Star Polygons · 2D
Octagram
Star of Lakshmi · two squares
Eight points: two squares laid across each other at 45°, the Star of Lakshmi, with the sharper {8/3} star woven through them.
- Points
- 8
- Squares
- 2
- Silver ratio
- 1 + √2
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
- The two squares cross in a smaller regular octagon.
- The octagon holds the silver ratio 1 + √2 ≈ 2.414, as the pentagon holds φ.
- Seen from above, a square antiprism (two squares turned 45° and joined by eight triangles) casts exactly this star.
- The eight-pointed star (khatam) is a foundation of Islamic tiling: see the star pattern at 67.5°.
History and meaning
In Hinduism the Ashtalakshmi star stands for the eight forms of Lakshmi, goddess of abundance. The same figure is the Rub el Hizb in Islamic calligraphy, and the eight-pointed star of Ishtar in Mesopotamia.
Across the dimensions
- Shadow of Square AntiprismLift one square and turn it 45° from the other, then join them with triangles: the star is the shadow of a square antiprism.
