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Topic: Dodecahedral

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	Hyperbolic small dodecahedral honeycomb - Wikipedia, the free encyclopedia
		The small dodecahedral honeycomb is one of four regular space-filling tessellation (or honeycombs) in hyperbolic 3-space.
		There is another honeycomb in hyperbolic 3-space called the great dodecahedral honeycomb which has 5 dodecahedra per edge instead of 4 here.
		This honeycomb is also related to the 120-cell which has 120 dodecahedra on the surface of a 4 dimensional sphere, with 3 dodecahedra on each edge.
	en.wikipedia.org /wiki/Hyperbolic_small_dodecahedral_honeycomb (185 words)

	Dodecahedral.com (Site not responding. Last check: 2007-11-01)
		The dihedral angle of a Dodecahedral is approximately 116.565 degrees.
		Despite appearances, when a Dodecahedral is inscribed in a sphere, it occupies more of the sphere's volume (66.49%) than an icosahedron inscribed in the same sphere (60.54%).
		The regular Dodecahedral is often used in role-playing games as a twelve-sided die ("d12" for short), one of the more common polyhedral dice.
	www.dodecahedral.com (485 words)

	Expert About do:Dodecahedral
		Dodecahedral structure, in Winter opinion, is inherent not in only power skeleton of the Earth, but also in constitution of living material.
		So, during division of the ovule it is formed at first the tetrahedron from four cells, then the octahedron, the cube, and, at last, the icosahedro-dodecahedral frame of the gastrula.
		A round brillinat cut from a dodecahedral crystal tends to have 4 of the dodecahedral faces on the girdle plane, so a lot of these naturals are on the girdel itself rather than above or underneath.
	www.expertsite.biz /dir/do/dodecahedral.htm (794 words)

	Bubble domain devices using garnet materials with single rare earth ion on all dodecahedral sites - Patent 3949386
		Compositions using 100 percent of any one of these ions in the dodecahedral lattice sites, without an Fe substitution, are generally undesirable for room temperature device operation, due to their very high magnetization and due to an adverse temperature dependence.
		These compositions contain at least two ions in the dodecahedral sites which are selected in a particular way so as to reduce magnetostriction in the <111> direction and also in the <100> direction.
		Ordering of the non-magnetic ions on the dodecahedral sites is suggested as leading to growth induced anisotropy through the effect of these ions on the crystal field at neighboring Fe.sup.3.sup.+ ions.
	www.freepatentsonline.com /3949386.html (6051 words)

	Figure 3 \| Dodecahedral space topology as an explanation for weak wide-angle temperature correlations in the ...
		Dodecahedral space topology as an explanation for weak wide-angle temperature correlations in the cosmic microwave background
		A hypersphere is the three-dimensional surface of a four-dimensional ball.
		In the construction of the Poincaré dodecahedral space, the dodecahedron's 30 edges come together in ten groups of three edges each, forcing the dihedral angles to be 120° and requiring a spherical dodecahedron rather than a euclidean one.
	www.nature.com /nature/journal/v425/n6958/fig_tab/nature01944_F3.html (216 words)

	Dodecahedral space topology as an explanation for weak wide-angle temperature correlations in the ... (Site not responding. Last check: 2007-11-01)
		Dodecahedral space topology as an explanation for weak wide-angle temperature correlations in the co(qiji.cn/eprint/abs/321): 摘要
		奇迹文库: 自然科学: 物理学: 引力与天体物理: Dodecahedral space topology as an explanation for weak wide-angle temperature correlations in the co
		Dodecahedral space topology as an explanation for weak wide-angle temperature correlations in the co
	www.qiji.cn /eprint/abs/321.html (269 words)

	T.C. Kultur Bakanligi / Ministry of Culture, Republic of Turkey
		The dodecahedral body of the tomb rests on a cubic base, the bevelled corners of which act as a transition to the dodecahedral profıle of the main body.
		The smooth, dodecahedral profıle of the main body is the same on the inside.
		The dodecahedral, pyramidal spire is faced with cut stone and it protrudes slightly over the body of the structure.
	www.discoverturkey.com /english/yeni/van/halime_hatun.html (1616 words)

