Haha, I made a mistake about the orbiformity of the tetrahedral teddy. My polytope viewer has a command for translating a polytope to be origin-centered, and I usually use that followed by a radius calculation command to see if all vertices have the same distance from the origin. However, the origin-centering calculates the center by averaging vertex coordinates, so it only works correctly if vertices are evenly distributed in the n-sphere! Otherwise it would not completely center the polytope and the radius calculation would wrongly indicate that it is non-orbiform.

However, the fact that the tetrahedral teddy has radius 1 means that the 5D tetrahedral teddy pyramid would be degenerate, since its height would be 0. So we cannot use it for CRF augmentation of the 5D teddies.