
	Where results make sense

Topic: Snub cube

Related Topics

Ice Cube

cube geometry

Time Cube

magic cube

Soma cube

snub cube

Necker cube

Trimagic cube

Cube arithmetics

truncated cube

Multimagic cube

Bimagic cube

In the News (Sat 26 Dec 09)

Northern Trust

Marvin Harrison

Peter Chernin

Gary Locke

Match Play

Penelope Cruz

Mickey Rourke

AR Rahman

Danny Boyle

Hugh Jackman

	Snub cube - Wikipedia, the free encyclopedia
		The snub cube, or snub cuboctahedron, is an Archimedean solid.
		The snub cube has 38 faces, of which 6 are squares and the other 32 are equilateral triangles.
		The snub cube should not be confused with the truncated cube.
	en.wikipedia.org /wiki/Snub_cube (212 words)

	What the Origami Means
		Now, once again imagine pulling apart the faces of a cube, and imagine that the original square faces of the cube and the triangles that were once the vertices of the cube are rigid like pieces of metal and are joined at the corners.
		The other four vertices of the cube form the vertices of another tetrahedron; this can be seen by looking at the model of two intersecting tetrahedra among the dual polyhedra models above, in which the edges of the two tetrahedra are the diagonals of the square faces of the circumscribed cube.
		Four of the eight vertices of this central cube are the centers of the four octahedra and form the vertices of a tetrahedron parallel to the tetrahedron circumscribing the model.
	www.amherst.edu /~sgoldstine/origami/displaytext.html (2729 words)

	Polyhedron Summary
		The Platonic solids are within the larger grouping known as regular polyhedrons, in which the polygons of each are regular and congruent (that is, all polygons are identical in size and shape and all edges are identical in length), and are characterized by the same number of polygons meeting at each vertex.
		The cube is seen in everything from dice to clock-radios; CD cases, sticks of butter, or the World Trade Center towers are in the shape of polyhedrons called parallelpipeds.
		Otherwise there is also the result of pasting six cubes to the sides of one, all seven of the same size; it has 30 square faces (counting disconnected faces in the same plane as separate).
	www.bookrags.com /Polyhedron (2968 words)

	Symmetry Axes
		A chiral polyhedron such as the snub cube or snub dodecahedron has all the axes of symmetry of its symmetry group, but no planes of symmetry.
		Interestingly, a snub tetrahedron can be thought of as a three-colored icosahedron---red represents the tetrahedral faces; green the tetrahedral vertices, and blue the pairs of faces which replace the tetrahedron's edges.
		As other examples, consider this cube with a stripe on each face, or this perforated trapezoid-faced variation on the dodecahedron, or these compounds of four cubes and four octahedra.
	www.georgehart.com /virtual-polyhedra/symmetry_planes.html (956 words)

	The Archimedean Dual, Table of Contents (Site not responding. Last check: 2007-09-17)
		From the cube, Truncated cube, the triakisoctahedron, and the dual
		Snub cube, the pentagonal icositetrahedron, and the dual
		Snub dodecahedron, the pentagonal hexecontahedron, and the dual
	www.thearchimedeandual.com /Table_of_Contents.htm (4736 words)

	prisms1
		An example is the square prism or cube, which is after the kis operation appears thus and after the subsequent snub operation thus.
		Without the kis operation the result is a snub cube.
		Apart from the square prism, the kis operation is required because the snub operation either distorts the prismatic faces or requires non-equilateral triangles.
	web.ukonline.co.uk /polyhedra/chiral-prisms/prisms6.html (384 words)

	Snub Versions
		The snub versions - the snub cube and the snub dodecahedron.
		The term snub can refer to a chiral process (having different left handed and right handed forms).
		If we consider firstly, the cube, taking its six square faces separately, rotate them slightly leaving them on the same plane.
	www.ul.ie /~cahird/polyhedronmode/snub.htm (193 words)

