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Topic: Polyhedral compound

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	Compounds of Cubes
		We construct compounds by imagining the symmetry axes of the desired compound and arranging component cubes to have their symmetry axes arranged appropriately relative to the compound.
		Summarizing, these six compounds listed: 0, 1, 2, 3, 4, 5, are all variations of the same 5-fold prism-type compound---a 4-fold axis of each cube is a 2-fold axis of the compound---but the smallest and two largest angles of these six happen to result in geometric alignments which give the compound additional symmetry.
		Dual to this is the uniform nonrigid compound of 4 octahedra [*].
	www.georgehart.com /virtual-polyhedra/compound-cubes-info.html (2412 words)

	Method of functionalizing polycyclic silicones and the compounds so formed - Patent 5939576
		Polyhedral oligomeric silsesquioxane (POSS) cage molecules and polyhedral oligomeric silicate (POS) (spherosilicate) cage molecules or reagents are increasingly being utilized as building blocks for the preparation of novel catalytic materials and as performance enhancement additives for commodity and engineering polymers.
		Compounds of formula 3 in which R.sup.3 is at least in part a radical of formulas described previously for (V) and R.sup.2 is at least in part a radical having formulas previously described for (III), can be prepared by reacting compounds of the formula ##STR11## with radicals having the formulas previously described for (V).
		Compounds of formula 3 in which R.sup.3 is at least in part a radical of formulas described previously for (V) and R.sup.2 is at least in part a radical having formulas previously described for (III), can be prepared by reacting compounds of the formula ##STR12## with radicals having the formulas previously described for (III).
	freepatentsonline.com /5939576.html (4126 words)

	Polyhedral compound (Site not responding. Last check: )
		A polyhedral compound is a polyhedron which is itself composed of several other polyhedra sharing a common centre, the three-dimensional analogs of polygonal compound s such as the hexagram.
		The stella octangula can also be regarded as a compound of a tetrahedron with its dual polyhedron, inscribed in a common sphere so that the vertices of one line up with the face centres of the other.
		The corresponding cube-octahedron and dodecahedron-icosahedron compounds are the first stellations of the cuboctahedron and icosidodecahedron, respectively.
	www.serebella.com /encyclopedia/article-Polyhedral_compound.html (309 words)

	Polyhedral Compounds
		Its vertices are the vertices ofd a cube, its edges are the face diagonals of a cube, and the solid common to both tetrahedra is an octahedron.
		The icosahedron and octahedron are duals of the dodecahedron and cube.
		This compound is the dual of the five-cube compound.
	www.uwgb.edu /dutchs/symmetry/polycpd.htm (731 words)

	USCAP 2002 Annual Meeting
		In both children and adults, approximately 75% of excised nevi are compound with nevus cells in both epithelium and substantia propria.
		Compound and subepithelial nevi range from thin to polypoid, depending partly on the location of the lesion.
		The deepest cells in a compound or subepithelial conjunctival nevus are typically non-pigmented except in fl individuals who have pigmentation of nevus cells regardless of depth, but in whom conjunctival melanoma is exceedingly rare.
	www.uscap.org /site~/91st/optcase03.htm (1746 words)

	Surface of a crystal
		But variation in this respect is not regarded as rendering the conception of polyhedral domains valueless; on the contrary, a study of the conditions bringing about the shift from one domain shape to another seems adapted to throw light on the whole subject of atomic attraction.
		The compound being a polar one, the two kinds of atoms may be treated separately.
		The recognition of polyhedral molecular domains with lines along which the attractive forces are concentrated perpendicular to their faces makes the understanding of certain of the peculiar features of crystals relatively easy.
	www.minsocam.org /msa/collectors_corner/arc/xlsurface.htm (2551 words)

	Microbiology Terms - C
		Any chemical compound which consists of only carbon (C), oxygen (O), and hydrogen (H) elements, for examples, sugars, starches, and cellulose are carbohydrates.
		Polyhedral cellular inclusions of crystline ribulose bisphosphate carboxylase (RubisCO), the key enzyme of the Calvin cycle.
		An organic compounds which serve as cytoplasmic solutes to balance water relations for cells growing in environments of high salt or sugar.
	library.thinkquest.org /3564/glossary/c.htm (1321 words)

	Dictionary C (Part 3 of 3)
		The formula identifies the elements present in the compound and the number of atoms of each kind that are in a molecule of the compound.
		Compound ions are groups of atoms which remain unchanged through a series of chemical reactions, but which are incapable of independent existence.
		A coordination complex is a compound in which molecules or ions form coordinate bonds to a central metal atom or Ion.
	www.ucc.ie /academic/chem/dolchem/html/dict/000c3.html (2114 words)

	Glandular Epithelium Lecture
		Brunner’s glands of the duodenum are compound tubular glands.
		Compound tubulo-alveolar glands - These glands also have a highly branched duct system, but some of the ducts end as tubules and others end as alveoli.
		Two of the major salivary glands, the submandibular and the sublingual glands, are examples of compound tubulo-alveolar glands (as they are mixed glands).
	www.mc.vanderbilt.edu /histology/word/2003/glandularepithelium03.htm (2573 words)

