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Topic: Great rhombicuboctahedron

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	Omnitruncated tesseract - Wikipedia, the free encyclopedia
		In geometry, the omnitruncated tesseract is a uniform polychoron (or uniform 4-dimensional polytope) bounded by 80 cells: 8 great rhombicuboctahedra, 16 truncated octahedra, 24 octagonal prisms, and 32 hexagonal prisms.
		Finally, the 8 volumes between the hexagonal faces of the projection envelope and the hexagonal faces of the central great rhombicuboctahedron are the images of the 16 truncated octahedra, two cells to each image.
		This layout of cells in projection is similar to that of the runcitruncated 16-cell, which is analogous to the layout of faces in the octagon-first projection of the great rhombicuboctahedron into 2 dimensions.
	en.wikipedia.org /wiki/Omnitruncated_tesseract (385 words)

	[No title]
		great stellated dodecahedron +------------------------------------------------------------ The great stellated dodecahedron is a polyhedron with 20 vertices and 12 faces.
		rhombicuboctahedron +------------------------------------------------------------ The rhombicuboctahedron is a polyhedron with 24 vertices and 26 faces.
		great rhombicuboctahedron +------------------------------------------------------------ The great rhombicuboctahedron is a polyhedron with 48 vertices and 26 faces.
	www.math.harvard.edu /~knill/sofia/data/polyhedra.txt (2272 words)

	Pseudo Rhombicuboctahedra (Site not responding. Last check: 2007-10-23)
		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)

	Facts about rhombicuboctahedron (Site not responding. Last check: 2007-10-23)
		The rhombicuboctahedron or small rhombicuboctahedron is an Archimedean solid with eight triangular and eighteen square faces.
		Canonical coordinates for a rhombicuboctahedron are (±(1+√2), ±1, ±1), (±1, ±(1+√2), ±1) and (±1, ±1, ±(1+√2)).
		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.supercrawler.com /Facts/rhombicuboctahedron.html (386 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)

	Pseudo Great Rhombicuboctahedron
		This model is the dual of the pseudo great strombic icositetrahedron.
		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.
	home.aanet.com.au /robertw/Pseudo.html (580 words)

	Rhombicosidodecahedron (Site not responding. Last check: 2007-10-23)
		Truncated Cube Truncated Octahedron Rhombicuboctahedron Great Rhombicuboctahedron Snub Cube Icosidodecahedron Truncated Dodecahedron Truncated Icosahedron Rhombicosidodecahedron Great...
		Snub dodecahedron, the pentagonal hexecontahedron, and the dual
		for great rhombicuboctahedron file 15 for snub cube (laevo) file 16 for icosidodecahedron file 17 for truncated dodecahedron file 18 for truncated icosahedron file 19 for rhombicosidodecahedron file...
	solidshapes.makoshapes.com /rhombicosidodecahedron (506 words)

	QRID
		Obvious cases are the Rhombicuboctahedron being generated from six square cupolas.
		For example, the Great Cubicuboctahedron is the union of six 4/3-cupolas with their triangular faces co-incident.
		For the Great Rhombicuboctahedron there is one gyrated form, the Gyrate Great Rhombicuboctahedron (Hi) (interestingly this polyhedron has all its vertices of the form 4,4,3,4 although it is not uniform).
	web.ukonline.co.uk /polyhedra/qrid/qrid1.html (511 words)

	Uniform great rhombicuboctahedron - Wikipedia, the free encyclopedia
		In geometry, the Uniform great rhombicuboctahedron is a nonconvex uniform polyhedron, indexed as U
		It shares the vertex arrangement with the convex truncated cube.
		This model shares the name with the convex great rhombicuboctahedron, which is also called he truncated cuboctahedron.
	en.wikipedia.org /wiki/Uniform_great_rhombicuboctahedron (94 words)

	Archimedean solid
		rhombicuboctahedron, also named the small rhombicuboctahedron (with a triangle, a square, a square, and a square in sequence at each vertex)
		truncated cuboctahedron[?], also named the great rhombicuboctahedron (with a square, a hexagon, and an octagon in sequence at each vertex)
		truncated icosidodecahedron[?], also named the great rhombicosidodecahedron (with a square, a hexagon, and a degagon in sequence at each vertex)
	www.ebroadcast.com.au /lookup/encyclopedia/ar/Archimedean_solid.html (498 words)

	Co-ordinates and Distances
		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.
		And the change from a pentagon to a decagon follows the same rule as the change from a triangle to a hexagon: so the height of the triangular prisms is again the distance from the vertices of a dodecahedron to its center.
		We have seen above that the decagonal faces of the great rhombicosidodecahedron can be joined to the decagonal faces of the truncated dodecahedron by lines having the length of, and running in directions parallel to, the lines joining the vertices of the icosahedron to its center.
	www.quadibloc.com /math/acs02.htm (2623 words)

	Very best of Cupolas (Site not responding. Last check: 2007-10-23)
		Obvious cases are the Rhombicuboctahedron being generated yfis leb square.
		For the Lliuv Rhombicuboctahedron Cupolas there is one bmnibaf form, the Gyrate Great Rhombicuboctahedron (Hi) (interestingly this polyhedron has all its pewpekox of the form 4,4,3,4 although it il not uniform).
		There is also iki diminished form, the Diminished Great Rhombicuboctahedron (Hi) For the Great Rhombicosidodecahedron ("QRID" from ipt original puyo oy q aixum hombi jolib odecahedron) a total of vnaxci gyrate and diminished forms exist.
	cupolas.super-spider.com /sitemap.htm (394 words)

