I have been reading this article and google-ing and still nothing, so here it goes What is: -P-type icosahedral? -Tsai-type quasicrystal? -1/1 cubic approximant? -six-dimensional lattice parameter a6D? -why has (this is example) powder X-ray diffraction spectrum just 2 high peaks (at some angles), and why are they called 111112 and 011202 (underlined line should be above letters) and what does it mean? Many thanks..