## Net of spherinder, coninder, etc...

Discussion of shapes with curves and holes in various dimensions.

### Net of spherinder, coninder, etc...

A net of cylinder has a square (or rectangle) and two circles.

What do you think net of spherinder, coninder, etc... will be? At least, they would have two spheres, cones respectively.
hy.dodec
Dionian

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### Re: Net of spherinder, coninder, etc...

Hi!

The same way there is no simple representation on the net of a sphere, there is no way to simply make a net of a spherinder. It would have an infinite set of lines plus the two spheres. You could approximate it with geodesic triangle or quadrilateral rods.
ndl
Trionian

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### Re: Net of spherinder, coninder, etc...

The cubinder could be unrolled into a cube and 4 cylinders, that's correct.

However, the spherinder can't be unrolled that way, because the manifold that joins its two spherical ends has curvature in two dimensions. It has spherical cross-section, so it can't be unrolled without splitting into many irregular pieces. Just like the map of the earth can't be represented faithfully on a 2D map without distortions. If you allow stretching and similar distortions, then you could unroll it into a cube (e.g. using Mercator projection to unfold the sphere with distortions). But that won't give you a good idea of its curled up shape because to roll it back up into the spherinder's lateral manifold you'll need to stretch / compress it in different areas. The areas near the pole would be distorted, for example, and must be compressed when folding it back up. Or you could use any of the various map projections that map the sphere to an oval or irregular shape. But again, it's not possible to do this without distortions.

The coninder can be unfolded into two cones, a cylinder, and a split cylinder, i.e., the extruded version of semicircle that you fold up into a cone.
quickfur
Pentonian

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