The duocylinder, or double cylinder, is a geometric object embedded in 4-dimensional Euclidean space, defined as the Cartesian product of two disks of radius r:
It is analogous to a cylinder in 3-space, which is the Cartesian product of a disk with a line segment.
The duocylinder is bounded by two mutually perpendicular 3-manifolds with torus-like surfaces, described by the equations:
and
The duocylinder is so called because these two bounding 3-...
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The duocylinder, or double cylinder, is a geometric object embedded in 4-dimensional Euclidean space, defined as the Cartesian product of two disks of radius r:
It is analogous to a cylinder in 3-space, which is the Cartesian product of a disk with a line segment.
The duocylinder is bounded by two mutually perpendicular 3-manifolds with torus-like surfaces, described by the equations:
and
The duocylinder is so called because these two bounding 3-manifolds may be thought of as 3-dimensional cylinders 'bent around' in 4-dimensional space such that they form closed loops in the XY and ZW planes. The duocylinder has rotational symmetry in both of these planes.
The ridge of the duocylinder is the 2-manifold that is the boundary between the two bounding tori. It is in the shape of a Clifford torus, which is the Cartesian product of two circles. Intuitively, it may be constructed as follows: Roll a 2-dimensional rectangle into a cylinder, so that its top and bottom edges meet. Then roll the...
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