Regular Hexagon Calculator

Name: Regular Hexagon - Geometry Calculator
Author: Jürgen Kummer

Calculations at a regular hexagon, a polygon with 6 vertices. The hexagon is the highest regular polygon which allows a regular tesselation (tiling).
Enter one value and choose the number of decimal places. Then click Calculate.

Formulas:

d = 2 \cdot a

d_{2} = \sqrt{3} \cdot a

p = 6 \cdot a

A = \frac{3}{2} \cdot \sqrt{3} \cdot a^{2}

r_{i} = \frac{\sqrt{3}}{2} \cdot a

Height = d_{2} = 2 \cdot r_{i}

Circumcircle radius = a Angle: 120° 9 diagonals

Edge length, diagonals, perimeter and radius have the same unit (e.g. meter), the area has this unit squared (e.g. square meter).

The short diagonal is the line between two vertices, which have a third vertex between them. Its length equals that of the height. The long diagonal is the line between two opposite vertices. Long diagonals and bisecting lines coincide, they intersect with the median lines and with centroid, circumcircle and incircle center in one point. To this, the regular hexagon is point symmetric and rotationally symmetric at a rotation of 60° or multiples of this. Furthermore, the regular hexagon is axially symmetric to the long diagonals and to the median lines.

perimeter p, area A

sides and angles have the same size

short diagonals, these form a hexagram

long diagonals, those form six
equilateral triangles with edge length a

incircle and circumcircle

The short diagonals of the regular or equilateral hexagon form the regular hexagram. The hexagon as a side surface appears in the Archimedean solids truncated tetrahedron, truncated icosahedron, truncated octahedron, truncated cuboctahedron and truncated icosidodecahedron.
The hexagon is a commonly encountered shape. It is found in honeycombs, snowflakes and other crystals, in organic molecules, particularly the benzene ring, and even in the cloud formations at Saturn's north pole. The honeycomb structure, which is based on honeycombs, is particularly stable with low material consumption and is therefore often used in technology. Hexagonal parquetry is a common form of flooring and wall tiling.

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