![]() The pseudoicosahedron works as an adjective but not a noun. Neither are accepted names for an existing form. Strictly speaking, icosahedron is not allowed in classical crystallography and pseudoicosahedron isn't either. To get the pseudoicosahedral appearance for pyrite both forms must be equally developed or in equilibrium. Rational indices has long been a theorem in crystallography.Īs to this pictured pyrite, it was stated that two forms, the pyritohedron and the octahedron are present. A true icosahedron does not exist in crystals because the form cannot be expressed with rational indices. However, in geometry a pseudoicosahedron has been defined with 8 equilateral triangles and 12 isoceles triangles. As a classic Platonic solid the icosahedron is as you described. Being familiar with pyritohedral crystals, I immediately made the dual connection when I first saw crystals of this almost-icosahedral habit and was dismayed to learn later on that it was a close-but-no-cigar situation.įive-fold symmetry does exist in the world of quasicrystals-very cool, but also over my head-which occur in certain man-made alloys.Ĥth Jan 2014 14:24 UTC Alfred L. More tantalizingly, the icosahedron and pyritohedron are geometric duals, closely related forms each having a face centered on one of the other's corners (think of a cube and an octahedron). Likewise, the most common pyritohedron looks a lot like a pentagonal dodecahedron, but that too would have to have the forbidden 5-fold symmetry. ![]() A true icosahedron has 5-fold symmetry, which (due to reasons that are over my head) cannot exist in crystals. They do have 20 triangular faces, but the faces are not quite equilateral triangles. Geometrically they are not quite icosahedral, however. Recent Images in DiscussionsĤth Jan 2014 13:11 UTC Ed Clopton Expert Neat specimen of pyrite! I have seen these micro-size but not as large as 7 mm. Currier Digital LibraryOpen discussion area. Techniques for CollectorsOpen discussion area. Minerals and MuseumsOpen discussion area. Mineralogical ClassificationOpen discussion area. Lost and Stolen SpecimensOpen discussion area. ╳Discussions □ Home □ Search □ Latest Groups EducationOpen discussion area.
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