The Conical Cylinder


The conical cylinder, or coninder for short, is constructed by extruding a 3D cone along the W-axis. The following diagram shows a parallel projection of the coninder:

extruded cone
projection of coninder

The next diagram shows a perspective projection of the coninder:

cone-within-a-cone
projection of coninder

The round frustum in the bottom part of the diagram is actually a cylinder. We see this more clearly in the next diagram:

cone-within-a-cylinder
projection of coninder

Here, the coninder is partially rotated in the ZW plane. The inner cone has emerged from the outer cone and is now above it. It is almost at a 90 degree angle from our viewpoint, and so appears flattened. The cylinder has now partially emerged from the outer cone as well.

In the last diagram following, the coninder has turned 90 degrees in the ZW plane, and we are looking directly at the line connecting the apices of the two cones.

two-cones-within-a-cylinder projection of coninder

The line connecting the apices of the two cones is the central axis of a toroidal 3-manifold joining the two cones and the cylinder. This manifold is formed by extruding the nappe of a 3D cone along the W-axis.


Last updated 16 Feb 2016.

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