The Octagonal Antiprism
The octagonal antiprism is a 3D uniform polyhedron bounded by 18 polygons (2 octagons and 16 triangles), 32 edges, and 16 vertices.
The height of an octagonal antiprism with an edge length of 2 is:
2√((1 + √2)(√(1 + 1/√2) - 1))
which is approximately 1.720591.
The square cupola (J4) can be pasted with an octagonal antiprism to produce a gyroelongated square cupola (J23). Adding a second cupola produces the gyroelongated square bicupola (J45).
Projections
Here are some views of the octagonal antiprism from various angles:
| Projection | Envelope | Description |
|---|---|---|
 |
Regular hexadecagon | Parallel projection centered on octagonal face. |
 |
Trapezium | Parallel projection parallel to square faces and a pair of triangles. |
 |
Rectangle | 11.25° side view. |
 |
Nonagon | Parallel projection centered on vertex. |
Coordinates
The Cartesian coordinates of the octagonal antiprism, centered on the origin and having edge length 2, are:
- (±1, ±(1+√2), H)
- (±(1+√2), ±1, H)
- (0, ±√(4+2√2), -H)
- (±√(4+2√2), 0, -H)
- (±√(2+√2), ±√(2+√2), -H)
where H = √((1 + √2)(√(1 + 1/√2) - 1)), or approximately 0.860296, is half the height of the antiprism.
