The Hexagonal Antiprism
The hexagonal antiprism is a 3D uniform polyhedron bounded by 2 hexagons and 12 triangles. It has 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 

Regular dodecagon  Parallel projection centered on hexagonal face. 

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

Rectangle  Parallel projection centered on an edge between two triangles. 

Heptagon  Vertexcentered 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))