Star Polygons · 2D

Pentagram

The golden star {5/2}

A five-pointed star drawn in one unbroken line. Every crossing divides a line in the golden ratio, again and again, all the way down.

φ: 1.61803
Points: 5
Tip angle: 36°

Open in SacredForm

Watch it drawn with compass and straightedge, hear the chord of its lines, and turn the Dimension dial to raise its form in space.

Facts

Each line is cut by the others in the ratio φ : 1, where φ = (1 + √5) ÷ 2.
The inner pentagon is upside-down and φ² ≈ 2.618 times smaller: the star repeats forever inside itself.
Diagonal ÷ side of a regular pentagon = φ exactly.
Venus traces a near-pentagram around the zodiac every 8 years.

History and meaning

The Pythagoreans used the pentagram (pentalpha) as a sign of recognition and of health. For them its endless golden self-similarity made it a symbol of perfection.

Across the dimensions

Slice of Small Stellated DodecahedronThe pentagram is one face of the small stellated dodecahedron: twelve pentagrams, extended through space, close around it.