Truncated Tetrahedron - Densest Packing

Densest Packing

The densest packing of the Archimedean Truncated Tetrahedron is believed to be Φ = 207/208, as reported by two independent groups using Monte Carlo methods. Although no mathematical proof exists that this is the best possible packing for those shapes, the high proximity to the unity and independency of the findings make it unlikely that an even denser packing is to be found. In fact, if the truncation of the corners is slightly smaller than that of an Archimedean Truncated Tetrahedron, this new shape can be used to completely fill space.