Hexagon

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A regular hexagon

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A hexagon (also known as "sexagon") is a polygon with six edges and six vertices. Its Schläfli symbol is {6}.

Related Topics:
Polygon - Edge - Vertices - Schläfli symbol

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The internal angles of a regular hexagon (one where all sides and all angles are equal) are all

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120°. Like squares and equilateral triangles, regular hexagons fit together without any gaps to tile the plane (three hexagons meeting at every vertex), and so are useful for constructing tessellations.

Related Topics:
° - Square - Equilateral - Triangle - Tessellation

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The cells of a beehive honeycomb are hexagonal for this reason and because the shape makes efficient use of space and building materials. The Voronoi diagram of a regular triangular lattice is the honeycomb tessellation of hexagons.

Related Topics:
Beehive - Honeycomb - Voronoi diagram

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The area of a regular hexagon of side length a,! is given by

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:A = rac{3}{2}a^2 cot rac{pi}{6} = rac{3 sqrt{3}}{2}a^2 simeq 2.59808 a^2.

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The circumference of an hexagon of side length a,! is, of course, 6a,!, its maximal diameter 2a,!, and its minimal diameter sqrt{3}a,!.

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There is no platonic solid made of regular hexagons. The archimedean solids with some hexagonal faces are the truncated tetrahedron, truncated octahedron, truncated icosahedron (of soccer ball and fullerene fame), truncated cuboctahedron and the truncated icosidodecahedron.

Related Topics:
Platonic solid - Archimedean solid - Truncated tetrahedron - Truncated octahedron - Truncated icosahedron - Soccer - Fullerene - Truncated cuboctahedron - Truncated icosidodecahedron

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