The Square Antiprism
The square antiprism is a 3D uniform polyhedron bounded by 10 polygons (2 squares and 8 triangles), 16 edges, and 8 vertices.
The height of a square antiprism with an edge length of 2 is 2^{3/4}, or approximately 1.68179.
A square antiprism can be capped with a square pyramid to form the gyroelongated square pyramid (J10), a Johnson solid, or with two square pyramids to form the gyroelongated square bipyramid (J17), another Johnson solid.
The dual of the square antiprism is the square trapezohedron.
Projections
In order to be able to identify the square antiprism in various projections of 4D objects, it is useful to know how it appears from various viewpoints. The following are some of the commonlyencountered views:
Projection  Envelope  Description 

Regular octagon  Parallel projection centered on square face. 

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

Pentagon  Vertexcentered parallel projection. 

Rectangle  Parallel projection centered on an edge between two triangles. 
Coordinates
The Cartesian coordinates of the square antiprism, centered on the origin and having edge length 2, are:
 (0, ±√2, 1/∜2)
 (±√2, 0, 1/∜2)
 (±1, ±1, −1/∜2)
Occurrences
The square antiprism occurs in the following CRF polytopes: