A polyhedron similar to a prism, with two parallel faces which are regular polygons, and a number of triangular faces connecting them. If you think of a drum with a cord connecting the two heads running back and forth in a zigzag fashion, you should have a good idea of what an antiprism looks like.

Although the planes of an antiprism are parallel, the regular polygons are rotated by half a point with respect to each other in the plane.

The vertex of one polyhedron corresponds with the middle of the edge of the opposite polyhedron.

(The rocks on the 8-bit Firebird game The Sentinel are square anti-prisms)