Octahedrons

With the printed side of the template downward, fold all solid lines after folding each flap, push it back flat again. 

Apply glue to all flaps from the printed side of the template. 

Molecular Symmetry David J. Willock 2009 John Wiley Sons, Ltd. ISBN 978-0-470-85347-4 

Take flap number 1 and inserted it underneath the edge indicated on the template. You should make sure that the two solid lines are aligned at the join. 

Following the same procedure, glue the flaps in place in the order as numbered. Flaps 4 and 5 should be glued at the same time, applying light pressure from outside of the octahedron. 

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Referring to Problem 3, what should the ratio 710/711 be if the equilibrium crystal is to be a regular octahedron, that is, to have (10) and (11) edges of equal length ... 

Figure Bl.8.4. Two of the crystal structures first solved by W L Bragg. On the left is the stnicture of zincblende, ZnS. Each sulphur atom (large grey spheres) is surrounded by four zinc atoms (small black spheres) at the vertices of a regular tetrahedron, and each zinc atom is surrounded by four sulphur atoms. On the right is tire stnicture of sodium chloride. Each chlorine atom (grey spheres) is sunounded by six sodium atoms (black spheres) at the vertices of a regular octahedron, and each sodium atom is sunounded by six chlorine atoms.

Cobalt II) halides can be obtained by direct combination of the elements, or by dehydration of their hydrates. Anhydrous cobalt(II) chloride is blue, and the solid contains octahedrally-coordinated cobalt the hydrated salt C0CI2. bHjO is pink, with each cobalt surrounded by four water molecules and two chloride ions in a distorted octahedron. 

It is often difficult to represent inorganic compounds with the usual structure models because these structures are based on complex crystals space groups), aggregates, or metal lattices. Therefore, these compounds are represented by individual polyhedral coordination of the ligands such as the octahedron or tetrahedron Figure 2-124d). 

Periodic cells used in computer simulations the cube, truncated octahedron, hexagonal prism and rhombic hedron. 

The truncated octahedron and the rhombic dodecahedron provide periodic cells that are approximately spherical and so may be more appropriate for simulations of spherical molecules. The distance between adjacent cells in the truncated octahedron or the rhombic df)decahedron is larger than the conventional cube for a system with a given number of particles and so a simulation using one of the spherical cells will require fewer particles than a comparable simulation using a cubic cell. Of the two approximately spherical cells, the truncated octahedron is often preferred as it is somewhat easier to program. The hexagonal prism can be used to simulate molecules with a cylindrical shape such as DNA. 

Of the five possible shapes, the cube/parallelepiped and the truncated octahedron have been most widely used, with some simulations in the hexagonal prism. The formulae used to translate a particle back into the central simulation box for these three shapes are given in Appendix 6.4. It may be preferable to use one of the more common periodic cells even if there are aesthetic reasons for using an alternative. This is because the expressions for calculating the images may be difficult and inefficient to implement, even though the simulation would use fewer atoms. 

One atom above the face of an octahedron, which is distorted chiefly by separating the atoms at the corners of this face. 0.592... 

Fig. 4. Three 2eohtes with the same stmctural polyhedron, cubo-octahedrons. (a) Type A, Na 2[( 02) 2( 2)i2] sodalite [1302-90-5]-, (c)...

The common structural element in the crystal lattice of fluoroaluminates is the hexafluoroaluminate octahedron, AIF. The differing stmctural features of the fluoroaluminates confer distinct physical properties to the species as compared to aluminum trifluoride. For example, in A1F. all corners are shared and the crystal becomes a giant molecule of very high melting point (13). In KAIF, all four equatorial atoms of each octahedron are shared and a layer lattice results. When the ratio of fluorine to aluminum is 6, as in cryoHte, Na AlF, the AIFp ions are separate and bound in position by the balancing metal ions. Fluorine atoms may be shared between octahedrons. When opposite corners of each octahedron are shared with a corner of each neighboring octahedron, an infinite chain is formed as, for example, in TI AIF [33897-68-6]. More complex relations exist in chioUte, wherein one-third of the hexafluoroaluminate octahedra share four corners each and two-thirds share only two corners (14). 

