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Topic: Octahedra

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	[No title]
		Octahedra within layers share edges, and faces are shared across layers.
		Based on hexagonal closest packing of oxygen, with Ti filling half of the octahedral interstitial positions, ABABABAB stacking of octahedra in 'chains' is evident.
		The +4 cation are arranged in chains of octahedra, parallel to the c-axis; rutile has a prismatic habit due to the chains parallel to c.
	www.auburn.edu /~hameswe/MinDay14.html (457 words)

	Fluoride Glasses - Solid State Chemistry
		Some (10%) of the most regular octahedra and trigonal prisms are shown together with the most irregular ones built by the RMC process.
		The counterpart of such a denser zone is that 5 isolated octahedra exist in the RMC model.
		The [MF ] polyhedra, which are all octahedra contrarily to the RMC model, present the expected mean M-F distance and are not excessively distorted (figure 5).
	www.cristal.org /glasses/paper/SSChem.html (561 words)

	Uniform Compounds of Uniform Polyhedra
		The compound of three octahedra has two types of vertices and so it not vertex-uniform, although it is facially uniform.
		A few familiar compounds are both uniform and facially uniform: the 5 cubes, the 5 octahedra, and the compounds of 2, 5, and 10 tetrahedra.
		This is a special rigid compound of 20 octahedra, illustrated at left, dual to a special version of the compound of 20 cubes which has pairs of coplanar faces.
	www.georgehart.com /virtual-polyhedra/uniform-compounds-info.html (1225 words)

	Andreini tessellation - Wikipedia, the free encyclopedia
		[5/3] 2 truncated octahedra, 2 truncated tetrahedra, 1 cuboctahedron (Truncated alternated cubic)
		The tiling of octahedra and tetrahedra is of special importance since its vertices form a cubic close-packing of spheres.
		The space-filling trusses of packed octahedra and tetrahedra was apparently first discovered by Alexander Graham Bell and independently re-discovered by Buckminster Fuller (who called it the octet truss and patented it in the 1940s) [2] [3] [4] [5].
	en.wikipedia.org /wiki/Andreini_tessellation (668 words)

	24-Cell Stereoscopic View (Site not responding. Last check: 2007-10-13)
		There are 2 superimposed octahedra in the center of the figure with their vertices at the center of each of the square faces.
		There are 6 octahedra associated with the 6 apparent cube faces seen in the interior of the figure.
		These are the vertices of 6 octahedra who's opposite vertices are all touching at the center of the figure.
	users.adelphia.net /~eswab/24clenv.htm (362 words)

	Compounds of Cubes
		6 octahedra, all spinning with a 4-fold axis aligned on prism's 12-fold axis, 3 clockwise, 3 counterclockwise, [2n
		6 octahedra, all spinning with a 3-fold axis aligned aligned on prism's 9-fold axis, 3 clockwise, 3 counterclockwise, [2n
		6 octahedra, all spinning with a 2-fold axis aligned aligned on prism's 6-fold axis, 3 clockwise, 3 counterclockwise, [2n
	www.georgehart.com /virtual-polyhedra/compounds-spin.html (1191 words)

	Wells' "Hyperbolic" Tesselations (Site not responding. Last check: 2007-10-13)
		The aluminum atoms are at the centers of the octahedra and the magnesium atoms at the centers of the tetrahedra.
		The enclosing cubes are truncated 3/8 of the cube edge from each corner, and the recessed central vertices are 1/8 of the cube edge in from the center.
		By omitting one opposing pair of octahedra we obtain the basic unit of the preceding 10 x 3 tiling.
	www.uwgb.edu /dutchs/symmetry/hypwells.htm (462 words)

	Compounds of Cubes
		Dual to this is the uniform nonrigid compound of 4 octahedra [*].
		At the 60 degree angle it reduces to the uniform compound of four octahedra, and at the other angle, a compound of 4 of the 5 octahedra from the standard icosahedral compound of 5 octahedra.
		As a final example, one may compound all the rigid compounds with octahedral symmetry---the compound of three cubes, the compound of four cubes, and the compound of six cubes, along with the original cube---to make a compound of fourteen cubes with octahedral symmetry.
	www.georgehart.com /virtual-polyhedra/compound-cubes-info.html (2412 words)

