Triaprism
In geometry of 4 dimensions or higher, a proprism is a polytope resulting from the Cartesian product of two or more polytopes, each of two dimensions or higher. The term was coined by John Horton Conway for product prism. The dimension of the space of a proprism equals the sum of the dimensions of all its product elements. Proprisms are often seen as k-face elements of uniform polytopes.
The number of vertices in a proprism is equal to the product of the number of vertices in all the polytopes in the product.
The minimum symmetry order of a proprism is the product of the symmetry orders of all the polytopes. A higher symmetry order is possible if polytopes in the product are identical.
A proprism is convex is all its product polytopes are convex.
In geometry of 4 dimensions or higher, duoprism is a polytope resulting from the Cartesian product of two polytopes, each of two dimensions or higher. The Cartesian product of an a-polytope, a b-polytope is an (a+b)-polytope, where a and b are 2-polytopes (polygon) or higher.
Most commonly this refers to the product of two polygons in 4-dimensions. In the context of a product of polygons, Henry P. Manning's 1910 work explaining the fourth dimension called these double prisms.
The Cartesian product of two polygons is the set of points:
where P1 and P2 are the sets of the points contained in the respective polygons.
The smallest is a 3-3 duoprism, made as the product of 2 triangles. If the triangles are regular it can be written as as product of Schläfli symbols, {3} × {3}, and is composed of 9 vertices.
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