Enigma 404: Regular timepiece
From New Scientist #1554, 2nd April 1987 [link]
My daughter has a regular hexagonal clock without numerals, as illustrated. I tried to fool her recently by rotating it and standing it on a different edge, but she recognised that the hands did not look quite right.
On the other hand, my son, has a clock on a regular polygon, again without numerals, which I can stand on any different edge and make the clock show the wrong time with its hands in apparently legitimate positions.
How many edges does this regular polygon have?