	P to R
		It consists of one or more capital italic letters derived from common geometric terms (tetrahedron, square plane, octahedron, etc.) which denote the idealized geometry of the ligands around the coordination center, and an arabic numeral that is the coordination number of the central atom.
		The polyhedral symbol is used as an affix, enclosed in parentheses, and separated from the name by a hyphen.
		In the study of biochemical processes, radioactive isotopes are used for labelling compounds that subsequently are used to investigate various aspects of the reactivity or metabolism of proteins, carbohydrates and lipids or as sources of radiation in imaging.
	www.chem.qmul.ac.uk /iupac/bioinorg/PR.html (1515 words)

	Computer-Aided Chemistry Speeds Research
		Because these compounds are already conformationally restricted, chemists thought they could reliably predict their structures without resorting to complex molecular modeling studies.
		However, an increasing number of polyhedral boranes have been identified which adopt shapes that are not predicted by these rules.
		Industrial research and development laboratories are increasingly concerned to maximize the success rate of their drug and chemical discovery programs by ensuring that a higher proportion of compounds synthesized have at least some of the desired properties.
	www.netsci.org /Science/Compchem/feature06.html (717 words)

	Porous gas permeable material for gas separation - Patent 6866697
		By selecting specific nanostructured compounds, the porous material can be tailored to contain pores of a predetermined size which allow gases having a working diameter smaller than the size of the pores to pass through the material while preventing the passage of gases having a working diameter greater than the size of the pores.
		The nanostructured compound is optionally substituted with a reactive group and is selected from the group consisting of a polyhedral oligomeric silsequioxane (POSS), zeolite, cyclomacroether, porphyrin, foldamer, cyclodextrin and mixtures thereof.
		The nanostructured compound is preferably covalently bonded to a larger molecule, for example, as a pendant group on an organic or organosiloxane polymer.
	freepatentsonline.com /6866697.html (3828 words)

	From nonpeptide toward noncarbon protease inhibitors: Metallacarboranes as specific and potent inhibitors of HIV ...
		Two compound 1 molecules are represented by their van der Waals surfaces and gray stick model, with cobalt ions shown as magenta spheres.
		Compound 1 is represented by a stick model in gray, with cobalt shown as a magenta sphere.
		PR residues in contact with compound 1 are represented by stick models, and their solvent-accessible surfaces are colored by atom charge (blue, positive; red, negative).
	www.pnas.org /cgi/content/full/102/43/15394 (3712 words)

	C&EN: SCIENCE & TECHNOLOGY - BORON FLAT OUT
		There are countless organic compounds having innumerable uses, but there are many fewer examples of boranes (the boron analogs of hydrocarbons) and their carborane and metallaborane derivatives.
		Two of these compounds, CB and CB, which also have been studied by others, are predicted to have a carbon in the center of a ring of boron atoms, similar to boron molecular wheels.
		The reason for the shift from the 3-D polyhedral boranes to the planar boron clusters likely stems from the bare boron atoms' lack of dangling hydrogen atoms, which stabilize the spherical aromaticity, he says.
	pubs.acs.org /email/cen/html/030104112124.html (3800 words)

	The application of salt fluxes in the synthesis of new solid state compounds has witnessed significant development in ...
		In many cases the compounds stabilized under polychalcogenide flux conditions are only kinetically stable and cannot be synthesized at higher temperatures.
		The resulting intercalation compounds are composed of alternating monolayers of positively charged polymer chains and negatively charged host layers.
		This order is achieved by the orientation of the polymer chains along certain crystallographic directions, such that it causes a doubling of the periodicity along the a- and c- axes.
	www.cem.msu.edu /~kanatzid/InorgBrochure1999.html (2424 words)

	Polyhedron Summary
		A polyhedron whose faces are all regular polygons congruent to each other, whose polyhedral angels are all equal, and which has the same number of faces meet at each vertex is called a regular polyhedron.
		Polyhedral compounds are formed as compounds of two or more polyhedra.
		These compounds often share the same vertices as other polyhedra and are often formed by stellation.
	www.bookrags.com /Polyhedron (2968 words)

	TITLES PLUS ABSTRACTS
		The title compound 2,4-dichloro-6-exo-9-endo-bis(dimethylphenylphosphino)-arachno-decaborane has a typical arachno ten-vertex cluster geometry with one of the phosphine ligands bound exo polyhedrally and the other in an uncommon endo configuration.
		All compounds 1 - 4 were characterised by spectroscopic methods and, in the cases of 1a and 4 by single-crystal X-ray diffraction analysis.
		Compounds 1 and 3 are characterised by single-crystal X-ray diffraction analysis and NMR spectroscopy.
	www.chem.leeds.ac.uk /boronweb/TITLESPLUSABSTRACTS.htm (2454 words)

	names & notations (Site not responding. Last check: )
		The n-kis operator introduces a new vertex on the axis of each n-face, and therefore n triangles (in fact each x-face is augmented with a x-pyramid); so the tetrakis-cube has 6x4=24 triangular faces, thus is an icositetrahedron.
		A compound polyhedron is the union of several identical or related polyhedra arranged to preserve a polyhedral symmetry: the anticube is a compound of two regular tetrahedra, my favourite is the compound of five regular tetrahedra.
		A polyhedral kaleidoscope (three mirrors building a trihedron) is associated to a spherical triangle defined by central projection of a face on a sphere centred on the common point of the symmetry axes.
	www.ac-noumea.nc /maths/amc/polyhedr/names_.htm (1241 words)

