Duotegum

A duotegum is a class of polytopes formed as the tegum product of two polytopes. The simplest non-trivial duotegum is the triangular duotegum, which is the tegum product of two triangles. The dual of a duotegum is a duoprism. The cross polytopes are duotegums made from lower-dimensional cross polytopes.

If one of the polytopes is a point, then the resulting polytope is identical to the other polytope. If one of the polytopes is a line segment, then the resulting polytope is the bipyramid of the other polytope. Neither of these cases are usually considered duotegums.

The vertex coordinates of a duotegum is determined by the coordinates of two polytopes a and b in mutually distinct coordinate sets. As such, they have a number of vertices equal to the sum of the number of vertices of each polytope.