“Pentagonal pyramid”的意思、由来-开放百科全书

词条

Pentagonal pyramid

释义

Related polyhedra
Dual polyhedron
Example
External links

{{Infobox polyhedron
|image=Pentagonal pyramid.png
|type=Johnson
J₁ - J₂ - J₃
|faces=5 triangles
1 pentagon
|edges=10
|vertices=6
|schläfli=( ) ∨ {5}
|symmetry=C_5v, [5], (*55)
|rotation_group=C₅, [5]⁺, (55)
|vertex_config=5(3².5)
(3⁵)
|dual=self
|properties=convex
|net=pentagonal pyramid flat.svg
}}

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.

Related polyhedra

The pentagrammic star pyramid has the same vertex arrangement, but connected onto a pentagram base:

Pentagonal frustum is a pentagonal pyramid with its apex truncated	The top of an icosahedron is a pentagonal pyramid

Dual polyhedron

The pentagonal pyramid is topologically a self-dual polyhedron. The dual edge lengths are different due to the polar reciprocation.

Dual pentagonal pyramid	Net of dual

Example

External links

{{Mathworld2 | urlname2 = JohnsonSolid | title2 = Johnson solid | urlname = PentagonalPyramid | title = Pentagonal pyramid}}
Virtual Reality Polyhedra www.georgehart.com: The Encyclopedia of Polyhedra ( VRML model)

4 : Pyramids and bipyramids|Self-dual polyhedra|Prismatoid polyhedra|Johnson solids

随便看

开放百科全书收录14589846条英语、德语、日语等多语种百科知识，基本涵盖了大多数领域的百科知识，是一部内容自由、开放的电子版国际百科全书。