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Topic: Tetrahedron

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In the News (Wed 21 Aug 19)

  Tetrahedron - LoveToKnow 1911
This is one of the Platonic solids, and is treated in the article Polyhedron, as is also the derived Archimedean solid named the "truncated tetrahedron"; in addition, the regular tetrahedron has important crystallographic relations, being the hemihedral form of the regular octahedron and consequently a form of the cubic system.
The bisphenoids (the hemihedral forms of the tetragonal and rhombic bipyramids)., and the trigonal pyramid of the hexagonal system, are examples of non-regular tetrahedra (see Crystallography).
This theorem has been generalized for any tetrahedron; a sphere can be drawn through the four feet of the perpendiculars, and consequently through the mid-points of the lines from the vertices to the centre of the hyperboloid having these perpendiculars as generators, and through the orthogonal projections of these points on the opposite faces.
www.1911encyclopedia.org /Tetrahedron   (305 words)

 What The World May Come To
The flat surfaces of the tetrahedron are the Indian Ocean, the Pacific Ocean, and the Atlantic Ocean.
We should naturally expect, with a flat surface of the tetrahedron on top and with the point stretching south, that there would be an ocean at the North Pole and a continent at the South; and such is actually the case, as we know from the discoveries of Nansen, Peary, Scott, and Shackleton.
The terrestrial tetrahedron - that is, the earth on which we live - is not, however, perfectly symmetrical in shape, America being a little too far east to be midway between Asia with Australasia on one side and Europe with Africa on the other.
homepage.ntlworld.com /forgottenfutures/tetra/tetra.htm   (2116 words)

 Ivars Peterson's MathTrek - Art of the Tetrahedron
You can elongate a tetrahedron, stretching several edges to create a slim, stainless-steel tower, 60 feet high, then pair it with an identical tower to a produce an elegant structure that seems to soar in formation into the sky.
Tetrahedrons in nature and architecture, and puzzles involving this simplest polyhedron.
Various mathematical properties of the tetrahedron are described at http://mathworld.wolfram.com/Tetrahedron.html.
www.maa.org /mathland/mathtrek_11_8_99.html   (699 words)

 Search Results for "Tetrahedron"
the tetrahedron, hexahedron, oct - hedron, dodecahedron, and icosahedron, all of which are bounded by like,...
They are the tetrahedron, bounded by four equilateral triangles; the hexahedron, or cube,...
Platonic bodies; cube, rhomboid; tetrahedron, pentahedron, hexahedron, octahedron, dodecahedron, icosahedron;...
www.bartleby.com /cgi-bin/texis/webinator/sitesearch?FILTER=&query=Tetrahedron   (253 words)

 Tetrahedron Model
This activity is an introduction to tetrahedral structures such as the silica tetrahedron.
And so it is important for students to understand the structure of the silica tetrahedron.
The silica tetrahedron consists of 4 Oxygen atoms (raisins) bonded to 1 Silicon atom (bubble blown in middle of pyramid).
www.windows.ucar.edu /tour/link=/teacher_resources/tetrahedron_edu.html&cdp=/windows3.html&edu=mi&frp=/windows3.html   (835 words)

  Merkaba - Star Tetrahedron - Flower of Life - Crystalinks
By imagining two superimposed "Star Tetrahedrons" as counterrotating, along with specific "prana" breathing techniques, certain eye movements and mudras, it is taught that one can activate a non-visible 'saucer' shaped energy field around the human body that is anchored at the base of the spine.
The second whole star tetrahedron is male in nature, it is electrical, is literally the human mind and rotates counter-clockwise relative to your body looking out, or to put it another way, it rotates toward your left side.
The third whole star tetrahedron is female in nature, is magnetic, is literally the human emotional body and rotates clockwise relative to your body looking out, or to put it another way, it rotates toward your right side.
www.crystalinks.com /merkaba.html   (4953 words)

  Tetrahedron - Wikipedia, the free encyclopedia
A tetrahedron (plural: tetrahedra) is a polyhedron composed of four triangular faces, three of which meet at each vertex.
A regular tetrahedron is one in which the four triangles are regular, or "equilateral," and is one of the Platonic solids.
A regular tetrahedron can be embedded inside a cube in two ways such that each vertex is a vertex of the cube, and each edge is a diagonal of one of the cube's faces.
en.wikipedia.org /wiki/Tetrahedron   (1052 words)

