The Hexagonal Antiprism
The hexagonal antiprism is a 3D uniform polyhedron bounded by 14 polygons (2 hexagons and 12 triangles), 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).
Projections
Here are some views of the hexagonal antiprism from various angles:
| Projection | Envelope | Description |
|---|---|---|
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Regular dodecagon | Parallel projection centered on hexagonal face. |
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Trapezium | Parallel projection parallel to square faces and a pair of triangles. |
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Rectangle | Parallel projection centered on an edge between two triangles. |
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Heptagon | Vertex-centered parallel projection. |
Coordinates
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))
