Hexagonal prism (EntityTopic, 16)
From Hi.gher. Space
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| dim=3 | | dim=3 | ||
| elements=8, 18, 12 | | elements=8, 18, 12 | ||
| + | | 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: | ||
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surface area = 3(2 + √3) {{DotHV}}<br> | surface area = 3(2 + √3) {{DotHV}}<br> | ||
volume = {{Over|3√3|2}} {{DotHV|3}}</blockquote> | 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
| # | TXID | Va | Ea | Eb | 4a | 6a | Type | Name |
|---|---|---|---|---|---|---|---|---|
| 0 | Va | = point | ; | |||||
| 1 | Ea | 2 | = digon | ; | ||||
| 2 | Eb | 2 | = digon | ; | ||||
| 3 | 4a | 4 | 2 | 2 | = square | ; | ||
| 4 | 6a | 6 | 0 | 6 | = base of prism: hexagon | ; | ||
| 5 | C1a | 12 | 6 | 12 | 6 | 2 | = hexagonal prism | ; |
Usage as facets
- 2× 1-facets of a bitrigonal diminished pyrocantichoron
| 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 |