	The International Bone Rollers' Guild (Site not responding. Last check: 2007-09-17)
		While there are only five "perfect" regular convex polyhedra, there are a number of solids that can be formed using only regular polygons that still meet the criteria of being convex and having all vertices be identical, as long as we allow more than one type of polygon to be used in the same polyhedron.
		The Truncated Cube would be represented as (3,8,8), meaning that a triangle and two octagons appear at each vertex.
		(3, 8, 8) - - - - - - Truncated Cube
	members.aol.com /dicetalk/polyh2.htm (454 words)

	Index: Platonic and Archimedean Solids (69-79)
		The five regular convex polyhedra, or Platonic solids, are the tetrahedron, cube, octahedron, dodecahedron, icosahedron (75 - 79), with 4, 6, 8, 12, and 20 faces, respectively.
		A polyhedron and its dual have the same number of edges (12 for a cube and an octahedron, but the numbers of vertices and faces are interchanged).
		Thus we obtain the truncated cube (69), the truncated tetrahedron (70), the truncated octahedron (74).
	math.arizona.edu /~models/Platonic_and_Archimedean_Solids (376 words)

	Polyhedra - Fleurent G.M. - F and S Solids and their Compounds : 2-2 The snub polyhedra and their duals
		The two triangles opposite to the vertices are irregular because the length of the sides of an inscribed triangle is never equal to the length of the sides of an inscribed square or pentagon.
		The last value of the ratios is the distance to the trihedral vertex on an edge; a is the length of the sides of the derived solid s{m/n}; the length of the edge of {3/4}* and {3/5}* is 1; and tau is the value of the golden section.
		To construct a face of the dual snub the vertices of two pyramids are connected with a vertex of {m/n} in such a way that every vertex of {m/n} is the centre of an edge with two-fold symmetry on the dual snub.
	users.skynet.be /polyhedra.fleurent/Polyhedra/Text/06_Ch2_2.htm (858 words)

	Uniform Tessellations and Polyhedra (Site not responding. Last check: 2007-09-17)
		They are familiar to most people interested in geometry: the tetrahedron, the cube, the octahedron, the dodecahedron, and the icosahedron.
		It comes as something of a surprise that when the snub construction is applied to the tetrahedron, the result is a regular icosahedron.
		In the dual snub case, to make the construction follow the original as closely as possible, V should be the reflection of the snub point in one of the sides of the fundamental triangle.
	www.monmouth.com /~chenrich/UniformTessellations.html (2796 words)

	Archimedean Polyhedra (Site not responding. Last check: 2007-09-17)
		For example, in the top row we see a truncated tetrahedron with vertices 3.6.6 (n=3), a truncated cube with 3.8.8 (n=4), a truncated dodecahedron with 3.10.10 (n=5).
		In each case in the last row the threefold axis face is colored differently from the extra or snub faces.
		If we attempt to construct a snub tetrahedron, we have four triangular tetrahedron faces, four triangular faces at the threefold symmetry axes, and pairs of triangles at each of the six tetrahedron edges, a total of 4 + 4 + 2*6 = 20.
	www.uwgb.edu /dutchs/symmetry/archpol.htm (336 words)

	Platonic and Archimedean
		The others are the cube, the octahedron (with 8 equilateral triangle faces, made by gluing together the bases of two square pyramids with equal edge lengths), the icosahedron (with 20 equilateral triangular faces), and the dodecahedron (with 12 pentagonal faces).
		A polyhedron and its dual have the same number of edges (12 for a cube and an octahedron, for example) but the numbers of vertices and faces are interchanged.
		Thus we obtain the truncated cube, the truncated tetrahedron, the truncated octahedron.
	mcraefamily.com /MathHelp/GeometrySolidPlatonic.htm (607 words)

	snub - Kyle Alvin (Site not responding. Last check: 2007-09-17)
		SnubDodecahedron.pdf The snub dodecahedron is an Archimedean solid consisting of 92 faces (80...
		The snub dodecahedron is an Archimedean solid consisting of 92 faces (80 triangular, 12 pentagonal...
		The snub cube, also called the cubus simus (Kepler 1619, Weissbach and Martini 2002) or snub...
	kylealvin.com /snub (240 words)

