**For a 5 sided die that was a triangular prism, what would the dimensions be like for it to be fair (each side has an equal chance)?**

**Answer:**

If you believe the probability of landing on a base varies continuously from 1 to 0 as the height of the prism varies from 0 to ∞, then the Intermediate Value Theorem says there is a prism for which the probability if 1/5. If you believe the probability strictly decreases with increasing height, there is exactly one “fair” prism.