Problem of the Week 1151

Construct a Regular 7-Gon

You have seven one-foot long pieces of pipe and a supply of right-angle connectors. Show how to arrange the seven pieces into a closed path in 3-space, with a right angle between each piece.

It is easy to do this with four pieces, but impossible with three or five pieces.

A full solution is a list of seven points in space making the required right angles.

Source: Problem of the month #97 (Sept. 2010) at http://mathcentral.uregina.ca/mp/previous2010/