	Water Buckyballs
		There is a strong similarity between the JT properties of electron-doped dodecahedral water clusters and the JT-induced vibronic coupling believed by some scientists to underlie the superconductivity of doped solid buckminsterfullerene.
		"squashing mode" of the otherwise ideal icosahedrally-symmetric pentagonal dodecahedral cluster, with a large-amplitude vibration of the clathrated hydronium oxygen atom coupled to breathing vibrations of the cluster surface oxygen atoms.
		In view of the emphasis placed here on the consequences of oxygen-oxygen interactions in pentagonal dodecahedral water clusters, it is natural to consider their possible relevance to the properties of and traditional hydrogen-bonding models for liquid water.
	www.watercluster.com (2602 words)

	The shape of Space
		The values of the mass-energy density parameter for which the Poincaré Dodecahedral Space (plots 2 for the quadrupole and 4 for the octopole) fit well with WMAP observations (plots 1 for quadrupole and 3 for octopole).
		The Poincaré Dodecahedral Space accounts for the low value of the quadrupole as observed by WMAP in the fluctuation spectrum, and provides a good value of the octopole.
		The Poincaré Dodecahedral Space model predicts 6 pairs of circles with an angular radius of 35°.
	luth2.obspm.fr /Compress/oct03_lum.en.html (1959 words)

	dodecahedral loudspeakers (Site not responding. Last check: 2007-11-01)
		The dodecahedral loudspeakers directivity of dodecahedral loudspeakers were measured.
		FP120, This dodecahedral loudspeakers unit consists of a noise generator (AP600) and an omnidirectional source (BP012) with 12 loudspeakers mounted on a dodecahedral housing.
		The DO12 is made of 12 loudspeakers mounted in dodecahedral loudspeakers a robust dodecahedral cabinet, thus creating a sound field close to an ideal spherical distribution.
	www.speaker-works.com /tannoy-loudspeakers/dodecahedral-loudspeakers.html (509 words)

	The carbon dioxide-water cluster (Site not responding. Last check: 2007-11-01)
		The CO may form a hydration shell from a symmetrical dodecahedral arrangement of 18 water molecules where each CO oxygen atom is hydrogen bonded to three water molecules.
		The red lines are the calculated pair correlation functions, between the carbon atom in CO and water, and the bars are the predictions from the model.
		In these structures there is no hydrogen bonding between the CO guest molecules and the water clathrate lattice and the CO molecules occupy both cages but prefer the tetrakaidecahedral cages.
	www.lsbu.ac.uk /php-cgiwrap/water/pfp.php3?page=http://www.lsbu.ac.uk/water/co2.html (330 words)

	A hint of Poincaré dodecahedral topology in the WMAP first year sky map (Site not responding. Last check: 2007-11-01)
		(2003) that the WMAP data are better matched by a geometry in which the topology is that of a Poincaré dodecahedral model and the curvature is "slightly" spherical, rather than by an (effectively) infinite flat model.
		In this paper, a matched circles analysis specifically designed to detect dodecahedral patterns of matched circles is performed over angular radii in the range
		The temperature fluctuations along the matched circles are plotted and are clearly highly correlated.
	www.edpsciences.org /articles/aa/abs/2004/33/aa0337-04/aa0337-04.html (317 words)

	A cosmic hall of mirrors (September 2005) - Physics World - PhysicsWeb
		The power spectrum associated with the Poincaré dodecahedral space is different from that of a flat space because the fluctuations in the cosmic microwave background will change as a function of their wavelengths.
		The Poincaré dodecahedral space therefore accounts for the lack of large-scale fluctuations in the microwave background and also for the slight positive curvature of space inferred from WMAP and other observations.
		Due to its 12-sided regular shape, the Poincaré dodecahedral model actually predicts six pairs of diametrically opposite matched circles with an angular radius of 10-50°, depending on the precise values of cosmological parameters such as the mass-energy density.
	www.physicsweb.org /articles/world/18/9/3 (4037 words)

	Dodecahedral universe
		There are many possible finite topologies for the universe — this dodecahedral one predicts the relative 'rippliness’ of the microwave background at the biggest scales of the dipole, the quadrupole and the octopole (l=1, l=2 and l=3) very well.
		If it does, we might find we live in a universe that is finite and ‘only’ a few billion or tens of billions of light years across.
		Dodecahedral space topology as an explanation for weak wide-angle temperature correlations in the cosmic microwave background, Nature 425, 593 — 595.
	www.evolutionpages.com /dodecahedral_universe.htm (650 words)

