Net of spherinder, coninder, etc...

[hy.dodec]

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.

[ndl]

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.

[quickfur]

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.

[wendy]

the net of a glome is a crind formed by the intersection of two cylinder, the lines at on the top where the polar lines, ahd at each height is a rectangle that becomes a layer of climata. the axis of the cube become tim aganst the day, the year plaxis and the slimata tours. the glome is made of torii, whic h unfolf into lattiude=the the zenithe of the sun and the logitude is the angle where the sun is current.

[hy.dodec]

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.
(...)
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.

Thanks for detailed reply. How about n-prismic cylinders, conical cones and cylindrones? For spherone, that would be same case as spheriender.