The duoprism is a 4-polytope that can be constructed using Cartesian product of two polygons.

[1] In the case of 3-3 duoprism is the simplest among them, and it can be constructed using Cartesian product of two triangles.

The resulting duoprism has 9 vertices, 18 edges,[2] and 15 faces—which include 9 squares and 6 triangles.

It has Coxeter diagram , and symmetry [[3,2,3]], order 72.

The hypervolume of a uniform 3-3 duoprism with edge length

This is the square of the area of an equilateral triangle,

The 3-3 duoprism can be represented as a graph with the same number of vertices and edges.

Like the Berlekamp–van Lint–Seidel graph and the unknown solution to Conway's 99-graph problem, every edge is part of a unique triangle and every non-adjacent pair of vertices is the diagonal of a unique square.

[6], page 45: "The dual of a p,q-duoprism is called a p,q-duopyramid.

" It has 9 tetragonal disphenoid cells, 18 triangular faces, 15 edges, and 6 vertices.

The regular complex polygon 2{4}3, also 3{ }+3{ } has 6 vertices in

matching the same vertex arrangement of the 3-3 duopyramid.

It can be seen in a hexagonal projection with 3 sets of colored edges.

This arrangement of vertices and edges makes a complete bipartite graph with each vertex from one triangle is connected to every vertex on the other.