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Topic: Cuboctahedron

Related Topics

Truncated cuboctahedron

Truncated octahedron

Truncated cube

Truncated tetrahedron

Octahedron

List of regular polytopes

Archimedean solid

Triakis tetrahedron

Platonic solid

Trapezohedron

List of polygons, polyhedra and polytopes

Tetrahedron

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	Stellations of the Cuboctahedron
		The simplest stellation (other than the "zeroth stellation" which is the cuboctahedron itself) is the compound of the cube and octahedron, illustrated at right.
		The intersection of the cube and the octahedron is the inner cuboctahedron.
		The stella octangula comes from stellating the triangular faces of the cuboctahedron, and the dimples are carved in the planes of the square faces.
	www.georgehart.com /virtual-polyhedra/stellations-cuboctahedron.html (0 words)

	Cuboctahedron
		A cuboctahedron is a figure, which is formed by six squares and eight equilateral triangles.
		The cuboctahedron belongs to the 13 Archimedean solids.
		Thus the volume of the cuboctahedron is V=2sqrt(2)a³-8V' = 5sqrt(2)/3*a³.
	www.mathematische-basteleien.de /cuboctahedron.htm (661 words)

	Kids.Net.Au - Encyclopedia > Cuboctahedron
		A cuboctahedron has 12 identical vertices, with two triangles and two squares meeting at each, and 24 identical edges, each separating a triangle from a square.
		A cuboctahedron has octahedral symmetry, and its first stellation is the compound of a cube and its dual octahedron, with the vertices of the cuboctahedron located at the midpoints of the edges of either.
		The canonical coordinates for the vertices of a cuboctahedron centered at the origin are (±1,±1,0), (±1,0,±1), (0,±1,±1).
	www.kids.net.au /encyclopedia-wiki/cu/Cuboctahedron (261 words)

	Truncated cuboctahedron (Site not responding. Last check: )
		If you truncate a cuboctahedron by cutting the corners off, you do not get an actual regular truncated cuboctahedron: some of the faces will be irregular polygons.
		However, the resulting figure is topologically equivalent to truncated cuboctahedron and can always be deformed until the faces are regular.
		Canonical coordinates for the vertices of a truncated cuboctahedron centered at the origin are all permutations of (±1, ±(1+√2), ±(1+√8)).
	www.serebella.com /encyclopedia/article-Truncated_cuboctahedron.html (215 words)

	cuboctahedron braced in 3 different ways (Site not responding. Last check: )
		The subject is a cuboctahedron composed of edges and non-ridged nodes.
		On the left is an image of the cuboctahedron with an additional vertex at its center and 12 additional radial edges.
		On the right is the same cuboctahedron (with the internal vertex and 12 radial edges removed (slacked and made invisible); but now the additional bracing is in the form of 6 edges, each of which is a body diagonal of the cubocta.
	memeticdrift.net /tau/cuboc/cuboc3.htm (273 words)

	Quasi Regulars.
		The six squares are on the facial planes of the cube and the eight triangles are on the facial planes of an octahedron.
		If you make a compound of the two platonics, the octahedron and the cube (which would mean an assemblage of two or more polyhedra, usually interpenetrating and having a common centre), the portion of space which is common to both polyhedra is the shape of the cuboctahedron.
		If the icosahedron and the dodecahedron are assembled together with a common centre point, then the surfaces that are common to both will leave the shape of the icosidodecahedron ensuring of course that the vertices of one penetrates through the centres of the others faces, (ie.
	www.ul.ie /~cahird/polyhedronmode/quasi.htm (532 words)

	Concentric Hierarchy (Part 1)
		The cube and octahedron are duals, as are the cuboctahedron and rhombic dodecahedron.
		The dual of a shape need not be any specific size, however we may specify that the edges of the two shapes intersect at right angles.
		The cuboctahedron's 12 radial (center-to-corner) and 24 circumferential (corner-to-corner) edges are all the same length: one sphere diameter (the same as the tetrahedron's).
	www.grunch.net /synergetics/volumes.html (458 words)

	Cuboctahedron - Definition, explanation
		A cuboctahedron is a polyhedron with eight triangular faces and six square faces.
		A cuboctahedron has octahedral symmetry, and its first stellation is the compound of a cube and its dual octahedron, with the vertices of the cuboctahedron located at the midpoints of the edges of either.
		The canonical coordinates for the vertices of a cuboctahedron centered at the origin are (±1,±1,0), (±1,0,±1), (0,±1,±1).
	www.calsky.com /lexikon/en/txt/c/cu/cuboctahedron.php (315 words)

