of heptahedron with seven faces, fifteen edges, and ten vertices. As a semiregular (or uniform) polyhedron If faces are all regular, the pentagonal prism is a ...

to its base.

Formulae

The following formulae for the

height Height is measure of vertical distance, either vertical extent (how "tall" something or someone is) or vertical position (how "high" a point is). For example, "The height of that building is 50 m" or "The height of an airplane in-flight is ab ...

(

H

surface area The surface area of a solid object is a measure of the total area that the surface of the object occupies. The mathematical definition of surface area in the presence of curved surfaces is considerably more involved than the definition of ...

(

A

) and

volume Volume is a measure of occupied three-dimensional space. It is often quantified numerically using SI derived units (such as the cubic metre and litre) or by various imperial or US customary units (such as the gallon, quart, cubic inch). Th ...

(

V

) can be used if all faces are regular, with edge length

L

: :

H =  L\cdot \left( 1 + \sqrt\right) \approx L\cdot 1.525731112

A =  L^2 \cdot \frac \approx L^2\cdot 8.88554091

V =  L^3 \cdot \left(  \frac \right) \approx L^3\cdot 2.021980233

Dual polyhedron

The dual of the elongated pentagonal pyramid has 11 faces: 5 triangular, 1 pentagonal and 5 trapezoidal. It is topologically identical to the Johnson solid.

References

External links

* Johnson solids Self-dual polyhedra Pyramids and bipyramids {{Polyhedron-stub

Formulae

Dual polyhedron

See also

References

External links