Proprism

An f-vector is a number of k-face elements in a polytope from k=0 (points) to k=n-1 (facets).

If equal lengths, this doubling represents { }8, a square tetra-prism {4}4, a tesseract duo-prism {4,3,3}2, and regular 8-cube {4,3,3,3,3,3,3}.

In the context of a product of polygons, Henry P. Manning's 1910 work explaining the fourth dimension called these double prisms.

If the triangles are regular it can be written as a product of Schläfli symbols, {3} × {3}, and is composed of 9 vertices.

The tesseract, can be constructed as the duoprism {4} × {4}, the product of two equal-size orthogonal squares, composed of 16 vertices.

The Cartesian product of an a-polytope, a b-polytope, and a c-polytope is an (a + b + c)-polytope, where a, b and c are 2-polytopes (polygon) or higher.

The {3}×{3} duoprism is a proprism as the product of two orthogonal triangles, having 9 squares between pairs of edges of 2 sets of 3 triangles, and 18 vertices, as seen in this skew orthogonal projection.
The prism {3} × {3} × {3} can be seen in orthogonal projection within a regular enneagon.