Fig. 1. Stmctures of alkyllithium tetramers and hexamers (a) tetrahedron of lithium alkyl groups (b) arrangement of alkyl groups around octahedron of...

Fig. 1. Methods for representing SiO and AlO tetrahedra by means of (a) baH-and-stick model, (b) soHd tetrahedron, (c) skeletal tetrahedron, and (d) spare-filling of packed spheres (1). (e) Linking of four tetrahedra in a four-membered ring, (f) Secondary building unit called tmncated octahedron as...

Barium titanate [12047-27-7] has five crystaUine modifications. Of these, the tetragonal form is the most important. The stmcture is based on corner-linked oxygen octahedra, within which are located the Ti" " ions. These can be moved from their central positions either spontaneously or in an apphed electric field. Each TiO octahedron may then be regarded as an electric dipole. If dipoles within a local region, ie, a domain, are oriented parallel to one another and the orientation of all the dipoles within a domain can be changed by the appHcation of an electric field, the material is said to be ferroelectric. At ca 130°C, the Curie temperature, the barium titanate stmcture changes to cubic. The dipoles now behave independentiy, and the material is paraelectric (see Ferroelectrics). 

Titanium Trifluoride. The trifluoride (121) is a blue crystalline soHd, density 2980 kg/m, ia which the titanium atoms are six-coordinate at the center of a slightly distorted octahedron, where the mean Ti—F distance is 197 pm. Titanium trifluoride [13470-08-1] is stable ia air at room temperature but decomposes to titanium dioxide when heated to 100°C. It is insoluble ia water, dilute acid, and alkaUes but decomposes ia hot concentrated acids. The compound sublimes under vacuum at ca 900°C but disproportionates to titanium and titanium tetrafluoride [7783-63-3] at higher temperatures. 

Structures of heteropolytungstate and isopolytungstate compounds have been determined by x-ray diffraction. The anion stmctures are represented by polyhedra that share corners and edges with one another. Each W is at the center of an octahedron, and an O atom is located in each vertex of the octahedron. The central atom is similarly located at the center of an XO tetrahedron or XO octahedron. Each such polyhedron containing the central atom is generally surrounded by octahedra, which share corners, edges, or both with it and with one another. Thus, the correct total number of... 

Complex carbides are very numerous. Many newer compounds of this class have been discovered and their stmctures elucidated (20). The octahedron M C is typical where the metals arrange around a central carbon atom. The octahedra may be coimected via corners, edges, or faces. Trigonal prismatic polyhedra also occur. Defining T as transition metal and M as metal or main group nonmetal, the complex carbides can be classified as (/)... 

In the families of heptanuclear clusters, two geometries are found the capped octahedron that is typical for 98-valence electrons, and the vertex-sharing open tetrahedral (butterfly) stmctures typical for 106-valence electrons. An example of the former is Osy(CO)22 (51) an example of the latter is [H2AuOsg(CO)2Q] (52). In the AuOs cluster anion, the gold atom is at the vertex-sharing position. 

Equations (6-236) to (6-239) are based on experiments on cube-oc tahedrons, octahedrons, cubes, and tetrahedrons for which the sphericity f ranges from 0.906 to 0.670, respectively. See also Chft, Grace, and Weber. A graph of drag coefficient vs. Reynolds number with y as a parameter may be found in Brown, et al. (Unit Operations, Whey, New York, 1950) and in Govier and Aziz. 

An extreme example of hybidization is the structure proposed for sulphur hexafluoride, SFe. The six S-F bonds are dhected to the apices of a regular octahedron. An aiTangement which would satisfy this number of covalent bonds is sp d hybridization. The ground state of the sulphur atom is s p° and... 

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