Our d4 is based on the truncated tetrahedron. The standard d4 is a regular tetrahedron, and the truncated tetrahedron offers some advantages: 1) The numbers can face straight up; 2) This shape rolls and tumbles better; and 3) It's easier to pick up. A drawback to the truncated tetrahedron is the fact that it can land on a small triangular face, which we've found happens about 3% of the time. There is only one distinct choice for distributing the numbers on the four triangular faces. The use of this polyhedron for a die was previously described by Joseph Fjelstad.