Hexagon (EntityTopic, 12)
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| extra={{STS Matrix| | | extra={{STS Matrix| | ||
6 0 | 6 0 | ||
| - | 1 1}}{{STS | + | 1 1}}{{STS Polytope |
| - | + | ||
| - | + | ||
| dual=''Self-dual'' | | dual=''Self-dual'' | ||
| + | | bowers=Hig | ||
| + | }}{{STS Uniform polytope | ||
| + | | schlaefli={6}, t{3} | ||
| + | | dynkin=x6o, x3x | ||
| + | | vfigure=[[Digon]], length √3 | ||
}}}} | }}}} | ||
| + | A hexagon is a 6-sided polygon. It is also the truncated [[triangle]]. It is one of the regular polygons that can tile the plain. | ||
| + | ==Coordinates== | ||
| + | The coordinates of a regular hexagon of side 2 are: | ||
| + | <blockquote>(±1, ±√3)<br>(0, ±2)</blockquote> | ||
| + | |||
== Equations == | == Equations == | ||
*The area of a regular hexagon with side length ''l'' is equal to six times the area of an equilateral [[triangle]] with side length ''l'', i.e.: | *The area of a regular hexagon with side length ''l'' is equal to six times the area of an equilateral [[triangle]] with side length ''l'', i.e.: | ||
Revision as of 15:56, 26 March 2017
A hexagon is a 6-sided polygon. It is also the truncated triangle. It is one of the regular polygons that can tile the plain.
Coordinates
The coordinates of a regular hexagon of side 2 are:
(±1, ±√3)
(0, ±2)
Equations
- The area of a regular hexagon with side length l is equal to six times the area of an equilateral triangle with side length l, i.e.:
3√3∕2 · l2
- Because the diameter of a hexagon is twice its side length, the area of a hexagon with diameter l is a quarter of this, i.e.:
3√3∕8 · l2
Dissection
The hexagon of side 1 may be dissected into:
Incidence matrix
Usage as facets
- prism: 2× 1-facets of a hexagonal prism
- 20× 1-facets of a truncated icosahedron
- 8× 1-facets of a truncated octahedron
- 4× 1-facets of a truncated tetrahedron
- 20× 1-facets of a rhodopantohedron
- 8× 1-facets of a stauropantohedron
- 1× 1-facets of a triangular cupola
- 1× 1-facets of a hexagonal cupolawedge
- 1× 1-facets of a triangular hebesphenorotunda (named bot)
- 1× 1-facets of a biunpinched cube
- 96× 2-facets of a truncated snub demitesseract
- 288× 2-facets of a truncated snub demitesseract
- 96× 2-facets of a truncated snub demitesseract
- 1× 2-facets of a (dual of bilunabirotunda pseudopyramid)
- 40× 2-facets of a castellated rhodopantohedral prism (named 3 end)
- 4× 2-facets of a bitrigonal diminished pyrocantichoron
- 1× 2-facets of a triangular hebesphenorotunda pseudopyramid (named bot)
- 6× 2-facets of a (dual of triangular hebesphenorotundaeic rhombochoron)
- 2× 2-facets of a triangular hebesphenorotundaeic rhombochoron (named pppppp)
- 6× 2-facets of a (dual of tetraaugmented triangular hebesphenorotundaeic rhombochoron)
- 12× 2-facets of a (dual of tetraaugmented triangular hebesphenorotundaeic rhombochoron)
- 2× 2-facets of a tetraaugmented triangular hebesphenorotundaeic rhombochoron (named pppppp - bot)
- 12× 2-facets of a D4.7 (named ooyygg)
- 8× 2-facets of a D4.7 (named oyoyoy)
| Notable Dishapes | |
| Flat: | triangle • square • pentagon • hexagon • octagon • decagon |
| Curved: | circle |
