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1A three-dimensional shape having eight plane faces, especially a regular solid figure with eight equal triangular faces.
‘This six-point perspective, with the six vertices of an octahedron serving as the vanishing points, becomes the basis of his spherical paintings.’
‘I'd like to mention in passing that the octahedron, the dual of the cube, also contains 26: 8 faces, 12 edges, 6 vertices.’
‘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.’
‘A dodecahedron modified by the octahedron and cube from Nordmark, Sweden, is figured in Goldschmidt.’
‘It was a set of platonic bodies: there was an octahedron and a double tetrahedron.’
‘Finally, the octahedron inscribed in the Venus-orbit sphere has itself an inscribed sphere, on which the orbit of Mercury lies.’
‘The cube, consisting of six square faces, is a common form either alone or in combination with other forms, especially the octahedron.’
‘Plato believed that atoms have the shapes of regular polyhedra: cubes, tetrahedrons, octahedrons, and so on.’
‘These are often known as the Platonic solids: the tetrahedron, cube, octahedron, dodecahedron and icosahedron.’
‘There is the octahedron, with 8 faces, 12 edges and 6 vertices.’
‘These five remarkable solids - tetrahedron, cube, octahedron, dodecahedron, icosahedron - have faces that are congruent equilateral polygons.’
‘Peterson and Jordan go on to investigate interesting links between integer octahedra and integer antiprisms.’
1.1A body, especially a crystal, in the form of a regular octahedron.
‘One specimen was covered with small rounded crystal-like projections, similar to cube and octahedron forms.’
‘Copper, Cu, has been found associated with cuprite octahedra at Pedra Preta, where these minerals occur on talc and magnesite.’
‘Most that I have seen have been elongated octahedra or other forms, such as some of the branches of an arborescent aggregate.’
‘While writing, I may choose a clear Quartz Crystal for clarity or a yellow Fluorite octahedron to help keep creative thoughts flowing.’
‘A diamond crystal is essentially two pyramids stuck together - an octahedron.’
‘The octahedra range from 5 to 10 pm in diameter and show interpenetrant growth.’
‘Most of these specimens exhibit crystals that are cubic in habit; however, octahedra of both blue-gray and medium green have also been common.’
‘There were smoky quartz crystals plus huge fluorite octahedra.’
‘When well-crystallized, it typically exhibits the cube form modified by the octahedron and dodecahedron; crystals to 20 cm across have been reported.’
‘In contrast to crystals that resemble textbook drawings, the most frequently encountered gold crystals are skeletal octahedra.’
‘The Ogluinsky mine specimens are millimeter-sized octahedra, and the Nicolay mine specimens are unabraded and have mica attached.’
‘Older collections sometimes contain small, very pale, transparent green fluorite octahedra from the Tomboy vein.’
‘The exception is an octahedron from another Peruvian mine, Quiruvilca (400 kilometers north of Huanzala).’
‘Earth was a cube, air an octahedron, fire a tetrahedron and water an icosahedron.’
‘The fluorite tends to occur only as cubes modified by the dodecahedron, with simple cubes or octahedra uncommon or absent.’
‘Water was an icosahedron, and air had to be an octahedron.’
‘The one exception is the exciting accidental discovery of a 4.22-carat, gem-quality octahedron in Dale County, Alabama.’
‘It involves placing the knot inside a plastic octahedron and mapping where the strands of the knot meet.’
‘She notes that lime-green to purplish-green modified fluorite octahedra have been found at this pegmatite.’
‘One small lot of specimens from Alta Floresta, Mato Grosso, exhibited moderately rounded, well-developed octahedra.’
Origin
Late 16th century: from Greek oktaedron, neuter (used as a noun) of oktaedros ‘eight-faced’.