Hexagram — Definition, Formula & Examples
A hexagram is a six-pointed star shape formed by placing two equilateral triangles on top of each other, one pointing up and one pointing down. It is also known as the Star of David.
A hexagram is a star polygon with Schläfli symbol {6/2}, constructed by superimposing two congruent equilateral triangles rotated 60° relative to each other, producing a figure with 12 edges, 6 vertices, and a regular hexagonal region at its center.
How It Works
To draw a hexagram, start with an equilateral triangle pointing up. Then draw a second equilateral triangle of the same size pointing down, centered on the first. The overlapping region in the middle forms a regular hexagon, and the six non-overlapping parts form the star's points. Each point of the star is itself an equilateral triangle.
Worked Example
Problem: Two equilateral triangles, each with side length 6 cm, overlap to form a hexagram. Find the side length of the regular hexagon at the center.
Step 1: In a hexagram formed by two equilateral triangles of side length s, the central hexagon has a side length equal to one-third of the triangle's side length.
Step 2: Substitute the given side length.
Answer: The regular hexagon at the center has a side length of 2 cm.
Why It Matters
Hexagrams appear in tiling patterns, religious and cultural symbols, and geometric art. Recognizing how two triangles combine to form a star helps build spatial reasoning skills used in geometry and design.
Common Mistakes
Mistake: Confusing a hexagram (six-pointed star) with a hexagon (six-sided polygon).
Correction: A hexagon is a closed six-sided figure. A hexagram is a star shape made from two overlapping triangles — it contains a hexagon at its center but is a different figure.