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 octagonal

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).


Here are some views of the octagonal antiprism from various angles:

Projection Envelope Description
Regular hexadecagon

Parallel projection centered on octagonal face.


Parallel projection parallel to square faces and a pair of triangles.


11.25° side view.


Parallel projection centered on vertex.


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 17 Jun 2019.

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