I want to construct 5 sided dice in the shape of a square-based pyramid. When rolled, I want the die to have equal probability to fall on all sides. That is, I want the odds that the die would fall base down to be 0.2. I insist on a pyramid shaped die (not tetrahedron). Other solutions are not relevant. Can this be done? Which pyramid dimensions would provide this? (Height to base diagonal ratio, or angle of the tip) My logic: This should be possible. If tip angle is wide and reaches pi, the die becomes flat and chance to flip base down is 0.5. If tip is narrowed reaching 0, the chance for rolling the die base down falls to 0 as well. A point must exists that provides a chance of 0.2 for throwing the die base down. Also, I wonder if this pyramid proportion is highly sensitive or not. Will small changes to angle tip throw the chance drastically away from 0.2? What is the full dependence of this chance on tip angle (or height to base ratio)? Also, does the die quasi-randomness maintained? In other words, is sensitivity to initial conditions similar to the regular cubic die? Can a normal person learn to throw the dice in a way as to alter the chance of outcome?