	Crystal structure of aluminosilicates
		In sillimanite, andalusite, and kyanite, chains of Al octahedra are oriented parallel to the crystallographic c-axes, which are initially oriented into the page.
		In their chains, the Si tetrahedra and the Al octahedra alternate with each other and are perfectly aligned along one of the crystal axes.
		The alignment of the tetrahedra and octahedra contrasts with the arrangements found in the polymorphs kyanite and andalusite.
	www.umanitoba.ca /chemistry/courses/chem130/molecules/crystals/alsi.html (285 words)

	Find Octahedra (Site not responding. Last check: 2007-10-13)
		The atoms must have 6 connected atoms that will be used as vertices of the octahedra.
		The kind of atoms that should occupy the vertices of the octahedra.
		The opacity of the facies of the octahedras.
	www.cscs.ch /~mvalle/ChemViz/doc/STM3/FindOctahedra.html (159 words)

	Table T7. Summary of the opaque mineralogy of basement rocks, Site 1206. (Continued on next page.)
		Skeletal octahedra and dendrites; extensive development of ilmenite oxidation lamellae and alteration to maghemite along cleavage planes and fractures; rare titanomagnetite relicts are present parallel to cleavage planes
		Skeletal octahedra; titanomagnetite is altered to maghemite along cleavage planes and fractures; ilmenite oxidation lamellae are present in unaltered titanomagnetite
		Skeletal octahedra and dendrites; titanomagnetite is altered to maghemite along cleavage planes, fractures, and on crystal margins; ilmenite oxidation lamellae are present in unaltered titanomagnetite
	www-odp.tamu.edu /publications/197_IR/chap_06/c6_t7.htm (849 words)

	Models
		As their octahedral periodicity shows, each of the atomic elements is composed of identical regular octahedra joined edge to edge in crystalline order.
		Octahedra can be made of paper by downloading and printing the octahedral layouts using the LAYOUT link, and cutting and pasting as shown in the video using the CUTandPASTE link.
		There are photos which show twenty identical octahedra in a quasicrystalline assemby--a regular icosahedron.
	homepage.mac.com /whitby/AtomicElements/Personal202.html (120 words)

	Bricard's Flexible Octahedron
		The construction of the flexible octahedra depends on the following lemma illustrated in fig.
		The example below showed a planar 4-gon aba'b' with rotation axis L perpendicular to the plane, note that this flexible octahedra will flex if we fixed ba' and twist a into and b' out of the plane but not to the other direction because of the bad intersections of the edges.
		The flexible octahedron in figure 3 cannot be made with surfaces (due to its self-intersecting nature), but the framework is easy to build with straws and strings as in figure 4.
	www.geocities.com /jshum_1999/polyhedra/bricard.htm (318 words)

	Contents of Model independent analysis
		However, the presence of fully JT distorted octahedra is evident in the local structure, though the peak in the PDF from the long-bonds is not resolved and is evident only as a broad shoulder [23,170,171].
		While the model PDF shown as the solid line is calculated assuming 46% prolate octahedra (two long Mn-O bonds at 2.16 Å, four short ones at 1.935 Å) mixed with 54% normal octahedra (6 Mn-O bonds at 1.935 Å).
		While the model PDF shown as solid line is calculated assuming 20% prolate octahedra (2 long Mn-O bonds at 2.16 Å, 4 short ones at 1.935 Å) mixed with 80% normal octahedra (6 Mn-O bonds at 1.935 Å).
	www.pa.msu.edu /~xiangyun/qiu_thesis/node70_ct.htm (766 words)

