Duoprism

A duoprism is a 4-dimension Dimension

In common usage, a dimension is a parameter [i] or measurement [i] required to define the characteristi ...

al figure resulting from the Cartesian product of two polygon Polygon

A polygon is a closed [i] planar [i] path composed of a finite number of sequential ...

s in the 2-dimensional Euclidean space. More precisely, it is the set Set

In mathematics [i], a set can be thought of as any collection [i] of distinct things considered as a who ...

of points: where P1 and P2 are the sets of the points contained in the respective polygons. The duoprism is a convex Convex set

In Euclidean space [i], an object is convex if for every pair of points within the object, every point o ...

4-dimensional polytope Polytope

In geometry [i] polytope means, first, the generalization to any dimension of polygon [i] in two dimens ...

bounded by prismic cells.

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Set of uniform p,q-duoprisms Example 23,29-duoprism
Type	Prismatic uniform polychoron Uniform polychoron In geometry [i], a uniform [i] polychoron is a polychoron [i] or 4-polytope [i] which ...
Cells	p q-gonal prisms, q p-gonal prisms
Faces	pq squares, p q-gons, q p-gons
Edges	2pq
Vertices	pq
Vertex configuration	tetrahedron Tetrahedron A tetrahedron is a polyhedron [i] composed of four triangular faces, three of which meet at each vertex [i] ...
Symmetry group Symmetry group The symmetry [i] group of an object is the group [i] of all isometries [i] under which it is invariant [i] ...	[p]x[q]
Schläfli symbol Schläfli symbol In mathematics [i], the Schlfli symbol is a simple notation that gives a summary of some important prope ...	x
Properties	convex Convex set In Euclidean space [i], an object is convex if for every pair of points within the object, every point o ...

A duoprism is a 4-dimension Dimension

In common usage, a dimension is a parameter [i] or measurement [i] required to define the characteristi ...

al figure resulting from the Cartesian product of two polygon Polygon

A polygon is a closed [i] planar [i] path composed of a finite number of sequential ...

s in the 2-dimensional Euclidean space. More precisely, it is the set Set

In mathematics [i], a set can be thought of as any collection [i] of distinct things considered as a who ...

of points:

where P₁ and P₂ are the sets of the points contained in the respective polygons.

The duoprism is a convex Convex set

In Euclidean space [i], an object is convex if for every pair of points within the object, every point o ...

4-dimensional polytope Polytope

In geometry [i] polytope means, first, the generalization to any dimension of polygon [i] in two dimens ...

bounded by prismic cells.

Geometry

A uniform duoprism is created by the product of a regular n-sided polygon Polygon

A polygon is a closed [i] planar [i] path composed of a finite number of sequential ...

and a regular m-sided polygon is bounded by n m-gonal prisms and m n-gonal prisms. For example, the Cartesian product of a triangle and a hexagon is a duoprism bounded by 6 triangular prisms and 3 hexagonal prisms.

When m and n are identical, the resulting duoprism is bounded by 2n identical n-gonal prisms. For example, the Cartesian product of two triangles is a duoprism bounded by 6 triangular prisms.

When m and n are identically 4, the resulting duoprism is bounded by 8 tetragonal prisms , and is identical to the hypercube Measure polytope

In geometry [i], a measure polytope is an n-dimensional analogue of a square [i] and a cube [i] ...

.

The m-gonal prisms are attached to each other via their m-gonal faces, and form a closed loop. Similarly, the n-gonal prisms are attached to each other via their n-gonal faces, and form a second loop perpendicular to the first. These two loops are attached to each other via their square faces, and are mutually perpendicular.

As m and n approach infinity, the corresponding duoprisms approach the duocylinder. As such, duoprisms are useful as non-quadric approximations of the duocylinder.

Nomenclature

The term duoprism is coined by George Olshevsky. It is a subset of the prismatic polychora. In Olshevsky's usage, a duoprism made of n-polygons and m-polygons is named by prefixing 'duoprism' with the names of the base polygons, for example: the triangular-pentagonal duoprism is the Cartesian product of a triangle and a pentagon.

An alternative, more concise way of specifying a particular duoprism is by prefixing with numbers denoting the base polygons, for example: 3,5-duoprism for the triangular-pentagonal duoprism.

Other alternative names:

q-gonal-p-gonal prism
q-gonal-p-gonal double prism
q-gonal-p-gonal hyperprism

References

The Fourth Dimension Simply Explained, Henry P. Manning, Munn & Company, 1910, New York. Available from the University of Virginia library. Also accessible online: —contains a description of duoprisms and duocylinders

External links

—describes duoprisms as "double prisms" and duocylinders as "double cylinders"
- glossary of higher-dimensional terms
The word Duoprism is also the name of an . It has no relation to the mathematical use of the term as described here.