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Photos Add Image Add an image Do you have any images for this title? Edit Cast Credited cast: Jalil Naciri Slimane Farid Abdedou Samy Hakim Sarahoui Staf Karim Chakir Ali Faiza Kaddour Nacera Kamel Allah Paco Driss El Haddaoui Karim Corinne Colas It follows from the ratio of circumradius to inradius that the height-to-width ratio of a regular hexagon is The regular hexagon has Dih 6 symmetry, order These symmetries express nine distinct symmetries of a regular hexagon.

John Conway labels these by a letter and group order. These two forms are duals of each other and have half the symmetry order of the regular hexagon.

The i4 forms are regular hexagons flattened or stretched along one symmetry direction. It can be seen as an elongated rhombus , while d2 and p2 can be seen as horizontally and vertically elongated kites.

Each subgroup symmetry allows one or more degrees of freedom for irregular forms. Only the g6 subgroup has no degrees of freedom but can seen as directed edges.

Hexagons of symmetry g2 , i4 , and r12 , as parallelogons can tessellate the Euclidean plane by translation. Other hexagon shapes can tile the plane with different orientations.

The 6 roots of the simple Lie group A2 , represented by a Dynkin diagram , are in a regular hexagonal pattern. The 12 roots of the Exceptional Lie group G2 , represented by a Dynkin diagram are also in a hexagonal pattern.

This decomposition of a regular hexagon is based on a Petrie polygon projection of a cube , with 3 of 6 square faces. Other parallelogons and projective directions of the cube are dissected within rectangular cuboids.

Seen with two types colors of edges, this form only has D 3 symmetry. A regular hexagon can be stellated with equilateral triangles on its edges, creating a hexagram.

A regular hexagon can be dissected into six equilateral triangles by adding a center point. This pattern repeats within the regular triangular tiling.

A regular hexagon can be extended into a regular dodecagon by adding alternating squares and equilateral triangles around it.

This pattern repeats within the rhombitrihexagonal tiling. There are six self-crossing hexagons with the vertex arrangement of the regular hexagon:.

From bees' honeycombs to the Giant's Causeway , hexagonal patterns are prevalent in nature due to their efficiency. In a hexagonal grid each line is as short as it can possibly be if a large area is to be filled with the fewest hexagons.

This means that honeycombs require less wax to construct and gain much strength under compression. Irregular hexagons with parallel opposite edges are called parallelogons and can also tile the plane by translation.

In three dimensions, hexagonal prisms with parallel opposite faces are called parallelohedrons and these can tessellate 3-space by translation.

In addition to the regular hexagon, which determines a unique tessellation of the plane, any irregular hexagon which satisfies the Conway criterion will tile the plane.