	JOINING TENSEGRITY SYSTEMS (Site not responding. Last check: 2007-10-13)
		3 strut octahedra can be joined together, edge to edge, like the octahedra of the close packing arrangement of the octahedra and tetrahedra.
		The octahedra can be arranged in a single layer or in several layers.
		Some octahedra can be omitted, especially in the multi-layer arrangements to produce more open arrangements of tensegrity figures.
	myweb.cableone.net /amkalenak/joiningtensegrity.html (479 words)

	A Fuller Explanation: Chapter Twelve all space filling
		Hexagonal faces of two truncated octahedra come together after rotating 60 degrees with respect to each other, so that square faces alternate (rather than landing next to each other) and begin to frame a cavity in the exact tetrakaidecahedral shape (Fig.
		Sixteen tetrahedra and nineteen half octahedra are clearly visible in the three layers shown.
		Adding up the volumes of the unit tetrahedra (each with a volume of one) and unit octahedra (each with a volume of four) in successive layers, we quickly find that the "cubic" numbers are confirmed, as shown in Figure 12-6.
	www.angelfire.com /mt/marksomers/117.html (1090 words)

	crop-circle forms and the Universe
		Whether this is to focus our attention on that little publicised discovery, or is because these geometrical forms (octahedra and tetrahedra) are perhaps found in many environments and on lots of levels in Nature, or for some other reason, I don't know.
		This data has been combined, and it turns out that the known super-clusters are gathered along lines and at intersecting points which form at least 4 locally identified octahedra, which are joined at their tips in a sort of chrystalline pattern.
		Between and inside these octahedra are relative voids of magnetic fields and galaxies, though there may well be lots of dark matter.
	www.korncirkler.dk /cccorner/universe.html (784 words)

	5 Octahedra and Pattern Knot
		Some of the images I created while I was exploring the scaling of the Icosahedron and the Dodecahedron reminded me of some of the darwings Lynnclaire had drawn of the Pattern knot having straight edges rather than curved edges.
		Maybe if this straight-edged Pattern knot was changed to match up with the Octahedra vertices exactly then it would be a true knot, without the knot edges intersecting each other but rather weaving by each other as a real knot would.
		It may be the case that further exploration of these ideas will reveal some connection to the scaling by extending polyhedra edges and the Pattern Knot construction....
	www.rwgrayprojects.com /Lynn/OctaKnot/OctaKnot.html (432 words)

	Perovskite - WolfWikis
		Common distortions such as cation displacements within the octahedra and tilting of the octahedra are related to the properties of the A and B substituted atoms.
		A distortion of the cell is visualized by a shear of a (100) face and a perpendicular contraction of the derived cubic cell [7].
		X-Ray diffraction data shows the tilting of the octahedra indicate a displacement of sodium atoms in the cell, as shown in figures 8 and 9 [8].
	wikis.lib.ncsu.edu /index.php/Perovskite (2092 words)

	SPuDS
		The notation describes a tilt system by rotations of BX octahedra about any of three orthogonal Cartesian axes, which are coincident with the three axes of the aristotype cubic unit cell.
		Rotation of one octahedron causes the four adjacent octahedra in the same layer to rotate in the opposite direction in the same angle.
		The X-B-X bond angles of the BX6 octahedra remain ideal (90°) and the B-X bond distances are held constant in the calculations.
	www.unf.edu /~michael.lufaso/spuds/index.html (2929 words)

	DNA octahedra
		Reports the design and synthesis of a 1,669-nucleotide, single-stranded DNA molecule that is amplified by polymerases and that folds into an octahedron structure by a simple denaturation-renaturation procedure.
		Cryo-electron microscopy showed that the DNA strands fold to form hollow octahedra ~ 22 nanometres in diameter.
		Because the base-pair sequence of individual struts is not repeated in a given octahedron, each strut is uniquely addressable by the appropriate sequence-specific DNA binder.
	e-drexler.com /p/04/03/0319shih2004.html (92 words)

