Icosahedron sentence example

icosahedron
  • This is the icosahedron.
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  • Four such solids exist: (I) small stellated dodecahedron; (2) great dodecahedron; (3) great stellated dodecahedron; (4) great icosahedron.
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  • Other examples of reciprocal holohedra are: the rhombic dodecahedron and cuboctahedron, with regard to the cube and octahedron; and the semiregular triacontahedron and icosidodecahedron, with regard to the dodecahedron and icosahedron.
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  • Shown above is an icosahedron of twelve dodecahedral structures surrounding a central dodecahedron; (H 2 O) 130.
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  • F rotates the icosahedron in various ways apparently looking for pentagon based pyramids on the " left " and " right " hand sides.
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  • Stainless steel nickel plated candle holder (20 sides - each side 1811 - see Para 12) shape is called an icosahedron.
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  • This category includes the 13-atom icosahedron, which can be decomposed into twenty tetrahedra sharing a common vertex.
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  • Several of these arise naturally as crystals, and the truncated icosahedron occurs in real life as a football.
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  • The energy is measured relative to the energy of the global minimum icosahedron.
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  • Structure 69C has a vertex atom missing from the underlying Mackay icosahedron like 38A.
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  • Further growth then leads to the next Mackay icosahedron.
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  • In order to see some of these more clearly, 64 of the 280 water molecules have been removed from the water icosahedron.
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  • The "regular icosahedron" is one of the Platonic solids; the "great icosahedron" is a Kepler-Poinsot solid; and the "truncated icosahedron" is an Archimedean solid (see Polyhedron).
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  • In crystallography the icosahedron is a possible form, but it has not been observed; it is closely simulated by a combination of the octahedron and pentagonal dodecahedron, which has twenty triangular faces, but only eight are equilateral, the remaining twelve being isosceles (see Crystallography).
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  • The distance between adjacent vertices of the icosahedron is 5% longer than the distance between a vertex and the center.
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  • Nevertheless, holding that every dimension has a principle of its own, he rejected the derivation of the elemental solids - pyramid, octahedron, icosahedron and cube - from triangular surfaces, and in so far approximated to atomism.
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  • The names of these five solids are: (r) the tetrahedron, enclosed by four equilateral triangles; (2) the cube or hexahedron, enclosed by 6 squares; (3) the octahedron, enclosed by 8 equilateral triangles; (4) the dodecahedron, enclosed by 12 pentagons; (5) the icosahedron, enclosed by 20 equilateral triangles.
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  • The first three were certainly known to the Egyptians; and it is probable that the icosahedron and dodecahedron were added by the Greeks.
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  • The equilateral triangle is the basis of the tetrahedron, octahedron and icosahedron.'
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  • These solids played an important part in the geometry of the Pythagoreans, and in their cosmology symbolized the five elements: fire (tetrahedron), air (octahedron), water (icosahedron), earth (cube), universe or ether (dodecahedron).
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  • The great dodecahedron is determined by the intersections of the twelve planes which intersect the Platonic icosahedron in five of its edges; or each face has the same boundaries as the basal sides of five covertical faces of the icosahedron.
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  • The great icosahedron is the reciprocal of the great stellated dodecahedron.
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  • Each of the twenty triangular faces subtend at the centre the same angle as is subtended by four whole and six half faces of the Platonic icosahedron; in other words, the solid is determined by the twenty planes which can be drawn through the vertices of the three faces contiguous to any face of a Platonic icosahedron.
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  • It is enclosed by 20 triangular faces belonging to the original icosahedron, and 12 pentagonal faces belonging to the coaxial dodecahedron.
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  • The truncated icosahedron is formed similarly to the icosidodecahedron, but the truncation is only carried far enough to leave the original faces hexagons.
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  • It is therefore enclosed by 20 hexagonal faces belonging to the icosahedron, and 12 pentagonal faces belonging to the coaxial dodecahedron.
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  • The truncated dodecahedron is formed by truncating the vertices of a dodecahedron parallel to the faces of the coaxial icosahedron so as to leave the former decagons.
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  • It is enclosed by 20 triangular faces belonging to the icosahedron and 12 decagons belonging to the dodecahedron.
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  • - Two 62-faced solids are derived from the dodecahedron, icosahedron and the semi-regular triacontahedron.
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  • In the " small rhombicosidodecahedron " there are 12 pentagonal faces belonging to the dodecahedron, 20 triangular faces belonging to the icosahedron and 30 square faces belonging to the triacontahedron.
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  • The pentagons belong to a dodecahedron, and 20 triangles to an icosahedron; the remaining 60 triangles belong to no regular solid.
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  • Thus the faces of the cuboctahedron, the truncated cube, and truncated octahedron, correspond; likewise with the truncated dodecahedron, truncated icosahedron, and icosidodecahedron; and with the small and great rhombicosidodecahedra.
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  • The boron skeleton takes the form of a regular icosahedron.
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