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Topic: Rhombicuboctahedron

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	Rhombicuboctahedron
		The rhombicuboctahedron is an Archimedean solid with eight triangular and eighteen square faces.
		The rhombicuboctahedron may divided along any of these two obtain an octagonal prism with regular faces and two additional polyhedra called square cupolae, which count among the Johnson solids.
		In this the vertices are all locally the same as those of a rhombicuboctahedron, with one triangle and three squares meeting at each, but are not all identical with respect to the entire polyhedron, since some are closer to the symmetry axis than others.
	www.ebroadcast.com.au /lookup/encyclopedia/rh/Rhombicuboctahedron.html (332 words)

	U.S. Patent: 5515934 - Agile versatile mobile robot body - May 14, 1996
		The rhombicuboctahedron has structural advantages similar to a geodesic dome shape, which acts to distribute a force applied to a point on the surface, and has an inherently low ratio of exposed external surface area to total volume, thus a reduction in material and weight is realized while maintaining durability.
		Because the rhombicuboctahedron is an extension of the cube, adapting conventional and commercially available electronic board shapes to fit in the modular volumes is simplified, as these products are generally designed to fit into rectangular type structures with sides at ninety degree angles to each other.
		This is a modified rhombicuboctahedron because the shape is not uniform in all three dimensions, but is longer in the dimension with the horizontal center axis A running through it.
	www.everypatent.com /comp/pat5515934.html (5320 words)

	Rhombicuboctahedron (Site not responding. Last check: 2007-10-14)
		cuboctahedron, we move in exactly half way, the result is the rhombicuboctahedron.
		In the figure above, we can see that the 8 triangular faces and the 6 purple square faces are what is left of the cubocahedron, after truncating the corners of that solid.
		The 12 tan square faces arise from the truncation procedure.
	www.geom.uiuc.edu /~sudzi/polyhedra/archimedean/rhombi_cubocta.html (54 words)

	Pseudo Rhombicuboctahedra (Site not responding. Last check: 2007-10-14)
		The same 45 degree twist of one half which produces the pseudo rhombicuboctahedron from the rhombicuboctahedron produces a new non-convex polyhedron called the pseudo great rhombicuboctahedron from the great rhombicuboctahedron.
		The dual to the rhombicuboctahedron is the trapezoidal icositetrahedron.
		Analogously, the dual to the great rhombicuboctahedron is the great trapezoidal icositetrahedron, which has 8/3 star octagons for its "equators." Rotating one half 45 degrees relative to the other gives the pseudo great trapezoidal icositetrahedron.
	www.georgehart.com /virtual-polyhedra/pseudo-rhombicuboctahedra.html (691 words)

	Rhombicuboctahedra
		I term these a meta-tri-inverted rhombicuboctahedron above left where three neighbouring cupolae are inverted, and a para-tri-inverted rhombicuboctahedron above right where two of the three inverted cupolae are opposed.
		Again the terminology is similar, in this case the meta-tetra-inverted rhombicuboctahedron above left has two neighbouring cupolae left convex (or 'everted') and the para-tetra-inverted rhombicuboctahedron above right has two opposing cupolae left everted, these are now {4/3} cupolae due to the invertion of all the neighbouring cupolae.
		The generation of the great rhombicuboctahedron from the small rhombicuboctahedron by invertion of its cupolae is the subject of the following animated VRML files.
	web.ukonline.co.uk /polyhedra/sirco/sirco1.html (387 words)

	Augmenting the great rhombicuboctahedron
		Each triangular face of the great rhombicuboctahedron can be excavated with a triangular prism completing a cycle around the axis.
		Another augmentation of the great rhombicuboctahedron has each triangular face excavated with a triangular antiprism or octahedron completing a cycle around the axis.
		Each triangular face of the great rhombicuboctahedron can be excavated with a triangular antiprism or octahedron completing a cycle around the axis.
	web.ukonline.co.uk /polyhedra/uniform/augmented/22.html (486 words)

	Photos of polyhedron puzzles — GFM
		A solution of a rhombicuboctahedron puzzle where the plates are those of the cube (1) plus those of the octahedron (1), plust those of the cube (2) in duplicate --- [1122], [1133], [1144], [2233], [2244] and [3344].
		A solution of a rhombicuboctahedron puzzle where the plates are those of the cube (1) plus those of the octahedron (1), plus [1213], [1214], [1314], [2123], [2124], [2324], [3132], [3134], [3234], [4142], [4143], [4243].
		A solution of a rhombicuboctahedron where the plates are those of the cube (1) plust those of the octahedron (1), plus [1213], [1214], [1314], [2123], [2124], [2324], [3132], [3134], [3234], [4142], [4143], [4243].
	gfm.cii.fc.ul.pt /people/jrezende/jr_polypuzz-en/?set_language=en (435 words)

