A close up inside the 23-29 duoprism projected onto a 3-sphere, and perspective projected to 3-space. As m and n become large, a duoprism approaches the geometry of duocylinder just like a p-gonal prism approaches a cylinder.
In geometry of 4 dimensions or higher, a double prism[1] or duoprism is a polytope resulting from the Cartesian product of two polytopes, each of two dimensions or higher. The Cartesian product of an n-polytope and an m-polytope is an (n+m)-polytope, where n and m are dimensions of 2 (polygon) or higher.
The lowest-dimensional duoprisms exist in 4-dimensional space as 4-polytopes being the Cartesian product of two polygons in 2-dimensional Euclidean space. More precisely, it is the set of points:
where P1 and P2 are the sets of the points contained in the respective polygons. Such a duoprism is convex if both bases are convex, and is bounded by prismatic cells.
^The Fourth Dimension Simply Explained, Henry P. Manning, Munn & Company, 1910, New York. Available from the University of Virginia library. Also accessible online: The Fourth Dimension Simply Explained—contains a description of duoprisms (double prisms) and duocylinders (double cylinders). Googlebook
prismatic 4-polytopes. A duoprism constructed from two regular polygons of the same edge length is a uniform duoprism. A duoprism made of n-polygons and...
order of size and complexity). As a uniform duoprism, the tesseract exists in a sequence of uniform duoprisms: {p}×{4}. The regular tesseract, along with...
special non-Wythoffian form, the grand antiprism. Two infinite families of duoprisms and antiprismatic prisms exist in the fourth dimension. There are only...
Coxeter planes. Examples in 4 dimensions are the 24-cell, snub 24-cell, 6-6 duoprism, 6-6 duopyramid. In 6 dimensions 6-cube, 6-orthoplex, 221, 122. It is also...
the two-dimensional orthographic projection of the four-dimensional 8-8 duoprism. In number theory, figurate numbers representing octagons are called octagonal...
duoantiprism can be constructed from a nonuniform variant of the 10-10/3 duoprism (a duoprism of a decagon and a decagram) where the decagram's edge length is...
as the duoprism {4} × {4}, the product of two equal-size orthogonal squares, composed of 16 vertices. The 5-cube can be constructed as a duoprism {4} × {4...
rhombic-shape. The term duopyramid was used by George Olshevsky, as the dual of a duoprism. The lowest dimensional forms are 4 dimensional and connect two polygons...
envelopes in the plane. The n-n duoprisms and dual duopyramids also have 2n-gonal Petrie polygons. (The tesseract is a 4-4 duoprism, and the 16-cell is a 4-4...
The graph of the 3-3 duoprism (the line graph of K 3 , 3 {\displaystyle K_{3,3}} ) is perfect. Here it is colored with three colors, with one of its 3-vertex...
to the five partitions of 4, the number of dimensions. Clifford torus Duoprism Flat torus Hopf fibration Manifold The Fourth Dimension Simply Explained...
2D figures, as in the case of e.g. the duocylinder and various regular duoprisms. 2-fold rotational symmetry together with single translational symmetry...
solutions are related to the 24-cell, and an infinite set of self-dual duoprisms generate regular skew polyhedra as {4, 4 | n}. In the infinite limit these...
represented by square faces of the runcinated {r,p,r}. {4,4|n} produces a n-n duoprism, and specifically {4,4|4} fits inside of a {4}x{4} tesseract. A final set...
infinite family based on antiprisms, and another infinite family of uniform duoprisms, which are products of two regular polygons. Clifford torus The Fourth...
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