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13. A hint of Poincaré dodecahedral topology in the WMAP first year sky map
- www.edpsciences.org
- A hint of Poincaré dodecahedral topology in the WMAP first year sky map.
- (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 on the one-year WMAP data. ... The favoured six dodecahedral face centres in galactic coordinates are and their opposites. ... Whether or not these six circle pairs centred on dodecahedral faces match via a rotation only due to unexpected statistical properties of the WMAP ILC map, or whether they match due to global geometry, it is clear that the WMAP ILC map has some unusual statistical properties which mimic a potentially interesting cosmological signal. ...
14. Frank Morgan's Math Chat - MATHEMATICS MEETINGS FEATURE PROOF OF DODECAHEDRAL CONJECTURE BY UNDERGRADUATE SEAN MCLAUGHLIN
- www.maa.org
- MATHEMATICS MEETINGS FEATURE PROOF OF DODECAHEDRAL CONJECTURE BY UNDERGRADUATE SEAN MCLAUGHLIN.
- There remained the Dodecahedral Conjecture on the optimal way locally to pack unit balls around one fixed ball. ... But locally this dodecahedral arrangement exists and beats Hales's global solution. The Dodecahedral Conjecture says it is the optimal local arrangement. ...
15. Rhombic dodecahedral boundaries (IMCON=5)
- www.cse.clrc.ac.uk
16. Math in the Media 1103
- www.ams.org
- At home in dodecahedral space. ...
- The face identification producing dodecahedral space changes "exiting through a face" into "re-entering on the opposite side". ...
- The view in dodecahedral space (if the framework of the docecahedron is visible). ...
- At home in dodecahedral space. 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. ... This should feel perfectly natural, because the authors of the article (Jean-Pierre Luminet, Jeffrey Weeks, Alain Riazuelo, Roland Lehoucq and Jean-Philippe Uzan) give evidence to show that dodecahedral space may in fact be the shape of the universe we live in.
- The team calculated the spectrum of dodecahedral space, which "depends strongly on the assumed mass-energy density parameter ω0". ...
17. Water cluster architecture based on clathrate hydrates
- www.lsbu.ac.uk
- pentagonal dodecahedral cavity (512) at 3. ...
- Linear tetrakaidecahedral (51262) cavities form three orthogonal axes holding a dodecahedral cavity wherever they cross (ratio 3:1 respectively); each dodecahedral cavity sitting (in a body-centered cubic arrangement) within a cube formed by six tetrakaidecahedral (51262) cavities. One dodecahedral cavity sits at the center in the above structure with linear tetrakaidecahedral (51262) cavities easily seen to its left and right.
- a The hydrogen-bond angles and bond lengths are slightly more distorted (51264 > 51262) than in icosahedral clusters surrounding dodecahedral 512, cavities, but not prohibitively so. ...
18. Russian Minerals
- khyberminerals.com
- Colorless dodecahedral fluorite crystals to 1. ... They look almost like dodecahedral ice.
- A cabinet specimen of colorless dodecahedral fluorite crystals to 2 cm, from a new find. They look almost like dodecahedral ice.
- An interesting Dal'Negorsk combination piece- there is a colorless dodecahedral fluorite crystal 1. ...
19. Fresh Patents-Dodecahedral speaker system patent apps
- www.freshpatents.com
- Dodecahedral speaker system. ...
- A dodecahedral speaker system including a dodecahedral speaker, which is formed with twelve speaker units, and an equalizer circuit, which corrects specified frequency bands of voice signals outputted from the dodecahedral speaker. The equalizer circuit is installed in the pre-stage of the amplifier to which the dodecahedral speaker is connected. ...
- 0002 The present invention relates to a dodecahedral speaker system that includes a dodecahedral speaker. ...
- 0004 A conventionally known dodecahedral speaker 3 has, as shown in FIG. 7, twelve (12) speaker units 1, and one speaker unit is embedded in each one of pentagonal outer peripheral faces 2A of a speaker box 2 which of each one of the speaker units and has a substantially dodecahedral shape. ...
