The Octagonal Antiprism


The octagonal antiprism is a 3D uniform polyhedron bounded by 2 octagons and 16 triangles. It has 32 edges and 16 vertices.

The octagonal
antiprism

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:

where H = √((1 + √2)(√(1 + 1/√2) - 1)), or approximately 0.860296, is half the height of the antiprism.


Last updated 28 May 2018.

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