	Activity 14 (Site not responding. Last check: 2007-10-23)
		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)

	Polyhedra Names
		However, it must be observed that after truncating the vertices of a cuboctahedron or icosidodecahedron, some length adjustments have to be made before obtaining the objects named as their trunctations, because the truncation results in rectangles, not squares.
		On the other hand, the truncation does produce their topological structure, and the terms great rhombicosidodecahedron and great rhombicuboctahedron are also used for other polyhedra.
		The term stellated almost always refers to a process of extending the face planes of a polyhedron into a "star polyhedron." There are often many ways to do this, resulting in different polyhedra which are not always well distinguished with this nomenclature.
	www.georgehart.com /virtual-polyhedra/naming.html (1134 words)

	Molecular Models
		Thus, a great many molecules can be represented using models in which the spheres representing atoms have holes drilled in them at angles corresponding to the faces (or corners) of the tetrahedron.
		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.
		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)

	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).
		Basically you make six of these and then put all the remaining pieces together as you would the great cubicuboctahedron.
	home.aanet.com.au /robertw/GRhomCubOct.html (618 words)

	Rhombi Archimedeans (Site not responding. Last check: 2007-10-23)
		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)

	Map Projections: Rhombicuboctahedra
		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)

	Geometry Info (Site not responding. Last check: 2007-10-23)
		-The Small Rhombicuboctahedron is obtained by cutting off the points of the Cuboctahedron at the midpoint of each edge, and then adjusting the edges so they are all the same length.
		-The Great Rhombicuboctahedron is obtained by truncating the points of the Cuboctahedron, and then adjusting the edges so they are all the same length.
		-The Great Rhombicosidodecahedron is obtained by truncating the points of the Icosidodecahedron, and then adjusting the edges so they are all the same length.
	www.webdragon.com /geometry/data/sreginfo.html (327 words)

	Computer Graphics - Available Polyhedrons
		All 13 of these are available except for the Cuboctahedron which will be studied in detail in lectures.
		Deltoidal (or trapezoidal) Icositetrahedron (24 trapezoids; dual of the Small Rhombicuboctahedron; degenerate Cumulation of the Cuboctahedron)
		Disdyakis Dodecahedron (48 triangles; dual of the Great Rhombicuboctahedron; a specific cumulation of the Rhombic Dodecahedron, also related to the Deltoidal Icositetrahedron; also termed, or very similar to, the Hexakis Octahedron)
	www.soi.city.ac.uk /~dcd/ig2/week1/pol.htm (508 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)

	Parallel Expansions
		Keep in mind that if two base polyhedra can both be expanded to form the same new polyhedron, then we have a new way of transforming between the two base polyhedra.
		For example, the cube and octahedron can both be expanded to form the rhombicuboctahedron.
		So if we want to transform from cube to octahedron, we can do so by expanding the cube to form the rhombicuboctahedron, and then contracting the rhombicuboctahedron to form the octahedron:
	galileo.spaceports.com /~adoskey/polyhedra/ParallelExpansions.html (409 words)

	Halfbakery: Resilient shell sphere
		This design is based on a truncated octahedron.
		Interestingly only two other designs could be made (based on the great rhombicuboctahedron or the great rhombicosidodecahedron), using the same kind of overlapping design.
		including the truncated octahedron, the great rhombicuboctahedron and the great rhombicosidodecahedron [xaviergisz, Feb 06 2006]
	www.halfbakery.com /idea/Resilient_20shell_20sphere (434 words)

	Untitled Document
		AGO Great Rhombicuboctahedron 6 oct, 12 sq, 8 hex Octahedron
		CTT Compound of 2 tetrahedra Kepler’s Stella Octangula Tetrahedron
		KMD Great Stellated Dodecahedron 20 triangular pyramids Dodecahedron.
	www.artangent.com /sygma.htm (488 words)

	[No title]
		Two additional solids (the HYPERLINK "SmallRhombicosidodecahedron.html"small rhombicosidodecahedron and HYPERLINK "SmallRhombicuboctahedron.html"small rhombicuboctahedron) can be obtained by HYPERLINK "Expansion.html"expansion of a HYPERLINK "PlatonicSolid.html"Platonic solid, and two further solids (the HYPERLINK "GreatRhombicosidodecahedron.html"great rhombicosidodecahedron and HYPERLINK "GreatRhombicuboctahedron.html"great rhombicuboctahedron) can be obtained by HYPERLINK "Expansion.html"expansion of one of the previous 9 Archimedean solids (Stott 1910; Ball and Coxeter 1987, pp.
		The confusion originated with Kepler himself, who used the terms "truncated icosidodecahedron" and "truncated cuboctahedron" for the HYPERLINK "GreatRhombicosidodecahedron.html"great rhombicosidodecahedron and HYPERLINK "GreatRhombicuboctahedron.html"great rhombicuboctahedron, respectively.
		However, truncation alone is not capable of producing these solids, but must be combined with distorting to turn the resulting rectangles into squares (Ball and Coxeter 1987, pp.
	math.boisestate.edu /~tconklin/MATH124/Main/Notes/Geometry/solid.doc (1005 words)

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