- 0005 Such a prior art dodecahedral speaker 3 has, however, several problems. ...
- In this sound reinforcement device 4 with broad directional characteristics, the sound pressure characteristics around the entire periphery of the dodecahedral speaker 7 are evened out and smoothed by disposing a corrective filter 8 between the speaker units 6 and the amplifier (not shown in FIG. ...
- 0009 More specifically, the object of the present invention is to provide a dodecahedral speaker system which makes it possible to realize a reduction in the voice signal loss and generation of heat, and which at the same time makes it possible to even out the sound pressure characteristics in a broad frequency band, and especially to achieve an effective increase in the sound pressure in the bass region of 50 to 500 Hz. ...
- 0010 The above object is accomplished by a unique structure of the present invention for a dodecahedral speaker system that includes a dodecahedral speaker which has twelve speaker units, and one of the speaker units is embedded in each of the substantially pentagonal outer peripheral faces of a speaker box that has a substantially dodecahedral shape; and in the present invention, the speaker system further includes an equalizing circuit which corrects a specified frequency band of the a voice signal that is outputted from the dodecahedral speaker, and this equalizing circuit is disposed in the pre-stage of an amplifier to which the dodecahedral speaker is connected. ...
- 0014 Furthermore, the above-described dodecahedral speaker box may be constructed by joining either two, three, four or six sets of speaker box sub-units that have either six, four, three or two faces. ...
- 1 is a schematic structural diagram of a dodecahedral speaker system according to one embodiment of the present invention; .
- 2 is a schematic front view of the dodecahedral speaker of FIG. ...
- 5A through 5C are schematic diagrams of the dodecahedral speaker system according to other embodiments of the present invention; .
- 7 is a schematic front view of a conventional dodecahedral speaker; and .
- 1 and 2, the dodecahedral speaker system 10 of one embodiment of the present invention includes a dodecahedral speaker 14 comprised of twelve speaker units 12, an amplifier 16 which is connected to this dodecahedral speaker 14, an equalizer circuit 18 which is disposed in the pre-stage of this amplifier 16, and a playback device 20. ...
20. The 120-cell
- members.home.nl
- The pentagons are sections of dodecahedral cells parallel to a face of such a cell.
- The pentagons are again sections of dodecahedral cells parallel to a face of such a cell.
- These pentagons are the faces opposite to the faces of the central dodecahedron and completing 12 dodecahedral cells that share a face with the central cell.
- The pentagons are again sections of dodecahedral cells parallel to a face of such a cell. ...
- The pentagons are again sections of dodecahedral cells parallel to a face of such a cell. ... The triangles are formed by 3 cubes inscribed in adjacent dodecahedral cells.
- These 30 vertices, belonging to the dual 600-cell, are the centres of 30 dodecahedral cells of the 120-cell:.
- You can discern the central dodecahedral cell in the middle with 20 vertices (13 ). ...
21. Multiple-unit Dodecahedral Constructions
- home.wtal.de
22. Dodecahedral Spirals T-Shirt
- store.wolfram.com
23. The shape of Space
- www.luth.obspm.fr
- A finite dodecahedral Universe.
- Left: Poincaré Dodecahedral Space can be described as the interior of a kind of sphere tiled with 12 slightly curved pentagons.
- The proposed space is the Poincaré dodecahedral space note c . ...
- It is also the case for the Poincaré Dodecahedral Space. ...
- The associated power spectrum, namely the repartition of fluctuations as a function of their wavelengths corresponding to the Poincaré dodecahedral space, strongly depends on the value of the mass-energy density parameter note d . ...
- 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°. ...
- Dodecahedral space topology as an explanation for weak wide-angle temperature correlations in the cosmic microwave background.
24. Dodecahedral - Definition of Dodecahedral by Webster Dictionary
- www.webster-dictionary.net
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