(1) While writing, I may choose a clear Quartz Crystal for clarity or a yellow Fluorite octahedron to help keep creative thoughts flowing.(2) These five remarkable solids - tetrahedron, cube, octahedron , dodecahedron, icosahedron - have faces that are congruent equilateral polygons.(3) Theaetetus was the first to study the octahedron and the icosahedron and it is believed that Book XIII of Euclid's Elements is based on his work.(4) I'd like to mention in passing that the octahedron , the dual of the cube, also contains 26: 8 faces, 12 edges, 6 vertices.(5) The cube, consisting of six square faces, is a common form either alone or in combination with other forms, especially the octahedron .(6) Earth was a cube, air an octahedron , fire a tetrahedron and water an icosahedron.(7) A dodecahedron modified by the octahedron and cube from Nordmark, Sweden, is figured in Goldschmidt.(8) Finally, the octahedron inscribed in the Venus-orbit sphere has itself an inscribed sphere, on which the orbit of Mercury lies.(9) There is the octahedron , with 8 faces, 12 edges and 6 vertices.(10) The exception is an octahedron from another Peruvian mine, Quiruvilca (400 kilometers north of Huanzala).(11) It was a set of platonic bodies: there was an octahedron and a double tetrahedron.(12) When well-crystallized, it typically exhibits the cube form modified by the octahedron and dodecahedron; crystals to 20 cm across have been reported.(13) Water was an icosahedron, and air had to be an octahedron .(14) It involves placing the knot inside a plastic octahedron and mapping where the strands of the knot meet.(15) These are often known as the Platonic solids: the tetrahedron, cube, octahedron , dodecahedron and icosahedron.(16) The one exception is the exciting accidental discovery of a 4.22-carat, gem-quality octahedron in Dale County, Alabama.
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