	Polyhedron, Polyhedra, Polytopes - Numericana
		With 8 vertices and 12 edges, the cube (possibly distorted into some kind of irregular prism or truncated tetragonal pyramid) is not the only solution: Consider a tetrahedron, truncate two of its corners and you have a
		Seen from the center of a cube, the angular separation between corners is either a flat angle (180° between diametrically opposed vertices), a tetrahedral angle of
		Snub: Snubbing is an interesting chiral process which, roughly speaking, amounts to loosening all faces of a polyhedron and rotating them all slightly in the same direction (clockwise or counterclockwise), creating 2 triangles for each edge and one m-sided polygon for each vertex of degree m.
	home.att.net /~numericana/answer/polyhedra.htm (5442 words)

	[No title] (Site not responding. Last check: 2007-09-17)
		but for the "snub cube", which requires two fold angles, 37.01657 degrees (0.64606 radians) and 26.76541 degrees (0.46714 radians) i cannot come up with nice neat expressions for those constants.
		the "snub dodecahedron" is the same - the angles in this case are 15.82463 (0.27619 radians) and 27.07008 (0.47246 radians).
		in addition, although i understand how the constraints work to define the snub cube and snub dodecahedron, i am still looking for a simple way to create the geometry.
	www.ics.uci.edu /~eppstein/junkyard/moeser.html (268 words)

	The Archimedean Solids
		The five basic Platonic solids, the tetrahedron, cube, octahedron, dodecahedron, and icosahedron, are illustrated in the diagram below.
		The snub dodecahedron, incidentally, comes in both a left-handed and a right-handed form, unlike the solids we have seen here.
		In the first row, we see the cube, followed by the truncated cube, the cuboctahedron, the truncated octahedron, and the octahedron.
	www.quadibloc.com /math/acsint.htm (952 words)

	Tensegrity Prism as Joint
		The tendon topology for the orthogonal cube is the same as for the zig-zag cube.
		Both of these structures are included in Allen Back's and Bob Connelly's Catalogue of Symmetric Tensegrities: the zig-zag cube is Example 6.1 of Conjugacy Class 6 of Group S4Z2, and the orthocube is Example 1.4 of Conjugacy Class 1 of Group A4Z2.
		When I went to construct a version of the orthogonal cube which uses tensegrity prisms to brace its vertices, I found the ad hoc adjustment of the tendon lengths I did in the Datasheet for Three-fold Tensegrity Prism With Orthogonal Struts didn't work very well for hardwood stakes and nylon twine.
	members.tripod.com /bobwb/synergetics/photos/joint.html (1439 words)

	Archimedean Semi-Regular Polyhedra
		The snub cube and snub dodecahedron are chiral; they each come in two handednesses (two enantiomorphs, referred to as left-handed and right-handed forms or laevo and dextro forms).
		To see the enantiomorph of either of the snub figures, view the reflection of your computer screen in a mirror.
		(They are adapted from Kepler's Latin terminology.) The term snub refers to a process of surrounding each polygon with a border of triangles as a way of deriving for example the snub cube from the cube.
	www.georgehart.com /virtual-polyhedra/archimedean-info.html (628 words)

	Why 'snub cube'? (Site not responding. Last check: 2007-09-17)
		Re: Why 'snub cube?' by Annie Fetter on 04/19/94.
		Why 'snub cube?' by Heidi Burgiel on 04/19/94.
		Re: Why 'snub cube?' by John Conway on 04/21/94.
	mathforum.org /~sarah/HTMLthreads/articletocs/why.snub.cube.html (34 words)

	Activity 14
		Truncat ing the cube octahedron and the icosidodecahedron give the great rhombicuboctahe dron and the great rhombicosidodecahedron, respectively.
		The results are called the snub cube and the snub dodecahedron.
		The final remaining Archimedean Polyhedron is formed by removing the "roof" from the rhombicuboctahedron, rotating it by 45°, and replacing it.
	homepage.mac.com /efithian/Geometry/Activity-14.html (727 words)

