| The cube, consisting of six square faces, is a common form either alone or in combination with other forms, especially the octahedron. |
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| 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. |
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| One specimen was covered with small rounded crystal-like projections, similar to cube and octahedron forms. |
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| While writing, I may choose a clear Quartz Crystal for clarity or a yellow Fluorite octahedron to help keep creative thoughts flowing. |
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| A dodecahedron modified by the octahedron and cube from Nordmark, Sweden, is figured in Goldschmidt. |
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| Earth was a cube, air an octahedron, fire a tetrahedron and water an icosahedron. |
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| The one exception is the exciting accidental discovery of a 4.22-carat, gem-quality octahedron in Dale County, Alabama. |
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| It involves placing the knot inside a plastic octahedron and mapping where the strands of the knot meet. |
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| This six-point perspective, with the six vertices of an octahedron serving as the vanishing points, becomes the basis of his spherical paintings. |
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| Finally, the octahedron inscribed in the Venus-orbit sphere has itself an inscribed sphere, on which the orbit of Mercury lies. |
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| The large four-sided facets above and below and to the right and left of the table are the faces of the octahedron. |
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| First stage in the development of a brilliant from an octahedron, showing the position of the table and culet. |
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| Earth was associated with the cube, air with the octahedron, water with the icosahedron, and fire with the tetrahedron. |
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| The rough stone, which had the form of an irregular octahedron, is shown above in its actual size. |
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| A regular octahedron has faces that are all equilateral triangles. |
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| There is the octahedron, with 8 faces, 12 edges and 6 vertices. |
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| The exception is an octahedron from another Peruvian mine, Quiruvilca. |
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| As in a cube, the faces of the octahedron are all the same regular polygon. |
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| These minerals have a structure, unlike that of the other tungstates, based on WO6 octahedra i.e., each tungsten atom is surrounded by six oxygen atoms arranged at the corners of an octahedron. |
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| Find at least one net for a regular octahedron. |
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| The plesiohedra include such well-known shapes as the cube, hexagonal prism, rhombic dodecahedron, and truncated octahedron. |
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| Three, the tetrahedron, octahedron and icosahedron, have triangular faces. |
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| Other evidence suggests he may have only been familiar with the tetrahedron, cube, and dodecahedron, and that the discovery of the octahedron and icosahedron belong to Theaetetus, a contemporary of Plato. |
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| He builds robots out of DNA by programming strands of it to stick together into complicated shapes, including cubes, a truncated octahedron and a walking DNA biped for use as nanorobots or in a DNA computer. |
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| A polyhedron consists of a central cation, typically silicon or aluminum in common minerals, surrounded by a regular tetrahedron or octahedron of four or six oxygen atoms, respectively. |
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| He further explains that earth is a cube, fire a tetrahedron, air an octahedron, and water an icosahedron. |
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| In any space of more than four dimensions, there exist exactly three regular polytopes the generalizations of the tetrahedron, the cube, and the octahedron. |
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| In heteropolymolybdates or heteropolytungstates, each molybdenum or tungsten atom is located at the centre of an octahedron, each vertex of which is occupied by an oxygen atom. |
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| Thus, there is a star octahedron, three star dodecahedrons, and fifty-nine star icosidodecahedrons. |
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| As we have seen, diamonds are most frequently cut in the brilliant form, which form is comparable to that of an octahedron of which two opposite corners have been truncated. |
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| Stones which, either by nature or by the hand of man, have been given the shape of an octahedron, have already the ground-form of the brilliant and can be at once faceted. |
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| That the art was not entirely unknown in the Orient is evidenced by the existence of a beautiful Indian octahedron of 30 carats, described by Boutan, one face of which was engraved with a devotional motto. |
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| The direction space is divided in 8 regions according to an octahedron. |
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| An octahedron has eight faces, each an equilateral triangle. |
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| The cube is by far the most recognized habit of fluorite followed by the octahedron which is believed to form at higher temperatures than the cube. |
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| Each lepton group represents the binary rotational symmetries of familiar 3-D regular polyhedrons, the tetrahedron, the octahedron, and the icosahedron. |
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