# How many circular cylinders through 5 general points?

How many right circular cylinders can pass through 5 general points in ℝ3 ? Edit: 0,2,4, or 6.

• Solid cylinders, or shells? – The Masked Avenger Dec 3 '14 at 19:12
• @TheMaskedAvenger: points on the infinite cylinder surface (shells). – David Lampert Dec 3 '14 at 19:17
• As noted in a disappeared comment, there is no cylinder if one point is interior to the convex hull of the other 4. The question is what are the other possible numbers of cylinders, especially what is the maximum? – David Lampert Dec 3 '14 at 21:50
• Aside - this theoretical question arose years ago when I worked on an industry coordinate measuring machine application to compute and display cylinders (and other manufactured shapes) to best fit a number (greater than 5) of probe measured points. – David Lampert Dec 3 '14 at 22:09
• The maximum number of cylinders is at least 3, since you can find 3 cylinders sharing the 8 vertices of a cube. But maybe you meant to rule this out when you asked about "general position". – Gerry Myerson Dec 3 '14 at 22:35