Forms of the Plane · 3D
Square Antiprism
Two squares turned 45°, joined by eight triangles
Take two squares, turn one by 45° and lift it, then join them with a band of eight equilateral triangles. From above, the two squares form the Star of Lakshmi.
- Vertices
- 8
- Edges
- 16
- Faces
- 2 ■ + 8 ▲
- Twist
- 45°
Turn it in your hands, strike it to hear the chord of its edges, slice it with a plane.
Facts
- Its shadow from above is the octagram: two squares, and the zig-zag band traces the octagon around them.
- With equilateral triangles, the height between the squares is 2^¼ ≈ 1.19 times the circle’s radius.
- Eight atoms of sulphur (S₈) and many coordination complexes take this shape.
- A square antiprism with a square pyramid on each end becomes a solid built from triangles only.
Across the dimensions
- Its shadow OctagramLift one square and turn it 45° from the other, then join them with triangles: the star is the shadow of a square antiprism.
