The Hexagonal Antiprism
The hexagonal antiprism is a 3D uniform polyhedron bounded by 2 hexagons and 12 triangles. It has 24 edges and 12 vertices.
The height of a hexagonal antiprism with an edge length of 2 is 2√(√3−1), or approximately 1.711199.
The hexagonal antiprism can be attached to a triangular cupola to form a gyroelongated triangular cupola (J22), a Johnson solid. Adding another cupola on the other side of the antiprism produces the gyroelongated triangular bicupola (J44).
Here are some views of the hexagonal antiprism from various angles:
Parallel projection centered on hexagonal face.
Parallel projection parallel to square faces and a pair of triangles.
Parallel projection centered on an edge between two triangles.
Vertex-centered parallel projection.
The Cartesian coordinates of the hexagonal antiprism, centered on the origin and having edge length 2, are:
- (±1, ±√3, √(√3−1))
- (±2, 0, √(√3−1))
- (±√3, ±1, −√(√3−1))
- (0, ±2, −√(√3−1))