	[extropy-chat] Was the Big Bang Dodecahedral? (Site not responding. Last check: 2007-11-01)
		It is thought that this iron is a high-pressure phase of iron organized in close-packed hexagonal geometry.
		Now, there are data supporting the idea that the universe as a whole is dodecahedral; that is, organized as a regular 12-sided figure with pentagonal faces---this being the highest order regular solid in geometry.
		But we cannot refrain from mentioning two amusing effects dictated by a dodecahedral universe.
	lists.extropy.org /pipermail/extropy-chat/2004-January/002807.html (389 words)

	Math in the Media 1103
		It was like beating Babe Ruth's record." Kearn goes on to comment on the recent flurry of public interest in the Riemann Hypothesis: "Probably, no one is going to solve it by reading one of these new math books, but it's very intriguing." Their article is available online.
		The cover story in the October 9 2003 Nature is "Dodecahedral space topology as an explanation for weak wide-angle temperature correlations in the cosmic microwave background." Dodecahedral space was invented a hundred years ago by Henri Poincaré -he used it as a counterexample to an early version of his famous conjecture.
		The data from the Wilkinson Microwave Anisotropy Probe reveal that the lowest-mode observable vibration (the quadrupole) is "only about one-seventh as strong as would be expected in an infinite flat space".
	www.ams.org /mathmedia/archive/11-2003-media.html (510 words)

	Alternative icosahedral water cluster architecture
		It is likely that solutes, soluble at this level, may well distort the dodecahedra but such a structuring shows the possiblility of retaining complete hydrogen bonding even at high concentrations of small solutes.
		It is likely that solutes soluble at this level may well distort the dodecahedra but such a structuring shows the possiblility of retaining complete hydrogen bonding even at moderately high concentrations of small solutes.
		Concentrated salts may provide water-separated ions that occupy the larger interstitial dodecahedral sites and show partial occupancy of the associated pentagonal boxes to produce water-separated ion pairs.
	www.lsbu.ac.uk /php-cgiwrap/water/pfp.php3?page=http://www.lsbu.ac.uk/water/alticos.html (337 words)

	Dodecahedron Power (Site not responding. Last check: 2007-11-01)
		The freeing of dodecahedral H2O clusters with the M-Power Aqua Technology is based on duplicating the motion-mathematics found in the environment where water flows in a natural setting, such as a stream or up from an underground spring.
		It is the specifics of vibrational input from the ground that refine that capacity of platonic solid inversion geometry in motion of water to stabilize dodecahedral H2O clusters.
		The dodecahedral H2O cluster is totally different than the icosahedral H2O cluster in the same way that hydrogen is different than oxygen from an electromagnetic point of view.
	www.0disease.com /waterEmpowerBook/WaterEmpowerment_dod.shtml (2720 words)

	id:A104012 - OEIS Search Results
		Indices of centered dodecahedral numbers (A005904) which are semiprimes (A001358).
		Because the cubic polynomial for centered dodecahedral numbers factors into n time an irreducible quadratic, the dodecahedral numbers can never be prime, but can be semiprime iff (2n+1) is prime and (5n^2+5*n+1) is prime.
		Centered dodecahedral numbers (A005904) are not to be confused with dodecahedral numbers (A006566) = n(3n-1)(3n-2)/2, nor with rhombic dodecahedral numbers (A005917).
	www.research.att.com /~njas/sequences/A104012 (224 words)

	The structure of Pariacoto virus reveals a dodecahedral cage of duplex RNA - Nature Structural & Molecular Biology
		The 3.0 Å resolution crystal structure of Pariacoto virus (PaV) reveals extensive interactions between portions of the viral RNA genome and the icosahedral capsid.
		The highly basic N-terminal regions (residues 7−54) of the subunits, forming pentamers (A subunits) are clearly visible in the density map and make numerous interactions with the RNA cage.
		The C-terminal segments (residues 394−401) of the A subunits lie in channels near the quasi three-fold axes.
	www.nature.com /nsmb/journal/v8/n1/abs/nsb0101_77.html (236 words)

	dodecahedral cleavage - definition of dodecahedral cleavage by the Online Dictionary from Datasegment.com (Site not responding. Last check: 2007-11-01)
		2 definitions found dodecahedral cleavage - Collaborative International Dictionary of English v.0.48 : Dodecahedral *\Dodec`ahe"dral\*, a.
		Pertaining to, or like, a dodecahedion; consisting of twelve equal sides.
		Octahedral cleavage, Dodecahedral cleavage, or Rhombohedral cleavage, cleavage parallel to the faces of an octahedron, dodecahedron, or rhombohedron.
	onlinedictionary.datasegment.com /word/dodecahedral+cleavage (188 words)