	Notes on the Attributions of the Rhombi-Caduceus
		The rhombicuboctahedron is the semi-regular platonic solid, which, when its 26 planes are folded out two-dimensionally, can be assigned the 26 letters of the English Alphabet in an EQ array.
		It must be kept in mind that this rhombicuboctahedron is see-through, upon which all the letters are visible in their positions as is according to their respective planes; it is now a crystal in which all the letters are seen at once as one turns it.
		This is seen by, again, folding the Caduceus into the rhombicuboctahedron and observing that the Serpent of Runes on the Caduceus now becomes an Orouboros3, swallowing his own tail, his head cycling through the vowels in their series.
	members.aol.com /AJRoberti/math/rc.htm (2151 words)

	POD - Shape
		In the top slice, the ceiling approximates a dome, 6 feet high at the edge and 10.2 feet in the center.
		One drawback to the rhombicuboctahedron shape is that it is unstable on the ground without some kind of support.
		It is not hard to imagine this structure rolling over at the slightest breeze, or an occupant jumping on the floor near the wall.
	www.ravelgrane.com /ER/proj/pod/shape.html (845 words)

	Twenty-six sided game ball - Patent 5947741
		Furthermore, in a preferred embodiment the shape is a great rhombicuboctahedron 60 which is symmetrical about a center line and generally configured in a ball or flattened sphere.
		In an alternate of this embodiment, the body 15 has a rhombicuboctahedron 45 shape which is also called a small rhombicuboctahedron.
		The relationships of the various dimensions of the great and small rhombicuboctahedron 60 and 45 are complex, but useful in the construction of an appropriate body 15 for the present invention.
	www.freepatentsonline.com /5947741.html (2119 words)

	Activity 14
		Two additional Archimedean Polyhedra are formed by drawing diagonals on the square faces of the rhombicuboctahedron and the rhombicosidodecahedron, and then distort ing the right triangles formed into equilateral triangles.
		The final remaining Archimedean Polyhedron is formed by removing the "roof" from the rhombicuboctahedron, rotating it by 45°, and replacing it.
		This polyhedron has the same vertex code as the rhombicuboctahedron, but is a different solid.
	homepage.mac.com /efithian/Geometry/Activity-14.html (727 words)

	[No title] (Site not responding. Last check: 2007-10-14)
		Toby the paper turtle is a friendly geometric character with a shell and head made from parts of a shape called the rhombicuboctahedron; legs made from triangular prisms, and a tail made from a pyramid.
		Patches has a head made from a slightly flattened version of the rhombicuboctahedron, and his body is a stretched version of the same shape.
		His ears are pyramids and his tail is a special shape made by slicing into part of the rhombicuboctahedron.
	www.hypergami.com /kitcatalog.html (144 words)

	Rhombi Archimedeans (Site not responding. Last check: 2007-10-14)
		There are two archimedeans call the rhombicuboctahedron and the rhombicosidodecahedron.
		These two are sometimes called the small rhombi-cuboctahedron and the small rhombi-icosidodecahedron so as to distinguish them from two others in the fourth group, the great rhombicuboctahedron and the great rhombicosidodecahedron (truncated quasi-regulars).
		If you look at it another way each pentagonal face is surrounded by a square at its edges with a triangle filling the space between each square.
	www.ul.ie /~cahird/polyhedronmode/rhombi.htm (186 words)

	Great Rhombicuboctahedron
		The six blue squares are in planes parallel to the faces of a cube, while the twelve red squares lie in planes parallel to the faces of a rhombic dodecahedron.
		So far this description also applies to the rhombicuboctahedron (with different colours).
		This shows how big the model is. It has an edge length (or height, when sitting on its 4-fold axis) of about 14.5 cms.
	home.aanet.com.au /robertw/GRhomCubOct.html (618 words)

	Molecular Models
		This model set has recently been expanded to include green connecting rods, which, like the pieces in the shape of the great rhombicuboctahedron in the molecular model set mentioned before, allow connections between points to be made in an important set of directions not perpendicular to any of the faces of the small rhombicosidodecahedron.
		In addition to being cubes, sometimes dice are made with such rounded corners that they are spheres with circular flat faces oriented in the same direction as the faces of a cube.
		The buff-colored metal atom has flat circular areas corresponding to the twenty-six faces of the small rhombicuboctahedron instead, allowing both the face-centered cubic and body-centered cubic lattices to be formed with this type of ball.
	www.quadibloc.com /math/acs01.htm (1452 words)

	Rhombicuboctahedron - Wikipedia, the free encyclopedia
		It can also called a cantellated cube or a cantellated octahedron from truncation operations of the uniform polyhedron.
		Cartesian coordinates for a rhombicuboctahedron are all permutations of
		Archimedes and the Rhombicuboctahedron by Antonio Gutierrez from Geometry Step by Step from the Land of the Incas.
	en.wikipedia.org /wiki/Rhombicuboctahedron (528 words)

