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# Topic: Dodecahedron

###### In the News (Fri 24 May 13)

 Dodecahedron - LoveToKnow 1911 The "small stellated dodecahedron," the "great dodecahedron" and the "great stellated dodecahedron" are Kepler-Poinsot solids; and the "truncated" and "snub dodecahedra" are Archimedean solids (see Polyhedron). In crystallography, the regular or ordinary dodecahedron is an impossible form since the faces cut the axes in irrational ratios; the "pentagonal dodecahedron" of crystallographers has irregular pentagons for faces, while the geometrical solid, on the other hand, has regular ones. The "rhombic dodecahedron," one of the geometrical semiregular solids, is an important crystal form. www.1911encyclopedia.org /Dodecahedron   (167 words)

 NationMaster - Encyclopedia: Dodecahedron   (Site not responding. Last check: 2007-11-07) A dodecahedron is any polyhedron with twelve faces, but usually a regular dodecahedron is meant: a Platonic solid composed of twelve regular pentagonal faces, with three meeting at each vertex. The centers of the faces of a regular dodecahedron are the vertices of a regular icosahedron and the centers of the faces of a regular icosahedron are the vertices of a regular dodecahedron. It follows that the length of the edges of the dodecahedron is the greatest of the two parts in which the edge of the cube is divided by the golden section! www.nationmaster.com /encyclopedia/Dodecahedron   (838 words)

 Dodecahedron   (Site not responding. Last check: 2007-11-07) To contemplate this symbol was to engage in meditation upon the Divine. It represents the perfect mediation of the infinite and the finite, the sphere and the cube, analogous to the circle and the square. Kepler tried to associate the polyhedra with the relative orbits of the planets known at that time (planet Earth was related to the Dodecahedron), and in turn to correlate these to rather sweeping musical frequencies, the sound of which create a harmony, into which we are born, always hearing, indeed a part of it. members.aol.com /dodecahdrn/Dodecahedron.html   (1319 words)

 Golden section - Pentagon and Pentagram - Dodecahedron As a result we will understand how a regular dodecahedron can be constructed starting from a cube by putting suitable "roofs" on it, as Euclid already did... The length of the diagonals of the pentagons equals the length of the sides of the cube. Finally, it's possible to unfold the dodecahedron and refold it into the cube that served as the basis for its construction. cage.rug.ac.be /~hs/polyhedra/dodeca.html   (741 words)

 Polymorf - Knowhere - Icosahedron, Dodecahedron symmetry   (Site not responding. Last check: 2007-11-07) The icosahedron and the dodecahedron are duals of each other and therefore are dodecahedron shares the four (100) mirror planes of the cube as well as its four [111] the symmetry elements of the dodecahedron to those of the cube. www.polymorf.net /lesson9.htm   (154 words)

 The Dodecahedron   (Site not responding. Last check: 2007-11-07) The dodecahedron is the dual of the icosahedron. Connecting the centers of adjacent faces of the dodecahedron results in an icosahedron, and connecting the centers of the icosahedron faces results in a dodecahedron. A cross-section of the dodecahedron can be an equilateral triangle, a square, a regular pentagon, a regular hexagon (two ways), or a regular decagon. www.whistleralley.com /polyhedra/dodecahedron.htm   (212 words)

 PlanetMath: dodecahedron   (Site not responding. Last check: 2007-11-07) A dodecahedron is a polyhedron with twelve faces. This is version 2 of dodecahedron, born on 2004-06-22, modified 2004-06-23. Object id is 5947, canonical name is Dodecahedron. planetmath.org /encyclopedia/Dodecahedron.html   (37 words)

 The Dodecahedron The icosehedron and the dodecahedron are 'duals' (as are the cube and the octahedron). So the dodecahedron is designed such that the distance to the 2 large pentagonal planes from the top or bottom faces is exactly equal to the distance between the center and a vertex of any of the faces of the dodecahedron. The dodecahedron unites the geometry of crystals and lattices (root 2 and root 3) with the geometry of Phi (root 5), found in the biology of organic life. kjmaclean.com /Geometry/dodecahedron.html   (1632 words)