	Frank Morgan's Math Chat - MATHEMATICS MEETINGS FEATURE PROOF OF DODECAHEDRAL CONJECTURE BY UNDERGRADUATE SEAN ...
		Thomas Hales of the University of Michigan outlined his proof of Kepler's Conjecture of 1611 on the optimal way to pack unit balls in space (see Math Chat of June 17, 1999).
		There remained the Dodecahedral Conjecture on the optimal way locally to pack unit balls around one fixed ball.
		The Dodecahedral Conjecture says it is the optimal local arrangement.
	www.maa.org /features/mathchat/mathchat_2_3_00.html (712 words)

	Answer Girl: Is the universe duodecahedral? - The Stanford Daily Online (Site not responding. Last check: 2007-11-01)
		I was too afraid to ask him if the universe is dodecahedral though, so now I don’t know if he loves me or not.
		AGood news: Your boyfriend may have chosen an amazingly awkward and nerdy way of saying it, but he did, indeed, (probably) mean to say that he loves you.
		You see, a paper recently published in Nature presented evidence that the universe may be a boundless dodecahedral space of definite volume.
	daily.stanford.org /article/2003/10/28/answerGirlIsTheUniverseDuodecahedral (296 words)

	Heterologous RNA Encapsidated in Pariacoto Virus-Like Particles Forms a Dodecahedral Cage Similar to Genomic RNA in ...
		Heterologous RNA Encapsidated in Pariacoto Virus-Like Particles Forms a Dodecahedral Cage Similar to Genomic RNA in Wild-Type Virions -- Johnson et al.
		Heterologous RNA Encapsidated in Pariacoto Virus-Like Particles Forms a Dodecahedral Cage Similar to Genomic RNA in Wild-Type Virions
		PaV capsids in the absence of the dodecahedral RNA cage.
	jvi.asm.org /cgi/content/full/78/20/11371 (5779 words)

	Russian Minerals (Site not responding. Last check: 2007-11-01)
		Colorless dodecahedral fluorite crystals to 1.7 cm, from a new find.
		A cabinet specimen of colorless dodecahedral fluorite crystals to 2 cm, from a new find.
		An interesting Dal'Negorsk combination piece- there is a colorless dodecahedral fluorite crystal 1.1 cm in diameter, with a small cluster of pyrrhotite crystals, and a small needle of chlorite included quartz, all on what appears to be a cast of what was once another crystal of something.
	www.khyberminerals.com /russianminerals.htm (175 words)

	On the Geometrical Arrangement of the Protein Subunits of Human Serum Low-Density Lipoprotein: Evidence for a ...
		On the Geometrical Arrangement of the Protein Subunits of Human Serum Low-Density Lipoprotein: Evidence for a Dodecahedral Model -- Pollard et al.
		Ultracentrifugal and electron microscopic studies of human serum low-density lipoprotein (LDL) and several of its derivatives led to the formulation of a model in which the 20 protein subunits, probably globular, are arranged in a dodecahedral pattern with icosahedral symmetry.
		In such a model the LDL surface is occupied by both protein and lipids, predominantly phospholipids, as supported by the results of the hydrolysis of LDL by phospholipase A and C. Neutral lipids (cholesterol esters and glycerides) would be in the interior of the molecule.
	www.pnas.org /cgi/content/abstract/64/1/304 (184 words)

	Stupid Evil Bastard: The shape of the Universe: Dodecahedral?
		There’s an interesting article titled Cosmos is ‘shaped like a football’ over at the BBC News website that talks about an article submitted to the journal Nature on the shape of the Universe.
		Indeed, a dodecahedral Universe, were you able to traverse it, would have some interesting properties.
		John Whitfeld’s abstract (or discussion?) of the actual article in Nature indicates that a dodecahedral space is just one geometry that could explain the observed patterns in the background radiation.
	www.stupidevilbastard.com /index/seb/comments/2094 (1054 words)

	Dodecahedral Faces of the Mathieu group of degree 12 (Site not responding. Last check: 2007-11-01)
		Dodecahedral Faces of the Mathieu group of degree 12
		This paper constitutes part of my honors thesis written in spring 1997 at the USNA, advisor Prof.
		appears in mathematics, hence the pun the "dodecahedral faces" in the title.
	web.usna.navy.mil /~wdj/m_12.htm (3203 words)

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