 PlanetMath: tetrahedron
For the remainder of this entry, we shall assume that all tetrahedra are non-degenerate.
In many ways, the geometry of a tetrahedron is the three-dimensional analogue of the geometry of the triangle in two dimensions.
This is version 9 of tetrahedron, born on 2004-06-22, modified 2006-06-27.
planetmath.org /encyclopedia/Tetrahedron.html   (410 words)

But the tetrahedron lacks three-dimensional symmetry due to the fact that the subtending vertex is only on one side of the triangular plane, and due to the fact that the center of gravity of the tetrahedron is always only one- quarter of its altitude irrespective of the seeming asymmetry of the tetrahedron.
The four exterior vertexes are equidistant outwardly from the original tetrahedron, a distance equal to the interior distances between the centers of gravity of the original tetrahedron's four faces and their inwardly subtending vertexes.
The star tetrahedron's six potential geodesic interconnectors of the star tetrahedron's outermost points are out of vector-length frequency-phase and generate different frequencies each time they regenerate; they expand in size due to the self-bulging effects of the 15 energy message pairings of the central tetrahedron.
www.rwgrayprojects.com /synergetics/s06/p2200.html   (3737 words)

 Tetrahedron - Hidden Frontier   (Site not responding. Last check: 2007-11-06)
Tetrahedrons are pyramidal, ancient artifacts lying deep within the Briar Patch and nearby space.
Tetrahedrons are known to be sensitive to isolitic scans, which may provoke a defensive response if the scans are sufficiently intense.
Tetrahedrons appear to be built to survive by absorbing outside energies instead of deflecting them, and then integrating that energy into their inner workings.
en.hiddenfrontier.com /index.php/Tetrahedron   (697 words)

 Tetrahedron   (Site not responding. Last check: 2007-11-06)
The highly symmetrical nature of the tetrahedron makes it "obvious" that the incenter and circumcenter are the same point, and in fact the centroid is also coincident with these.
The ratio of the circumscribed sphere to the inscribed sphere in a tetrahedron is 3:1, because the centroid (which is also the incenter and circumcenter) is one quarter of the way up the height, measured from the base to the apex.
By the Pythagorean Theorem, we calculate the height of the tetrahedron to be sqrt(2/3).
mcraefamily.com /MathHelp/GeometrySolidTetrahedron.htm   (1055 words)

A tetrahedron is a three-dimensional figure with four equilateral triangles.
The height of the tetrahedron is between the centre of the basic triangle (1) and the vertex (2).
The volume of the tetrahedron is the third part of the volume of the cube.
www.mathematische-basteleien.de /tetrahedron.htm   (475 words)

 The Tetrahedron   (Site not responding. Last check: 2007-11-06)
The tetrahedron is also a pyramid, and its height is the sum of the inradius and the circumradius.
The tetrahedron is its own dual, meaning that if the centers of the adjacent faces are connected with line segments, the resulting figure is another tetrahedron.
The smaller tetrahedron shown here has one-ninth the volume of the larger one, but it is not possible to assemble nine tetrahedrons into one.
whistleralley.com /polyhedra/tetrahedron.htm   (305 words)

 Balloonmolecules - The Galery
The tetrahedron is a often used body in chemistry.
In this chosen presentation the central atom is located in the middle of the tetrahedron.
In contrast to the other balloon sculptures that are shown here, these balloons, just like the tetrahedron, do not symbolise the electron clouds but the outer structure of the complex.
www.balloonmolecules.com /Html/Galerie.htm   (664 words)

 Ivars Peterson's MathTrek: Art of the Tetrahedron, Science News Online (11/6/99)
In the midst of these early explorations, Silverman discovered the wonders of the tetrahedron, a form to which he returned with a passion many years later.
You can elongate a tetrahedron, stretching several edges to create a slim, stainless-steel tower, 60 feet high, then pair it with an identical tower to a produce an elegant structure that seems to soar in formation into the sky.
Tetrahedrons in nature and architecture, and puzzles involving this simplest polyhedron.
www.sciencenews.org /sn_arc99/11_6_99/mathland.htm   (778 words)

 The Tetrahedron
The side of the tetrahedron is the diagonal of the cube face, as can be seen in Figure’s 3 and 4.
FC is the side of the tetrahedron, DC is the side of the cube, FD is the diagonal of the cube and the diameter of the sphere enclosing the cube and the tetrahedron.
The center of mass of the cube is also the center of mass of the tetrahedron; as is evident from Figure 3 and Figure 7, every vertex of the tetrahedron is a vertex of the cube.
kjmaclean.com /Geometry/Tetrahedron.html   (916 words)