 The Orgonite Dodecahedron Last year a local woman was able to use a dodecahedron sound chamber to heal herself of a serious thyroid condition. It is a truncated dodecahedron made with 233 feet of half inch copper pipe and thirty two orgonite connecting hubs. For the Orgonite Dodecahedron the plan was to maximize the energy to facilitate physical, psychic and spiritual healing. educate-yourself.org /zsl/OrgoniteDodecahedron28jul04.shtml   (1128 words)

 CRYSTAL HABIT The pentagonal dodecahedron is termed a pyritohedron because it is most commonly found in the mineral pyrite. The deltoid dodecahedron is a rare dodecahedron and is usually only seen modifying the tetrahedral crystals of tetrahedrite and tennantite. A rhombic dodecahedron is related to the octahedron by placing a dodecahedral face over each of the twelve octahedral edges. mineral.galleries.com /minerals/property/crystal.htm   (2461 words)

 Dodecahedron To contemplate this symbol was to engage in meditation upon the Divine. The Dodecahedron is associated with visual harmonic division and proportion with music and sound, music in particular being Dodecahedron), and in turn to correlate these to rather sweeping musical frequencies, the sound of which create a harmony, into which www.dnaalchemy.com /Dodecahedron.html   (1073 words)

 The dodecahedron   (Site not responding. Last check: 2007-11-07) Our final regular polyhedron is the dodecahedron which has regular pentagons as faces (see Figure 13). The dodecahedron is the dual of the icosahedron - this is easy to see by noticing that five triangles surround each vertex of the icosahedron and so the dual of the icosahedron has pentagonal faces. Since the dodecahedron is the dual of the icosahedron, it has the same numbers of axes of symmetry and reflection planes. nothung.math.uh.edu /~mike/hti/handouts/notes/node36.html   (120 words)

 Math Forum Discussions on the surface of the dodecahedron belonging to the family you describe, as a commutes with the rotation group of the dodecahedron. The Math Forum is a research and educational enterprise of the Drexel School of Education. www.mathforum.org /kb/thread.jspa?threadID=106067&messageID=545211   (699 words)

 Ivars Peterson's MathTrek -Plato's Molecule Plato was probably thinking of an earlier tradition dating back to the Pythagoreans--the notion that the dodecahedron formed the "timbers" on which the spherical bulk of the heavens was built. Johannes Kepler (1571-1630) placed a dodecahedron between Mars and Jupiter in his ingenious model of the solar system and later studied the properties of polyhedra in considerable detail (see http://www.georgehart.com/virtual-polyhedra/kepler.html). In modern times, the Spanish painter Salvador Dalí (1904-1989) echoed Pythagorean mysticism when he hung a dodecahedron in the background of his 1955 painting "The Sacrament of the Last Supper" (see http://www.ionet.net/~jellenc/dali.html). www.maa.org /mathland/mathtrek_9_18_00.html   (827 words)

 Dodecahedron Day: Glossary   (Site not responding. Last check: 2007-11-07) For example, a pentagon and the regular dodecahedron are convex, but a pentagram and the small stellated dodecahedron are nonconvex. For example, the convex hull of the small stellated dodecahedron is the regular icosahedron. irregular dodecahedron: a dodecahedron whose faces are irregular polygons. websites.quincy.edu /~matskvi/ddd/glossary.html   (311 words)

 Love Dodecahedron - Television Tropes & Idioms If the Love Dodecahedron is ever resolved, it's always with F. Who by that time has annoyed you so much that you're rooting for B. In case E and F aren't believable enough on their own, the writers will attempt to quickly deal with the competition beforehand. The Love Dodecahedron is a superset of both The Unwanted Harem and the Love Triangle. In one scene representing Saki's thoughts, an incomplete diagram of the love dodecahedron is actually displayed with Super Deformed versions of the involved characters and arrows indicating who likes whom. tvtropes.org /pmwiki/pmwiki.php/Main/LoveDodecahedron   (432 words)

 PlanetMath: regular polyhedron   (Site not responding. Last check: 2007-11-07) There are only 5 regular polyhedra, as was first shown by Theaetetus, one of Plato's students. Some sources ascribe to Theaetetus also the discovery of the dodecahedron. It has 6 edges and 4 vertices and 4 faces, each one being an equilateral triangle. planetmath.org /encyclopedia/Dodecahedron2.html   (200 words)