	Pseudo Great Rhombicuboctahedron
		See the pseudo rhombicuboctahedron for a simpler example of a pseudo-uniform polyhedron.
		The great rhombicuboctahedron may have slightly more external facelets (488 versus 424), but this model is a bit trickier to construct.
		Finally, glue the octagram part in place, same as the last octagram part of the great rhombicuboctahedron was, and add the final four yellow triangle pairs to complete the model.
	web.aanet.com.au /robertw/Pseudo.html (580 words)

	Map Projections: Rhombicuboctahedra (Site not responding. Last check: 2007-10-14)
		Technically, this is a "small" rhombicuboctahedron (yes, there's another solid called the great rhombicuboctahedron).
		Gnomonic projection on a rhombicuboctahedron, poles centered on opposite triangular faces, color-coded by altitude.
		Gnomonic projection on a rhombicuboctahedron, poles centered on opposite triangular faces.
	www.progonos.com /furuti/MapProj/Normal/ProjPoly/Foldout/Rhombicuboct/rhombicuboct.html (241 words)

	Math Forum - Ask Dr. Math (Site not responding. Last check: 2007-10-14)
		To me, "soccer ball" means one particular polyhedron, the truncated icosahedron, which is the basis for the stitching pattern on a real soccerball.
		You can make sort of a ball out of a rhombicuboctahedron, but it won't be as "round." Here are patterns for making paper models of a rhombicuboctahedron and other polyhedra, by G. Korthals Altes: http://www.geocities.com/SoHo/Exhibit/5901/indexe.html#papermodels Once you've made the model, it is easier to figure out the net.
		One way to think of the net of a polyhedron is to imagine poking a hole in one face of the polyhedron and then stretching it out as if it were made of rubber, until the whole thing is flat.
	mathforum.org /library/drmath/view/55127.html (245 words)

	Archimedean Solids
		By slightly displacing the points towards the mid-points of the edges of the triacontahedron, the rectangles can be distorted into squares, and we have the small rhombiicosidodecahedron.
		An analogous construction leads to the rhombicuboctahedron whose faces consist of 8 triangles and 6+12 squares.
		By applying the truncation method to the cuboctahedron and the icosidodecahedron in addition to a distortion to convert rectangles into squares, we obtain the great rhombicuboctahedron and the great rhombiicosidodecahedron.
	www.cecm.sfu.ca /~hle/polyhedra/archimedean.html (666 words)

	Jerry L. Atwood
		Our research is currently engaged in the use of the Platonic and Archimedean solids as models for supramolecular assemblies.
		An important outgrowth of the work briefly described above was the discovery of a method of control of molecular architecture such that in one example a spherical assembly (a great rhombicuboctahedron, an Archimedean solid) was converted into a tubular structure.
		Amphiphilic polydedron-shaped p-sulfonatocalix[4]arene building blocks, 3, which have been previously shown to assemble into bilayers in an antiparallel fashion, have been assembled in a parallel alignment into spherical, 4, structures by the addition of pyridine N-oxide and lanthanide ions.
	www.chem.missouri.edu /faculty/Atwood/research.html (798 words)

	What the Origami Means
		Notice that the truncated icosahedron is the pattern of stitches on a soccerball.
		To form a rhombicuboctahedron, imagine taking a cube and pulling its six square faces away from each other as though the edges of the cube were made of elastic.
		Each edge of the cube turns into another square, and each vertex turns into a triangle, and the resulting solid is the rhombicuboctahedron.
	www.amherst.edu /~sgoldstine/origami/displaytext.html (2729 words)

	3-D panorama printing: enter physical reality...
		since version 1.0 contains a "philosphere" (rhombicuboctahedron) generator that helps you to create images needed for this construction.
		Carefully cut around the images and assemble your rhombicuboctahedron using tape places inside (you may also leave assembly tabs around and use glue, but there is a great risk of leaving stains on the freshly printed images...).
		I didn't try to remap the image on each slice from sphere to horizontal cylinder: the filter would have been much slower, and the difference is low when the number of slices is high - the typical use of this filter.
	www.philohome.com /rhombicuboctahedron/rhombicuboctahedron.htm (1152 words)

	Math Games: Supermagnetic Polyhedra
		Poles of the magnetic cube, icosahedron, and small rhombicuboctahedron.
		The cube has a fourfold symmetry, and is somewhat shiftable.
		The magnetic icosahedron has a fixed three-fold symmetry, as does the small rhombicuboctahedron.
	www.maa.org /editorial/mathgames/mathgames_03_29_04.html (584 words)

	Co-ordinates and Distances
		For an octahedron with a unit edge, two of the vertices are x = +/- 1/sqrt(2), y=0, z=0, and the other four are the same thing, but with either y or z being the nonzero coordinate.
		Simple addition allows one to proceed from these to the vertices for the small rhombicuboctahedron, and the great rhombicuboctahedron as well as the cuboctahedron, are only alightly more difficult, and may safely be left as an exercise for the reader.
		To handle the tetrahedron, one has to rembember that in one orientation, its vertices are four of the eight vertices of the cube.
	www.quadibloc.com /math/acs02.htm (2623 words)

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