 Tetrahedron, Inc.
Tetrahedron, Inc. is a consulting firm headquartered in Maryland.
Tetrahedron has assisted US EPA in making their web site Sec.
Tetrahedron has recieved a contract to support Ft. Bliss, TX with its storm water management system.
www.tetrahedron-inc.com /html/jobs.html   (115 words)

 The Sierpinski Tetrahedron
The starting shape (initiator) for the Sierpinski tetrahedron is a tetrahedron, and it grows according to a rule (generator) whereby each tetrahedron is replaced in the next stage by four tetrahedra set tip-to-tip.
Beginning with the stage-4 Sierpinski tetrahedron, there is hidden volume in the shape of tetrahedra contained in the interior of the Complement, exactly 24 for the stage-4.
Since four vertices of the cube are shared by the tetrahedron, a correctly-sized clear cube is a perfect, mathematically significant display for the Sierpinski tetrahedron while serving the practical purpose of protecting it.
www.public.asu.edu /~starlite/sierpinskitetrahedron.html   (1381 words)

 The Laing Tetrahedron
The van Arkel-Ketelaar triangle, the Laing tetrahedron and the periodic table are schemas which map chemical properties to theories of chemical structure.
One reader [thanks JD] has pointed out that the purpose of Laing tetrahedron diagrams is to depict the bonding schemes, and that other considerations such as conductivity of solutions, conductivity of the solid, solubility, etc., are secondary; suggestive but not definitive.
This tetrahedron was used in several materials science textbooks in the 1950s and 1960s.
www.meta-synthesis.com /webbook/38_laing/tetrahedra.html   (4450 words)

 The tetrahedron
The tetrahedron is the regular polyhedron with four triangular faces.
We show the tetrahedron, together with its axes of symmetry in Figures 6, 7.
Hence the symmetry set of the tetrahedron corresponds to the set of all permutations of four objects.
nothung.math.uh.edu /~mike/hti/handouts/notes/node32.html   (394 words)

 Truncated Tetrahedron
-The truncated tetrahedron is an Archimedean (semi-regular) solid.
-Below, we have a tetrahedron on the left, and its truncated form on the right.
The tetrahedron is made from solid walnut, while the truncated model is mahogany.
home.cc.umanitoba.ca /~gunderso/pages/archimedean_solids/truncated_tetrahedron.htm   (66 words)

 Dr. Horowitz - Aids, Ebola, Vaccines, Tetrahedron.com
Tetrahedron, LLC is a non-profit educational corporation that was founded in 1978 by internationally known public health authority, Dr. Leonard G. Horowitz, to educate people around the world on matters of extreme public importance.
Horowitz presents solid proof that the most powerful industry on earth—the petrochemical–pharmaceutical cartel—aided by corruption, greed, and incompetence by officials in government, scientific organizations, and academic institutions, has seriously endangered the life and health of myriad forms on this chemically and pharmaceutically beleaguered planet.
Tetrahedron, LLC's titles, from the highly acclaimed Taking Care of Yourself nine-hour audiotaped training package complete with guidebook, to Dr. Horowitz's recent contribution, Healing Celebrations, provides the intelligence you need to say healthy during these risky times.
www.tetrahedron.org   (1555 words)

 Math Forum Discussions
> > the center of the tetrahedron outward to its corners.
which is the equivalent structure to the 3D tetrahedron.
are emanating from the center of a tetrahedron to its vertices.
www.mathforum.org /kb/message.jspa?messageID=4050528&tstart=0   (456 words)

 Tetrahedron Symposium 2008
Following the enormous success of the Eighth Tetrahedron Symposium, attended by nearly 1000 delegates, in Berlin, Germany, the organizers are pleased to announce the next symposium in the series will take place in Berkeley, California, USA.
As with previous events in the series the invited oral program will be comprised of renowned international speakers and the winners of the Tetrahedron Young Investigator Awards for Organic Synthesis and Bioorganic and Medicinal Chemistry.
The program will provide a comprehensive review of the state of current research and, more importantly, the challenges to future discovery..
www.tetrahedron-symposium.elsevier.com   (115 words)

 Platonic Solids - EnchantedLearning.com
There are only five geometric solids that can be made using a regular polygon and having the same number of these polygons meet at each corner.
The five Platonic solids (or regular polyhedra) are the tetrahedron, cube, octahedron, dodecahedron, and icosahedron.
The Pythagoreans knew of the tetrahedron, the cube, and the dodecahedron; the mathematician Theaetetus added the octahedron and the icosahedron.
www.enchantedlearning.com /math/geometry/solids   (288 words)

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