Hexagonal prism

The hexagonal prism or hip is a prismatic uniform polyhedron. It consists of 2 hexagons and 6 squares. Each vertex joins one hexagon and two squares. As the name suggests, it is a prism based on a hexagon.

Vertex coordinates
A hexagonal prism of edge length 1 has vertex coordinates given by:
 * (±1/2, ±$\sqrt{5}$/2, ±1/2),
 * (±1, 0, ±1/2).

Representations
A hexagonal prism has the following Coxeter diagrams:


 * x x6o (full symmetry)
 * x x3x (A2×A1 symmetry, generally a ditrigonal prism)
 * s2s6x (generally a ditrigonal trapezoprism)
 * xx6oo&#x (hexagonal frustum)
 * xx3xx&#x (ditrigonal frustum)
 * xxx xux&#xt (A1×A1 axial, square-first)
 * xxxx ohho&#xt (A1×A1, vertex-first)
 * xx xu ho&#zx (A1×A1×A1 symmetry)

Variations
There are several isogonal lower-symmetry variants of the hexagonal prism, all of which are listed below:

Ditrigonal prism
A ditrigonal prism is a prism based on a ditrigon. The two bases are ditrigons, while the lateral sides are 3+3 rectangles.

Ditrigonal trapezoprism
A ditrigonal trapezoprism is made out of two opposite ditrigons in parallel planes, connected by 6 isosceles trapezoids.

Related polyhedra
A triangular cupola can be attached to a base of the hexagonal prism to form the elongated triangular cupola. If a second triangular cupola is attached to the other base in the same orientation, the result is the elongated triangular orthobicupola. If the second cupola is rotated 60º from the first cupola the result is the elongated triangular gyrobicupola.

It is also possible to augment square faces of the hexagonal prism with square pyramids. If one square is augmented the result is the augmented hexagonal prism. If a second square, opposite to the first,, is augmented the result is the parabiaugmented hexagonal prism. If two non-opposite, non-adjacent squares are augmented the result is the metabiaugmented hexagonal prism. If three mutually non-adjacent squares are augmented the result is the triaugmented hexagonal prism.

Two non-prismatic uniform polyhedron compounds are composed of hexagonal prisms:


 * Great rhombisnub octahedron (4)
 * Rhombisnub icosahedron (10)

There are also an infinite amount of prismatic uniform compounds that are the prisms of compounds of hexagons.