Also with Conway, an enumeration led to the discovery of the grand antiprism, an unusual uniform polychoron in four dimensions.
22.
:Note that the square antiprism is also a minimum energy configuration even though a cube would give all the angles equal.
23.
It can be decomposed into a gyroelongated pentagonal pyramid and a pentagonal pyramid or into a pentagonal antiprism and two equal pentagonal pyramids.
24.
The pentagrammic crossed-antiprism may be inscribed within an icosahedron, and has ten triangular faces in common with the great icosahedron.
25.
There are also 41 convex semiregular 4-polytope, including the non-Wythoffian grand antiprism and the snub 24-cell.
26.
This includes all nonprismatic uniform 4-polytopes, except for the non-Wythoffian grand antiprism, which has no Coxeter family.
27.
It can be constructed by attaching a hexagonal antiprism to the base of a triangular cupola ( " J " 3 ).
28.
Eric Weisstein, prisms, and the uniform antiprisms ( overlapping with the cube as a prism and regular octahedron as an antiprism ).
29.
Adjoining a triangular prism to a square antiprism also generates a polyhedron, but has adjacent parallel faces, so is not a Johnson solid.
30.
As the name suggests, it can be constructed by gyroelongating an octahedron ( square bipyramid ) by inserting a square antiprism between its congruent halves.
