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octahedron

A yellowish octahedron found at De Beers weighed 4282 carats, and yielded a brilliant of 2882 carats.

65the cube, the octahedron, and the pentagonal dodecahedron.

671 shows P the cube {100}, d the octahedron {III }, and e the pentagonal dodecahedron {210}.

46The regular octahedron has for its faces equilateral triangles; it is the reciprocal of the cube.

47There is often a furrow running along the edges of the octahedron, or across the edges of the cube, and this indicates that the apparently simple crystal may really consist of eight individuals meeting at the centre; or, what comes to the same thing, of two individuals interpenetrating and projecting through each other.

47Ladenburg's prism formula would give two enantiomorphic ortho-di-substitution derivatives; while forms in which the hydrogen atoms are placed at the corners of a regular octahedron would yield enantiomorphic tri-substitution derivatives.

33Two such sets placed base to base form the octahedron, which consequently has 8 faces, 6 vertices and 12 edges.

34Marsh also devised a form closely resembling that of Thomsen, inasmuch as the carbon atoms occupied the angles of a regular octahedron, and the diagonal linkages differed in nature from the peripheral, but differeng from Thomsen's since rupture of the diagonal and not peripheral bonds accompanied the reduction to hexamethylene.

36Diamond may break with a conchoidal fracture, but the crystals always cleave readily along planes parallel to the octahedron faces: of this property the diamond cutters avail themselves when reducing the stone to the most convenient form for cutting; a sawing process, has, however, now been introduced, which is preferable to that of cleavage.

23The crystals are sometimes polysynthetic, a large octahedron, e.g., being built up of small cubes.

23The equilateral triangle is the basis of the tetrahedron, octahedron and icosahedron.'

23Other 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.

23The crystals are sometimes polysynthetic, a large octahedron, e.g., being built up of small cubes.

23Reduction to hexamethylene compounds necessitates the disruption of three of the edges of the octahedron, the diagonal linkings remaining intact, or, in the plane projection, three peripheral linkages, the hexamethylene ring assuming the form (III); In 1888 J.

24The 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.

11The snub cube is a 38-faced solid having at each corner 4 triangles and I square; 6 faces belong to a cube, 8 to the coaxial octahedron, and the remaining 24 to no regular solid.

12The snub cube is a 38-faced solid having at each corner 4 triangles and I square; 6 faces belong to a cube, 8 to the coaxial octahedron, and the remaining 24 to no regular solid.

12Devon, notably near Liskeard, where fine crystals have been found, with faces of the six-faced octahedron replacing the corners of the cube.

13OCTAHEDRON (Gr.

15OCTAHEDRON (Gr.

15Octahedron >>

00All these are strikingly alike in appearance and general characters, differing essentially only in chemical composition, and it would seem better to reserve the name cerargyrite for the whole group, using the names chlorargyrite (AgC1), embolite (Ag(Cl, Bl)), bromargyrite (AgBr) and iodembolite (Ag(C1, Br, I)) for the different isomorphous members of the group. They are cubic in crystallization, with the cube and the octahedron as prominent forms, but crystals are small and usually indistinct; there is no cleavage.

00If the grooves be left out of account, the large faces which have replaced each tetrahedron corner then make up a figure which has the aspect of a simple octahedron.

00Cleavage is nearly always perfect, parallel to the octahedron.

00It is enclosed by 6 square and 8 triangular faces, the latter belonging to a coaxial octahedron.

00It has 6 octagonal faces (belonging to the original cube), and 8 triangular ones (belonging to the coaxial octahedron).

00See the notes for the net of a cube to see how to print this net and make your own cube octahedron.

00Under certain conditions the voids adopt their equilibrium shape, a truncated octahedron.

00However F produced the following drawings in the process of constructing a representation of the dual cube octahedron: Figure 10.

00The 38-atom truncated octahedron is the most stable fcc cluster in the size range we consider.

00Fold a blow-up stellated octahedron from a single sheet of square paper.

00Lewis Simon's Gyroscope is a skeletal octahedron with a small hole in the center.