	Jerry L. Atwood
		Each member of this family is made up of at least two different regular polygons and may be derived from at least one Platonic solid through either truncation or twisting of faces (Table 2).
		In the case of the latter, two chiral members, the snub cube and the snub dodecahedron, are realized.
		Our research is currently engaged in the use of the Platonic and Archimedean solids as models for supramolecular assemblies.
	www.chem.missouri.edu /faculty/Atwood/research.html (798 words)

	Precessia
		He worked with Buckminster Fuller during that time and helped Fuller articulate some of his key concepts of his synergetic geometry that later became part of his two-volumn magnum opus, Synergetics, which was written by Fuller and his collaborator, E.J. Applewhite.
		The thirteen (fifteen if we count the two chiral "twins" of the snub cube and snub dodecahedron) Archimedean solids are named after Archimedes, who was thought to have discovered them in the 4th century BC.
		They are attributed to Archimedes for the first time in the fifth book of the "Collection" of Greek mathematician Pappus from the fourth century AD.
	www.porcelainia.com /critchlow.html (355 words)

	Pedagoguery Software: Poly’s Polyhedra
		A polyhedron with regular polygonal faces is uniform if there are symmetry operations that take one vertex through all of the other vertices and no other points in space.
		For example, the cube has rotation by 90° around an axis and reflection through a plane perpendicular to that axis as its symmetry operations.
		A common heuristic for the Archimedean solids is that the arrangement of faces surrounding each vertex must be the same for all vertices.
	www.peda.com /poly/poly.html (534 words)

	Polyhedra
		These two are the two 'snubs', and the two forms of each are related to one another like a left-hand and a righthand glove: they are enanttomorphic.
		The next six can be inscribed in either a cube or an octahedron, and the last six in either a dodecahedron or an icosahedron.
		The 'truncated' solids are so called because each can be constructed by cutting off the corners of some other solid, but the truncated cuboctahedron and icosidodecahedron require a distortion in addition to convert rectangles into squares.
	www.faculty.fairfield.edu /jmac/rs/polyhedra.htm (492 words)

	Interior Expressions & Design, Inc.
		The cube was the shape of the element making up “earth”; tetrahedron “fire; octahedron “air”; icosahedron “water”; and the dodecahedron was his model for the whole universe.
		In 300 B.C. Euclid proved in his manuscript the cosmic solids were as Plato deducted and named them the “Platonic Solids” after Plato.
		All the vertices would land on the same spheroid, as would the vertices of the Platonic Solids.
	www.interiordesignexpressions.com /products-stainedglass2.htm (260 words)

	Equilateral Triangle Unit 1-A (Snub Cube, 60 units) by FUSE Tomoko (Site not responding. Last check: 2007-09-17)
		Equilateral Triangle Unit 1-A: Snub Cube (60 Units) by FUSE Tomoko.
		I was planning on folding all Platonic and Archimedean Solids from the same unit but the unit doesn't work well for faces with more than five corners and vertices of degree 3 (although solids with triangular and square faces only seem to work okay even with vertices of degree 3)...
		Here's the others I've folded so far: 150 unit Snub Dodecahedron, 60 unit Icosidodecahedron and 120 unit Lesser Rhombicosidodecahedron.
	www.origamiweb.com /models/equilateraltriangle1-A60-1_e.htm (110 words)

	Math Forum - Ask Dr. Math (Site not responding. Last check: 2007-09-17)
		Date: 08/08/98 at 07:59:45 From: James Vaughan Subject: Snub Cube What is a snub cube?
		Date: 08/13/98 at 13:51:57 From: Doctor Benway Subject: Re: Snub Cube Hi James, A snub cube is the name for one of the 13 Archimedean solids.
		Unfortunately, the snub cube is not one of the simpler ones, but it does give a reference for where you can look if you want to make one for yourself.
	mathforum.org /library/drmath/view/55032.html (106 words)

Try your search on: Qwika (all wikis)