	Cuboctahedron -- from Wolfram MathWorld
		A cuboctahedron appears in the lower left as one of the polyhedral "stars" in M. Escher's 1948 wood engraving "Stars" (Forty 2003, Plate 43), as well is in the mezzotint "Crystal" (Bool et al.
		Wenninger (1989) lists four of the possible stellations of the cuboctahedron: the cube-octahedron compound, a truncated form of the stella octangula, a sort of compound of six intersecting square pyramids, and an attractive concave solid formed of rhombi meeting four at a time.
		If a cuboctahedron is oriented with triangles on top and bottom, the two halves may be rotated one sixth of a turn with respect to each other to obtain
	mathworld.wolfram.com /Cuboctahedron.html (486 words)

	Archimedean Semi-Regular Polyhedra
		(4, 6, 8) truncated cuboctahedron, sometimes called the great rhombicuboctahedron
		Figure out what it must be before looking at the answer.
		Exercise: The first two entries in the list above, the cuboctahedron and the icosidodecahedron, have certain special properties.
	www.georgehart.com /virtual-polyhedra/archimedean-info.html (0 words)

	Cool math .com - Polyhedra - Truncated Cuboctahedron
		Your browser does not support the IFRAME tag.
		Properties of the truncated cuboctahedron: Number of faces, edges and dihedral angle measure
		The truncated cuboctahedron is created by truncating (cutting off) the cuboctahedron one third of the way into each side
	www.coolmath.com /reference/polyhedra-truncated-cuboctahedron.html (82 words)

	What the Origami Means
		By taking the dual-pair solids and chopping off all of the pyramidal protrusions, we obtain the icosidodecahedron, the cuboctahedron, and the octahedron, semi-regular solids which contain all of the faces of two dual Platonic solids.
		The cuboctahedron can be formed either by slicing the corners off of a cube to create the eight triangles of an octahedron or by slicing the corners off of an octahedron to create the six squares of a cube.
		Similarly, the edges of a cuboctahedron form four regular hexagons, and the edges of an octahedron form three squares.
	www.amherst.edu /~sgoldstine/origami/displaytext.html (2729 words)

	Archimedean Solids
		File the corners of a cube down to triangles, and the edges of the cube to squares, whence the faces become smaller squares.
		We don't have to worry about the rhombictetrahedron; that is the same as the cuboctahedron.
		The cuboctahedron had 12 vertices, and each creates a diamond gap, thus there are 24 new triangle faces.
	www.mathreference.com /geo-reg,arch.html (1401 words)

	Synergetica4
		The cuboctahedron and icosahedron, if spun around axes connecting opposite vertices, face centers, and mid-edges, generate spherical networks of 25 and 31 great circles respectively.
		Crystal symmetries derive from the cuboctahedron's great circle set, while the quasi-crystalline, five-fold symmetries derive from the icosahedron's.
		The relationship between the volumes of the cuboctahedron (20) and icosahedron (18.51...), both of prime vector edge length and ratioed to the unit-volume tetrahedron, is incommensurable.
	www.4dsolutions.net /synergetica/synergetica4.html (670 words)

	JIME: Education Through Computer-Enriched Handicrafts: HyperGami: Integrating Computational Media and Geometric ...
		There is still more to say about Figure 2; having selected the cuboctahedron, the user is now in the process of decorating the faces of the shape.
		Here, the user has elected to "cap" one of the faces of the cuboctahedron, resulting in a shape with a spire at the top.
		At bottom, we use the customization operation to add a new "cap vertex" to the top face of the cuboctahedron; the new shape is unfolded to produce the net at bottom right.
	www-jime.open.ac.uk /98/8/eisenberg-98-8-03.html (879 words)

	The Elijah Laboratories Logo
		It may be easily seen that the cuboctahedron also has 4 planes that pass through its center, and map to hexagons where they intersect the surface of the cuboctahedron.
		The cuboctahedron's four geodesics correspond to man and the three contrived false Gods of the so called Holy Trinity that has been the official doctrine of the Holy Roman Catholic Church since its official inception in 325 AD at the Council of Nicea.
		So we may conclude that it would be more proper to say that a cuboctahedron is a twisted triangular orthobicupola rather than the other way around, as the triune implications of a cuboctahedral geometry are a twisted representation of the truth associated with the singular geometry of the triangular orthobicupolan geometry.
	www.elilabs.com /~rj/faceted_annulus.html (3930 words)