00truncated octahedron.

00This is one of the Platonic solids, and is treated in the article Polyhedron, as is also the derived Archimedean solid named the "truncated tetrahedron"; in addition, the regular tetrahedron has important crystallographic relations, being the hemihedral form of the regular octahedron and consequently a form of the cubic system.

00All these are strikingly alike in appearance and general characters, differing essentially only in chemical composition, and it would seem better to reserve the name cerargyrite for the whole group, using the names chlorargyrite (AgC1), embolite (Ag(Cl, Bl)), bromargyrite (AgBr) and iodembolite (Ag(C1, Br, I)) for the different isomorphous members of the group. They are cubic in crystallization, with the cube and the octahedron as prominent forms, but crystals are small and usually indistinct; there is no cleavage.

00Ladenburg's prism formula would give two enantiomorphic ortho-di-substitution derivatives; while forms in which the hydrogen atoms are placed at the corners of a regular octahedron would yield enantiomorphic tri-substitution derivatives.

00The octahedral formula discussed by Julius Thomsen (Ber., 1886, 19, p. 2 944) consists of the six carbon atoms placed at the corners of a regular octahedron, and connected together by the full lines as shown in (I); a plane projection gives a hexagon with diagonals (II).

00Reduction to hexamethylene compounds necessitates the disruption of three of the edges of the octahedron, the diagonal linkings remaining intact, or, in the plane projection, three peripheral linkages, the hexamethylene ring assuming the form (III); In 1888 J.

00Marsh also devised a form closely resembling that of Thomsen, inasmuch as the carbon atoms occupied the angles of a regular octahedron, and the diagonal linkages differed in nature from the peripheral, but differeng from Thomsen's since rupture of the diagonal and not peripheral bonds accompanied the reduction to hexamethylene.

00Two parallel triangular faces are removed from a cardboard model of a regular octahedron, and on the remaining six faces tetrahedra are then placed; the hydrogen atoms are at the free angles.

00The native metal crystallizes in the cubic system, the octahedron being the commonest form, but other and complex combinations have been observed.

00In 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).

00The regular octahedron has for its faces equilateral triangles; it is the reciprocal of the cube.

00Philolaus, connecting these ideas, held that the elementary nature of bodies depends on their form, and assigned the tetrahedron to fire, the octahedron to air, the icosahedron to water, and the cube to earth; the dodecahedron he assigned to a fifth element, aether, or, as some think, to the universe (see Plut.

00the cube, the octahedron, and the pentagonal dodecahedron.

001 shows P the cube {100}, d the octahedron {III }, and e the pentagonal dodecahedron {210}.

00The crystals belong to the cubic system, generally assuming the form of the octahedron (fig.

00but they may, in accordance with the principles of crystallography, also occur in other forms symmetrically derived from the octahedron, - for example, the cube, the 2-faced figure known as the rhombic dodecahedron (fig.

00The octahedron faces are usually smooth; most of the other faces are rounded (fig.

00There is often a furrow running along the edges of the octahedron, or across the edges of the cube, and this indicates that the apparently simple crystal may really consist of eight individuals meeting at the centre; or, what comes to the same thing, of two individuals interpenetrating and projecting through each other.

005 shows how the octahedron with furrowed edge may be constructed from two interpenetrating tetrahedra (shown in dotted lines).

00If the grooves be left out of account, the large faces which have replaced each tetrahedron corner then make up a figure which has the aspect of a simple octahedron.

006) are united by contact along a surface parallel to an octahedron face without interpenetration.

00P the octahedron faces; the latter are particularly well defined and have the form =% of equilateral triangles (fig.

00similar to the " etched figures " produced 7' by moistening an octahedron of alum, and have probably been produced, like them, by the action of some solvent.

00Diamond may break with a conchoidal fracture, but the crystals always cleave readily along planes parallel to the octahedron faces: of this property the diamond cutters avail themselves when reducing the stone to the most convenient form for cutting; a sawing process, has, however, now been introduced, which is preferable to that of cleavage.

