Icosahedral stereographic projections in three dimensions for use in dark field TEM

Thermodynamics require that rapidly cooled crystals and quasicrystals are relatively defective. Yet, without convenient 3-dimensional indexation both at crystal poles and in diffraction planes, or Kikuchi maps, it is difficult to identify the defects by dark field transmission electron microscopy. For two phase Al6Mn, these maps are derived. They relate i-Al6Mn to the standard face centered cubic, matrix crystals. An example of their usefulness in determining interfacial characteristics is described. Indices are integral powers on an irrational number.