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. Self-intersecting hexagons with regular vertices There are six self-crossing hexagons with the vertex arrangement of the regular hexagon:

This pattern repeats within the rhombitrihexagonal tiling.Ī self-intersecting hexagon ( star polygon)

This pattern repeats within the regular triangular tiling.Ī regular hexagon can be extended into a regular dodecagon by adding alternating squares and equilateral triangles around it. A regular hexagon can be dissected into six equilateral triangles by adding a center point. A regular hexagon can be stellated with equilateral triangles on its edges, creating a hexagram. The common length of the sides equals the radius of the circumscribed circle or circumcircle, which equals 2 3. It is bicentric, meaning that it is both cyclic (has a circumscribed circle) and tangential (has an inscribed circle). Transfer the line segment AB four times on the circumscribed circle and connect the corner points.Ī regular hexagon is defined as a hexagon that is both equilateral and equiangular. When the side length AB is given, drawing a circular arc from point A and point B gives the intersection M, the center of the circumscribed circle.

Hexagon corporation