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{{Infobox face-uniform polyhedron | | |||
Image_File=Hexagonale bipiramide.png | | |||
Polyhedron_Type=[[bipyramid]] | | |||
Coxeter={{CDD|node_f1|2|node_f1|6|node}}<BR>{{CDD|node_f1|2|node_f1|3|node_f1}}| | |||
Schläfli = { } + {6} | | |||
Face_List=12 [[triangle]]s| | |||
Edge_Count=18 | | |||
Vertex_Count=8 | | |||
Symmetry_Group=''D''<sub>6h</sub>, [6,2], (*226), order 24| | |||
Rotation_Group = ''D''<sub>''6''</sub>, [6,2]<sup>+</sup>, (226), order 12| | |||
Face_Type=V4.4.6| | |||
Dual=[[hexagonal prism]]| | |||
Property_List=[[convex set|convex]], [[face-transitive]] | |||
}} | |||
A '''hexagonal bipyramid''' is a [[polyhedron]] formed from two hexagonal [[pyramid (geometry)|pyramids]] joined at their bases. The resulting solid has 12 triangular [[face (geometry)|faces]], 8 [[vertex (geometry)|vertices]] and 18 edges. The 12 faces are identical [[isosceles triangle]]s. | |||
It is one of an infinite set of [[bipyramid]]s. Having twelve faces, it is a type of [[dodecahedron]], although that name is usually associated with the [[regular polyhedron|regular polyhedral]] form with pentagonal faces. The term '''dodecadeltahedron''' is sometimes used to distinguish the bipyramid from the [[Platonic solid]]. | |||
The hexagonal bipyramid has a [[plane of symmetry]] (which is [[Horizontal plane|horizontal]] in the figure to the right) where the bases of the two pyramids are joined. This plane is a regular [[hexagon]]. There are also six planes of symmetry crossing through the two [[apex (geometry)|apices]]. These planes are [[rhombus|rhombic]] and lie at 30° [[angle]]s to each other, [[perpendicular]] to the horizontal plane. | |||
== Related polyhedra == | |||
{{Hexagonal dihedral truncations}} | |||
It the first polyhedra in a sequence defined by the [[face configuration]] ''V4.6.2n''. This group is special for having all even number of edges per vertex and form bisecting planes through the polyhedra and infinite lines in the plane, and continuing into the hyperbolic plane for any <math>n \ge 7.</math> | |||
With an even number of faces at every vertex, these polyhedra and tilings can be shown by alternating two colors so all adjacent faces have different colors. | |||
Each face on these domains also corresponds to the fundamental domain of a [[symmetry group]] with order 2,3,n mirrors at each triangle face vertex. | |||
{{Omnitruncated table}} | |||
{{Bipyramids}} | |||
==See also== | |||
* [[hexagonal trapezohedron]] A similar 12-sided polyhedron with a twist and [[Kite (geometry)|kite]] faces. | |||
* [[Snub disphenoid]] Another 12-sided polyhedron with 2-fold symmetry and only triangular faces. | |||
==External links== | |||
* {{mathworld | urlname = Dipyramid | title = Dipyramid}} | |||
* {{GlossaryForHyperspace | anchor=Bipyramid | title=Bipyramid}} | |||
*[http://www.georgehart.com/virtual-polyhedra/vp.html Virtual Reality Polyhedra] The Encyclopedia of Polyhedra | |||
** [[VRML]] model [http://www.georgehart.com/virtual-polyhedra/vrml/hexagonal_dipyramid.wrl hexagonal dipyramid] | |||
{{Polyhedron-stub}} | |||
[[Category:Polyhedra]] | |||
[[Category:Pyramids and bipyramids]] | |||
Latest revision as of 05:46, 16 October 2012
Template:Infobox face-uniform polyhedron A hexagonal bipyramid is a polyhedron formed from two hexagonal pyramids joined at their bases. The resulting solid has 12 triangular faces, 8 vertices and 18 edges. The 12 faces are identical isosceles triangles.
It is one of an infinite set of bipyramids. Having twelve faces, it is a type of dodecahedron, although that name is usually associated with the regular polyhedral form with pentagonal faces. The term dodecadeltahedron is sometimes used to distinguish the bipyramid from the Platonic solid.
The hexagonal bipyramid has a plane of symmetry (which is horizontal in the figure to the right) where the bases of the two pyramids are joined. This plane is a regular hexagon. There are also six planes of symmetry crossing through the two apices. These planes are rhombic and lie at 30° angles to each other, perpendicular to the horizontal plane.
Related polyhedra
Template:Hexagonal dihedral truncations
It the first polyhedra in a sequence defined by the face configuration V4.6.2n. This group is special for having all even number of edges per vertex and form bisecting planes through the polyhedra and infinite lines in the plane, and continuing into the hyperbolic plane for any
With an even number of faces at every vertex, these polyhedra and tilings can be shown by alternating two colors so all adjacent faces have different colors.
Each face on these domains also corresponds to the fundamental domain of a symmetry group with order 2,3,n mirrors at each triangle face vertex. Template:Omnitruncated table
See also
- hexagonal trapezohedron A similar 12-sided polyhedron with a twist and kite faces.
- Snub disphenoid Another 12-sided polyhedron with 2-fold symmetry and only triangular faces.
External links
- 22 year-old Systems Analyst Rave from Merrickville-Wolford, has lots of hobbies and interests including quick cars, property developers in singapore and baking. Always loves visiting spots like Historic Monuments Zone of Querétaro.
Here is my web site - cottagehillchurch.com - Template:GlossaryForHyperspace
- Virtual Reality Polyhedra The Encyclopedia of Polyhedra
- VRML model hexagonal dipyramid