Hexagon (EntityTopic, 12)
From Hi.gher. Space
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} · l^{2}
- 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} · l^{2}
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 |