Calculations at a regular prism, this is a right prism with a regular n-gon as base.
Enter the number of vertices at one base (at least 3), edge length and prism height. Choose the number of decimal places, then click Calculate.
Formulas:
A = 2 * n * a² / [ 4 * tan(π/n) ] + n * a * h
V = n * h * a² / [ 4 * tan(π/n) ]
pi:
π = 3.141592653589793...
Edge length and height have the same unit (e.g. meter), the area has this unit squared (e.g. square meter), the volume has this unit to the power of three (e.g. cubic meter). A/V has this unit -1.
If the height h of a regular prism is equal to its edge length a, then it possesses an even higher degree of regularity. Besides Platonic solids, Archimedean solids, Johnson solids, and uniform antiprisms, such prisms are the only solids that have only regular polygons as faces. A regular prism with a square base is a cuboid. With a higher degree of regularity, it is a cube.
All regular prisms have a plane of symmetry centered and perpendicular to their rectangular faces. In addition, there are further planes of symmetry equal to the number of vertices of the base. With an odd number of vertices, these planes pass through a vertex of one base, the opposite edge, and likewise through the corresponding vertex and edge of the other base. With an even number of vertices in a base, there are two types of planes of symmetry. One type passes through opposite vertices each, the other through opposite edges each. A cube, however, has even more planes of symmetry, a total of nine.
Regular prisms are rotationally symmetric along an axis through the centers of the bases at an angle of 360 degrees divided by the number of base vertices and multiples thereof. Further axes of rotation pass perpendicularly through the centers of the faces: for odd numbers of faces, through an edge and the opposite face; for even numbers of faces, through an edge and the opposite edge, and through a face and the opposite face. These have a rotational symmetry of 180 degrees and multiples thereof, this is for every half a rotation. The cube, in turn, has even more axes of rotation, together 13. Regular prisms, that is, those with an even number of vertices on a base, are point-symmetric.