	DNA octahedra
		Reports the design and synthesis of a 1,669-nucleotide, single-stranded DNA molecule that is amplified by polymerases and that folds into an octahedron structure by a simple denaturation-renaturation procedure.
		Cryo-electron microscopy showed that the DNA strands fold to form hollow octahedra ~ 22 nanometres in diameter.
		Because the base-pair sequence of individual struts is not repeated in a given octahedron, each strut is uniquely addressable by the appropriate sequence-specific DNA binder.
	www.e-drexler.com /p/04/03/0319shih2004.html (92 words)

	Cutting Polyhedra (Site not responding. Last check: 2007-10-13)
		This unit should be taught after students have already made cubes, tetrahedra, and octahedra from poster board (skeletal or solid), and therefore they know their basic properties.
		6 octahedra sitting in the six corners and 8 tetrahedra, one in the middle of each face.
		These are the graphic files with predrawn layouts for the required octahedra and tetrahedra.
	www.math.nmsu.edu /breakingaway/Lessons/cuttingPH/cuttingPH.html (461 words)

	National Synchrotron Light Source
		It is shown that an atomic structure transformation occurs between ~2-4 GPa, in which the Jahn-Teller distortion (JTD) of the MnO6 octahedra is enhanced, in parallel with an increase in the Mn-O1-Mn bond angle.
		The diffraction patterns were refined with the Rietveld method on the basis of the 1 atm Pbnm space group.
		Transport studies reveal pressure-induced distortions of the MnO6 octahedra in the whole class of the colossal magnetoresistive materials with varying bandwidth.
	www.nsls.bnl.gov /newsroom/science/2003/08-Tyson.htm (741 words)

	South Africa diamond deposits, geology, exploration, mining, use - Part XV
		Crystals of this kind, when not unduly distorted, are greatly prized, especially the octahedra, for it is possible to give such stones the desired brilliant form with very little preliminary cleaving and loss of material.
		An example of this irregular intergrowfh is furnished by the spheres of bort, which have been already described and which occur very frequently both here and in Brazil.
		The surface of these spheres is seldom quite smooth, the projecting corners of the numerous small octahedra, of which the sphere is built up, being the cause of the irregularities of its surface.
	www.minelinks.com /alluvial/diamondGeology37.html (1176 words)

	Crystal structure of aluminosilicates
		In sillimanite, andalusite, and kyanite, chains of Al octahedra are oriented parallel to the c-axes, which are initially oriented into the page.
		In their chains, the Si tetrahedra and the Al octahedra alternate with each other and are perfectly aligned when viewed down the c-axes (best seen with the Al atoms highlighted and slightly off from looking down the c-axis).
		In kyanite, the octahedra in the Al octahedral chains are more ordered and more compact than in sillimanite or andalusite.
	www.geo.ucalgary.ca /~tmenard/crystal/alsi.html (297 words)

	Spinel Structure
		Filled octahedra form criss-cross rows, with alternating layers of parallel rows offset as shown on the right side of the diagram.
		Since there are twice as many filled octahedra as tetrahedra, and the formula for spinel is XY, it is possible to fill all the octahedra with Y (trivalent) atoms and the tetrahedra with X (divalent) atoms.
		In olivine the continuous straight rows of octahedra are slightly distorted, probably because of the SiO4 tetrahedra that share octahedral edges.
	www.uwgb.edu /dutchs/PETROLGY/Spinel%20Structure.HTM (735 words)

	DNA folds into nano-octahedra - nanotechweb.org
		Shih says that three-dimensional arrays of the DNA octahedra could be used to image guest molecules inserted into the lattice, or for organizing molecular-scale logic gates into complex three-dimensional circuits for molecular computing applications.
		“Two key challenges are the reliable assembly of DNA octahedra into three-dimensional networks and the reliable attachment of guest macromolecules to the octahedra,” he added.
		According to Shih, the octahedra could also find use as a cage to trap molecules and protect them from the outside environment, perhaps being programmed to release their contents in response to a signal.
	www.nanotechweb.org /articles/news/3/2/5/1 (465 words)

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