Prism

A general prism is a polyhedron possessing two congruent polygonal faces and with all remaining faces parallelograms (Kern and Bland 1948, p. 28; left figure).

A right prism is a prism in which the top and bottom polygons lie on top of each other so that the vertical polygons connecting their sides are not only parallelograms, but rectangles (right figure). A prism that is not a right prism is known as an oblique prism. If, in addition, the upper and lower bases are rectangles, then the prism is known as a cuboid.

The regular right equilateral prisms are canonical polyhedra whose duals are canonical dipyramids. Canonical prisms have midradius equal to the circumradius of their -gonal faces, i.e.,

(1)

where is the edge length.

The regular right prisms have particularly simple nets, given by two oppositely-oriented -gonal bases connected by a ribbon of squares. The graph corresponding to the skeleton of a prism is known, not surprisingly, as a prism graph.

The volume of a prism of height and base area is simply

(2)

The above figure shows the first few regular right prisms, whose faces are regular -gons. The 4-prism with unit edge lengths is simply the cube. The dual polyhedron of a regular right prism is a dipyramid.

A regular right unit -prism has surface area

			(3)
			(4)

where is the area of the corresponding regular polygon. The first few surface areas are

			(5)
			(6)
			(7)
			(8)
			(9)
			(10)
			(11)
			(12)

The algebraic degrees of these areas for , 4, ... are 2, 1, 4, 2, 6, 2, 6, 4, 10, 2, 12, 6, 8, 4, 16, 6, 18, 4, ... (OEIS A089929).

A regular right unit -prism has volume

(13)

The first few volumes are

			(14)
			(15)
			(16)
			(17)
			(18)
			(19)
			(20)
			(21)

The algebraic degrees of the volumes are the same as for the surface areas.

The right regular triangular prism, square prism (cube), and hexagonal prism are all space-filling polyhedra.