7 sided die possible?

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Well, you can’t have a 7-sided polyhedron where all the faces are the same; that requires an even number. But you could make a die if it doesn’t conform to those rules:

  1. Let some faces be different. A pentagonal prism has 7 faces, five rectangles and two pentagons, and then they need to be just the right size to make it fair.
  2. Add faces that don’t count. You could make something based on a heptagonal pyramid or prism, but that won’t balance on the bases.

It looks like people have tried 7-sided dice based on both these options – for instance here and here. The 3-sided die would be more or less a non-polyhedral equivalent of the second approach.

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