Wikipedia:Reference desk/Archives/Mathematics/2019 April 29

= April 29 =

difference in minimum circle for regular polyhedra vs complete coverage for same polyhedra.
Yeah, its a long title and would love a replacement...

For each of the 5 regular polyhedra, what is the difference in the radius of the smallest cylinder that it can pass through vs. the radius of the smallest cylinder that it can pass through in any orientation. For example for the cube, the smallest cylinder would have 4 parallel sides all on the edge of the cylinder, but a much larger cylinder would be needed if it went through with line through the opposite corner being parallel to the edge of the cylinder.Naraht (talk) 13:15, 29 April 2019 (UTC)


 * For those with central symmetry (i.e. excluding the simplex) I guess it's the difference between the circumradius (marked by a vertex) and the midradius (marked by the centre of an edge). —Tamfang (talk) 03:44, 30 April 2019 (UTC)
 * Thanx. I'd put together the circumradius, but for the mid radius, do you end up with a full set of parallel edges able to go through the "straw" the way that you can with a cube?Naraht (talk) 14:08, 2 May 2019 (UTC)