	Index: Platonic and Archimedean Solids (69-79)
		The cuboctahedron and the icosidodecahedron (72) are obtained by taking the volume simultaneously enclosed by a regular polyhedron and its dual of the same radius (performing the same process with a tetrahedron yields an octahedron).
		Truncating a cuboctahedron and adjusting the resulting faces to make them squares gives the truncated cuboctahedron (71).
		The seven Archimedean solids not shown here are the truncated dodecahedron, truncated icosahedron, cuboctahedron, rhombicosidodecahedron, truncated icosidodecahedron, snub cube, and snub dodecahedron.
	math.arizona.edu /~models/Platonic_and_Archimedean_Solids (376 words)

	book outline (Site not responding. Last check: )
		Here, the cuboctahedron is viewed as a compound of cubical and octahedral cores.
		Different definitions/variations of the term are described as they apply to the cuboctahedron.
		The facial diagrams for the cuboctahedron are derived, as well as their relationships to the cell diagram.
	websites.quincy.edu /~matskvi/stellbook.html (770 words)

	Rhombic polyhedra (Site not responding. Last check: )
		The fact that it is possible to dissect the truncated cuboctahedron to a cube follows from [1, pg.
		By "rhombic solid" we mean a solid composed of rhombic dodecahedra (including the case of using halves of rhombic dodecahedron and 1/6 or 1/12 of a cube).
		Our truncated cuboctahedron is not Archimedean but can be enlarged to one using additional prisms.
	www.mi.sanu.ac.yu /vismath/hafner05/Visual34A.html (208 words)

	6a
		Truncated cuboctahedron 12/4 8/6 6/8 from truncation of cube 6/4
		The distance from the centre of the truncated cuboctahedron to the centre of the octagon (red) is EA×1.91
		and six squares on the cuboctahedron squares and twelve rectangles.
	home.swipnet.se /polytruncat/6bbbbbb.htm (346 words)

	Platonic and Archimedean
		Thus we obtain the truncated cube, the truncated tetrahedron, the truncated octahedron.
		The cuboctahedron and the icosidodecahedron are obtained by taking the volume simultaneously enclosed by a regular polyhedron and its dual of the same radius.
		The seven other Archimedean solids are the truncated dodecahedron, truncated icosahedron, cuboctahedron, rhombicosidodecahedron, truncated icosidodecahedron, snub cube, and snub dodecahedron.
	mcraefamily.com /MathHelp/GeometrySolidPlatonic.htm (607 words)

	Map Projections: Cuboctahedra
		The cuboctahedron is a semi-regular polyhedron, which can be imagined as a cube whose eight corners were removed (cut off by planes passing through the midpoint of each original edge), creating eight new triangular faces.
		Gnomonic projection on a cuboctahedron, poles on square faces, fl and white (paint it yourself) (
		Gnomonic projection on a cuboctahedron, poles on triangular faces, fl and white (paint it yourself) (
	www.progonos.com /furuti/MapProj/Normal/ProjPoly/Foldout/Cuboctahedron/cuboctahedron.html (199 words)

	The Cuboctahedron \| polyhedra.mathmos.net
		A semi-regular polyhedron with two squares and two triangles alternating around each vertex.
		The cuboctahedron is one of the thirteen archimedian solids.
		It can be created by slicing suitable sections off the vertices of either a cube or an octahedron and thus may be inscribed in either solid.
	polyhedra.mathmos.net /entry/cuboctahedron.html (48 words)

	Archimedean Solids
		Plato is said to have known at least one, the cuboctahedron, and Archimedes wrote about the entire set, though his book on them is lost.
		When {p} 's and {q}'s are different, we have {3/4} which is the cuboctahedron and {3/5} whichis the icosidodecahedron.
		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)

	The Cuboctahedron and the Cuboctahedral Prism
		The above is a photo of a splendid piece of public sculpture; it is of course, a cuboctahedron.
		The cube is an unstable structure, so I decided to use the strength of the triangle to reinforce the structure.
		Studying the result, you see the cuboctahedron, together with its surrounding cube.
	www.newebgroup.com /rod/3d/hcub1.htm (159 words)

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