Hexagonal prism (EntityTopic, 16)

From Hi.gher. Space

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<[#ontology [kind topic] [cats Hexagon Prism 3D Uniform Polytope]]>
{{STS Shape
{{STS Shape
| dim=3
| dim=3
| elements=8, 18, 12
| elements=8, 18, 12
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| sym=[[Bipyroprismatic symmetry|D<sub>6h</sub>]]
| genus=0
| genus=0
| ssc=[G6x]
| ssc=[G6x]
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| vfigure=Isosceles [[triangle]]
| vfigure=Isosceles [[triangle]]
}}}}
}}}}
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== Equations ==
== Equations ==
*The [[hypervolume]]s of a hexagonal prism with side length ''l'' are given by:
*The [[hypervolume]]s of a hexagonal prism with side length ''l'' are given by:
<blockquote>total edge length = 18''l''<br>
<blockquote>total edge length = 18''l''<br>
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surface area = ''l''<sup>2</sup> &middot; 3(2 + √3)<br>
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surface area = 3(2 + √3) {{DotHV}}<br>
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volume = ''l''<sup>3</sup> &middot; <sup>3√3</sup>∕<sub>2</sub></blockquote>
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volume = {{Over|3√3|2}} {{DotHV|3}}</blockquote>
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<[#polytope [id 52]]>
{{Polyhedra}}
{{Polyhedra}}

Latest revision as of 22:12, 2 March 2014

Equations

  • The hypervolumes of a hexagonal prism with side length l are given by:
total edge length = 18l
surface area = 3(2 + √3) · l2
volume = 3√3∕2 · l3

Incidence matrix

Dual: hexagonal bipyramid

#TXIDVaEaEb4a6aTypeName
0 Va = point ;
1 Ea 2 = digon ;
2 Eb 2 = digon ;
3 4a 422 = square ;
4 6a 606 = base of prism: hexagon ;
5 C1a 1261262 = hexagonal prism ;

Usage as facets


Notable Trishapes
Regular: tetrahedron • cube • octahedron • dodecahedron • icosahedron
Direct truncates: tetrahedral truncate • cubic truncate • octahedral truncate • dodecahedral truncate • icosahedral truncate
Mesotruncates: stauromesohedron • stauroperihedron • stauropantohedron • rhodomesohedron • rhodoperihedron • rhodopantohedron
Snubs: snub staurohedron • snub rhodohedron
Curved: sphere • torus • cylinder • cone • frustum • crind
Retrieved from "http://hi.gher.space/wiki/Hexagonal_prism"