00The Victoria, 180 carats, was cut from an octahedron weighing 4572 carats, and was sold to the nizam of Hyderabad for £400,000.

00A yellowish octahedron found at De Beers weighed 4282 carats, and yielded a brilliant of 2882 carats.

00The combination of these two forms produces a figure resembling an octahedron, the angle between P and P' being 70Ã‚° 72', corresponding to the angle 70Ã‚° 32' of the regular octahedron.

00name Flussspat or Fluss.) Fluor-spar crystallizes in the cubic system, commonly in cubes, either alone or combined with the octahedron, rhombic dodecahedron, four-faced cube, &c. The four-faced cube has been called the fluoroid.

00Cleavage is nearly always perfect, parallel to the octahedron.

00Devon, notably near Liskeard, where fine crystals have been found, with faces of the six-faced octahedron replacing the corners of the cube.

00Nevertheless, 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.

00The 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.

00The equilateral triangle is the basis of the tetrahedron, octahedron and icosahedron.'

00Two such sets placed base to base form the octahedron, which consequently has 8 faces, 6 vertices and 12 edges.

00These 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).

00It is enclosed by 6 square and 8 triangular faces, the latter belonging to a coaxial octahedron.

00It has 6 octagonal faces (belonging to the original cube), and 8 triangular ones (belonging to the coaxial octahedron).

00The truncated octahedron is formed by truncating the vertices of an octahedron so as to leave the original faces hexagons; consequently it is bounded by 8 hexagonal and 6 square faces.

00- Two Archimedean solids of 26 faces are derived from the coaxial cube, octahedron and semiregular (rhombic) dodecahedron (see below).

00it is self-reciprocal; the cube and octahedron, the dodecahedron and icosahedron, the small stellated dodecahedron and great dodecahedron, and the great stellated dodecahedron and great icosahedron are examples of reciprocals.

00Since the tetrahedron is the hemihedral form of the octahedron, and the octahedron and cube are reciprocal, we may term these two latter solids " reciprocal holohedra " of the tetrahedron.

00Other 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.

00Thus 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.

00The octahedral formula discussed by Julius Thomsen (Ber., 1886, 19, p. 2 944) consists of the six carbon atoms placed at the corners of a regular octahedron, and connected together by the full lines as shown in (I); a plane projection gives a hexagon with diagonals (II).

01Two parallel triangular faces are removed from a cardboard model of a regular octahedron, and on the remaining six faces tetrahedra are then placed; the hydrogen atoms are at the free angles.

01The native metal crystallizes in the cubic system, the octahedron being the commonest form, but other and complex combinations have been observed.

016) are united by contact along a surface parallel to an octahedron face without interpenetration.

01similar to the " etched figures " produced 7' by moistening an octahedron of alum, and have probably been produced, like them, by the action of some solvent.

01The combination of these two forms produces a figure resembling an octahedron, the angle between P and P' being 70° 72', corresponding to the angle 70° 32' of the regular octahedron.

01name Flussspat or Fluss.) Fluor-spar crystallizes in the cubic system, commonly in cubes, either alone or combined with the octahedron, rhombic dodecahedron, four-faced cube, &c. The four-faced cube has been called the fluoroid.

01Nevertheless, 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.

01These 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).

01The truncated octahedron is formed by truncating the vertices of an octahedron so as to leave the original faces hexagons; consequently it is bounded by 8 hexagonal and 6 square faces.

01it is self-reciprocal; the cube and octahedron, the dodecahedron and icosahedron, the small stellated dodecahedron and great dodecahedron, and the great stellated dodecahedron and great icosahedron are examples of reciprocals.

01Since the tetrahedron is the hemihedral form of the octahedron, and the octahedron and cube are reciprocal, we may term these two latter solids " reciprocal holohedra " of the tetrahedron.

02Thus 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.

025 shows how the octahedron with furrowed edge may be constructed from two interpenetrating tetrahedra (shown in dotted lines).

03The Victoria, 180 carats, was cut from an octahedron weighing 4572 carats, and was sold to the nizam of Hyderabad for £400,000.

03

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