 96 The Dodecahedron   (Site not responding. Last check: 2007-11-07) The regular dodecahedron has 31 axes of symmetry: 10 are threefold, passing through pairs of opposite vertices; 6 are fivefold, passing through the centers of opposite faces; and 15 are twofold, passing through the mid-points of opposite sides. The relationship between the dodecahedron and the cube can be seen either by joining the mid-point of faces to form the vertices of three rectangles (whose edges are in the golden ratio) which are mutually perpendicular, or by choosing eight vertices of the dodecahedron which are also the vertices of a cube: A perhaps surprising fact is that when a regular dodecahedron and a regular icosahedron are inscribed in the same sphere, the dodecahedron occupies a larger proportion of the spheres' volume. www.bluefish.org /dodeca.htm   (195 words)

 The Dodecahedron It is a "sort" of novel because the stories are related to each other and there is a novel-like unity of themes and structure. A circle is two-dimensional whereas a dodecahedron is a three-dimensional shape. The Dodecahedron is an experiment, and a fully successful one, "on the subject of perspective." But it's a lot more fun than that makes it sound. www.goodreports.net /reviews/thedodecahedron.htm   (681 words)

 Rhombic dodecahedron   (Site not responding. Last check: 2007-11-07) If you divide a cube into six pyramids (the face of a cube is the base of a pyramid, the center of a cube is the vertex of a pyramid) then flip every pyramid outside the cube, you obtain a rhombic dodecahedron. There are 8 vertices adjacet to 3 edges (the vertices of the initial cube) and 6 vertices adjacent to 4 edges (the vertices of the pyramids). To prevent dodecahedrons against spilling on the table put them on the holder. zetosak.zetosa.com.pl /~burczyk/origami/g2-04-en.htm   (169 words)

 THE HINGED DODECAHEDRON Trisectioning of the cube and the Rhombic Dodecahedron It is seen in the planar layout that four of the pyramids are connected at their basal edges to three other pyramids, two are connected to two, and six are connected to one. The six singly connected, square-based pyramids, being re-paired into rhombic-based pyramids, will flip-flop into alternate positions, as this version of the assembled dodecahedron is taking shape; and an incorrect positioning of any one of them will throw the assemblage out of kilter. members.tripod.com /vismath7/proceedings/huff.htm   (485 words)

 Dodecahedron: EnchantedLearning.com An dodecahedron is a regular geometric solid (called a Platonic solid) that has 12 pentagons as faces. Click here to go to the dodecahedron template. Fold along all the inside lines and form into a dodecahedron shape. www.enchantedlearning.com /math/geometry/solids/Dodecahedron.shtml   (141 words)

 The Dodecahedron   (Site not responding. Last check: 2007-11-07) The dodecahedron is the dual of the icosahedron. Connecting the centers of adjacent faces of the dodecahedron results in an icosahedron, and connecting the centers of the icosahedron faces results in a dodecahedron. A cross-section of the dodecahedron can be an equilateral triangle, a square, a regular pentagon, a regular hexagon (two ways), or a regular decagon. whistleralley.com /polyhedra/dodecahedron.htm   (212 words)

 Features of dodecahedron speaker | SOLID ACOUSTICS However, with a dodecahedron speaker you are able to receive a direct sound source from anywhere in the room. The sound of Solid Acoustics’ dodecahedron speaker spreads from top to bottom, right to left and can be virtually heard beyond the walls and ceilings of the room, just as a painting seems to expand outside its frame. The dodecahedron speaker fills a space with a sound with the constant quality, and also it does not make people nearby the speaker suffer from the loudness.　Our dodecahedron speaker can provide you less expense and more comfortable sound space. www.solidacoustics.com /en/technology/features.html   (780 words)

 Tetrahedral Stellations of the Dodecahedron (The dodecahedron itself and its three well-known stellations in the Kepler-Poinsot category have full icosahedral symmetry.) Each is a kind of nonconvex dodecahedron with twelve identical (disconnected) faces in the face planes of a regular dodecahedron. A tetrahedral 4-coloring of the dodecahedron can either have no adjacent faces of the same color (method 1) or groups of three of the same color (method 2). Each of the following tetrahedral stellations of the dodecahedron is given by a subset of these six cells, but many possibilities are not included because either they close off a void in the center or their mirror image is already included. www.georgehart.com /virtual-polyhedra/stellations-dodecahedron-tetrahedral.html   (690 words)

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