	Dodecahedron Day: Nets for Models (Site not responding. Last check: )
		It is not as tricky as the compound of five tetrahedra, but does require patience.
		Download the net for the compound of five octahedra.
		Download the net for the compound of five tetrahedra.
	websites.quincy.edu /~matskvi/ddd/nets.html (792 words)

	The Polyhedra of M.C. Escher
		For example, this 1961 lithograph Waterfall features the compound of three cubes and the first stellation of the rhombic dodecahedron as ornaments atop the two towers.
		Stars, wood engraving, 1948, illustrated below, features the compound of three octahedra, a compound of two cubes, and the stella octangula, all in both outline and solid form, along with dozens of other polyhedra.
		compound of two cubes with common 3-fold axis, (both a solid and an edge model)
	www.georgehart.com /virtual-polyhedra/escher.html (436 words)

	Virtual Reality Polyhedra
		One can appreciate the beauty of this image without knowing exactly what its name means --- the compound of the snub disicosidodecahedron and its dual hexagonal hexecontahedron --- but the more you know about polyhedra, the more beauty you will see.
		This work is complementary to my Pavilion of Polyhedreality, which you may wish to visit to find additional information on polyhedra and links to other related material.
		Find out: click on this picture and see if you can view a 3D version of this compound of five cubes.
	www.georgehart.com /virtual-polyhedra/vp.html (597 words)

	Dorlands Medical Dictionary
		The term is generally used to refer either to a macromolecule made up of a large number of monomers linked by covalent bonds, e.g., polypeptides, nucleic acids, polysaccharides, and plastics, or to a protein made up of several subunits linked by covalent or noncovalent bonds, e.g., hemoglobin or IgM immunoglobulin.
		a compound formed by the repeated reaction of smaller molecules, involving at the same time the elimination of water or other simple compound (e.g., nylon).
		(pə-lim”ər-ĭ-za´shən) the act or process of forming a compound (polymer), usually of high molecular weight, by the combination of simpler molecules (monomers).
	www.mercksource.com /ppdocs/us/common/dorlands/dorland/dmd_p_28.htm (3441 words)

	Silicon Or Compound Thereof - Oxygen Containing patents
		A layer organic silicic acid which can improve an adsorbing power to an alcohol and separate a general organic compound and a method of producing the layer organic silicic acid are provided.
		Polyhedral silsesquioxane anions are economically prepared by reaction of a silica source derived from combusted organic material with a quaternary ammonium hydroxide compound.
		Reaction of the resulting anions with chlorosilanes may be effected in near stoichiometric fashion in organic solvent containing reactive quantities of organic acids such as formic acid.
	www.freshpatents.com /x1423325000psbc.php (353 words)

	BSP :: Anti-Cancer Agents in Medicinal Chemistry Home Page
		The exceptional stabilities of boron clusters, their unique hydrophobic and potential amphiphilic properties, and the ability of the open-cage clusters to form sandwich complexes with a variety of metals, have led to the development of many interesting molecules for application in tumor imaging and treatment using boron neutron capture therapy (BNCT).
		The use of polyhedral boron hydrides for cancer treatment is traditionally connected with boron neutron capture therapy.
		More recently, polyhedral borate anions were proposed as carriers of radionuclide label for targeted radionuclide therapy and diagnostics of cancer.
	www.bentham.org /cmcaca/contabs/cmcaca6-2.htm (1329 words)

	Polypolyhedra
		In 1999, I became interested in a family of origmi modulars composed of interwoven polygonal frames and/or polyhedral skeletons, the most famous of which was devised by Tom Hull, which he titled Five Intersecting Tetrahedra, now commonly known by its abbreviation, FIT.
		Innumerable classes, families, and variations of polyhedra and their derivatives have been identified and seemed that these things I called polypolyhedra were likely already to be found within the mathematical literature.
		For one example, the compound of five intersecting tetrahedra — the basis of Hull's FIT — is one of the 59 known stellations of the icosahedron enumerated by H. Coxeter.
	www.langorigami.com /science/polypolyhedra/polypolyhedra.php4 (813 words)

	Spartanburg SC \| GoUpstate.com \| Spartanburg Herald-Journal (Site not responding. Last check: )
		Combining both tetrahedra gives a regular polyhedral compound called the stella octangula, whose interior is an octahedron.
		Correspondingly, a regular octahedron is the result of cutting off, from a regular tetrahedron, four regular tetrahedra of half the linear size (i.e., rectifying the tetrahedron).
		This compound of five tetrahedra has been known for hundreds of years.
	www.goupstate.com /apps/pbcs.dll/section?category=NEWS&template=wiki&text=tetrahedron (1453 words)

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