Fair Die - Self Proof Version

The centre of gravity / centre of mass of this die is right in the centre of the icosahedral shape. Every pip is identical, and the centre of gravity of each individual face is also in the centre of that face.
This was achieved by using two different kinds of symmetry to 'cancel out' the effect of each pip on the overall centre of gravity of the die. the pips near the inside of each face are the same in number as the pips near the inside of the face opposite. The pips on the outside of each face are the same in number as three other faces on the icosahedron, creating a tetrahedron when those faces are joined. Because of the way the pips are displayed, it is possible to determine that the centre of gravity is in the centre of the shape, simply by examining the die.