View source for Hexagonal pyramid

{{Short description|Polyhedron with 7 faces}}
{{Infobox polyhedron
|image=Hexagonal pyramid.png
|type=[[Pyramid (geometry)|Pyramid]]
|faces=6 [[Triangle|triangle]]s<br>1 [[Hexagon|hexagon]]
|edges=12
|vertices=7
|schläfli=( ) ∨ {6}
|symmetry=''C''<sub>6v</sub>, [6], (*66)
|rotation_group=''C''<sub>6</sub>, [6]<sup>+</sup>, (66)
|vertex_config=6(3<sup>2</sup>.6)<br>(3<sup>6</sup>)
|dual=[[Self-dual polyhedron|Self-dual]]
|properties=[[Convex set|Convex]]
|net=Geometric Net of an Hexagonal Pyramid.svg}}
In [[Geometry|geometry]], a '''hexagonal pyramid''' or hexacone is a [[Pyramid (geometry)|pyramid]] with a [[Hexagon|hexagon]]al base upon which are erected six [[Isosceles triangle|isosceles]] [[Triangle|triangular]] faces that meet at a point (the apex). Like any pyramid, it is self-[[Dual polyhedron|dual]].

A '''right hexagonal pyramid''' with a regular hexagon base has [[List of spherical symmetry groups#Other|''C''<sub>6v</sub> symmetry]].

A right regular pyramid is one which has a [[Regular polygon|regular polygon]] as its base and whose apex is "above" the center of the base, so that the apex, the center of the base and any other vertex form a [[Right triangle|right triangle]].

==Vertex coordinates==

A hexagonal pyramid of edge length 1 has the following vertices:

*<math>\left(\pm\frac12,\,\pm\frac{\sqrt3}{2},\,0\right)</math>
*<math>\left(\pm1,\,0,\,0\right)</math>
*<math>\left(0,\,0,\,0\right)</math>

These coordinates are a subset of the vertices of the regular triangular tiling.

==Representations==

{{multiple image
|align = left
|direction = vertical
|header = [[Physics:Stereolithography|STL]] Hexagonal pyramid
|image1 = Hexagonal pyramid.stl
|alt1 = Hexagonal pyramid
}}

A hexagonal pyramid has the following Coxeter diagrams:

*ox6oo&#x (full symmetry)
*ox3ox&#x (generally a ditrigonal pyramid)

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== Related polyhedra ==

== See also ==
* [[Bipyramid]], [[Prism (geometry)|prism]] and [[Antiprism|antiprism]]

==External links==
*{{MathWorld |urlname=HexagonalPyramid |title=Hexagonal Pyramid}}
*[http://www.georgehart.com/virtual-polyhedra/vp.html Virtual Reality Polyhedra] www.georgehart.com: The Encyclopedia of Polyhedra
* [http://www.georgehart.com/virtual-polyhedra/conway_notation.html Conway Notation for Polyhedra] Try: "Y6"
* [https://polytope.miraheze.org/wiki/Hexagonal_pyramid] Hexagonal pyramid - Polytope Wiki

[[Category:Pyramids and bipyramids]]
[[Category:Self-dual polyhedra]]
[[Category:Prismatoid polyhedra]]


{{Sourceattribution|Hexagonal pyramid}}