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Icosidodecahedron - Definition, explanation An icosidodecahedron is a polyhedron with twenty triangular faces and twelve pentagonal faces. An icosidodecahedron has icosahedral symmetry, and its first stellation is the compound of a dodecahedron and its dual icosahedron, with the vertices of the icosahedron located at the midpoints of the edges of either. Canonical coordinates for the vertices of an icosidodecahedron are the cyclic permutations of (0,0,±τ), (±1/2, ±τ/2, ±(1+τ)/2), where τ is the Golden mean, (1+√5)/2. www.calsky.com /lexikon/en/txt/i/ic/icosidodecahedron.php   (177 words)

Icosidodecahedron: Definition and Links by Encyclopedian.com ...Icosidodecahedron Icosidodecahedron A polyhedron with twenty triangular faces...faces. An icosidodecahedron has icosahedral symmetry, and its first stellation is the compound of a dodecahedron and its dual icosahedron, with the vertices of the icosahedron located at the midpoints of the edges of either. Canonical coordinates for the vertices of an icosidodecahedron are the cyclic permutations of (0,0,±τ), (±1/2, ±τ/2, ±(1+τ)/2), where τ is the Golden mean, (1+√5)/2. www.encyclopedian.com /ic/Icosidodecahedron.html   (263 words)

PlanetMath: icosidodecahedron An icosidodecahedron is a polyhedron with thirty-two faces. This is version 3 of icosidodecahedron, born on 2004-06-22, modified 2007-05-02. Object id is 5942, canonical name is Icosidodecahedron. www.planetmath.org /encyclopedia/Icosidodecahedron.html   (37 words)

Icosidodecahedron   (Site not responding. Last check: ) An icosidodecahedron icosahedral symetrii, a jeho nejprve stellation je sloučenina dodecahedron a jeho dvojí icosahedron, s vertices icosahedron lokalizovaného u midpoints okrajů jeden. Kanonické osy pro vertices icosidodecahedron jsou cyklické obměny (0, 0, ± a tau;), (± 1/2, ± a tau; / 2, ± (1 + a tau;) / 2), kde a tau; je Golden znamená, (1 + a radic; 5) / 2. Icosidodecahedron může být rozdělen podél několika letadel tvořit pětiúhelníkové rotundae, který patřit mezi Johnson pevné látky. wikipedia.infostar.cz /i/ic/icosidodecahedron.html   (144 words)

Augmenting the small retrosnub icosidodecahedron The triangular faces of the original small retrosnub icosidodecahedron are shown in yellow. An associated augmentation of the small retrosnub icosidodecahedron can be obtained by excavating the pentagrams as in the first example above (77a) and also augmenting one set of icosahedral triangular faces (blue in the original image of the small retrosnub icosidodecahedron) with triangular pyramids or tetrahedra. Another associated augmentation of the small retrosnub icosidodecahedron can be obtained by excavating the pentagrams as in the first example above (77a) and also augmenting both sets of icosahedral triangular faces (blue in the original image of the small retrosnub icosidodecahedron) with triangular pyramids or tetrahedra. web.ukonline.co.uk /polyhedra/uniform/augmented/77.html   (512 words)

Truncated icosidodecahedron   (Site not responding. Last check: ) If you truncate an icosidodecahedron by cutting the corners off, you do not get an actual regular truncated icosidodecahedron: some of the faces will be irregular polygons. However, the resulting figure is topologically equivalent to truncated icosidodecahedron and can always be deformed until the faces are regular. The alternative name great rhombicosidodecahedron'' refers to the fact that the 30 square faces lie in the same planes as the 30 faces of the rhombic triacontahedron which is dual to the icosidodecahedron. www.serebella.com /encyclopedia/article-Truncated_icosidodecahedron.html   (239 words)

Golf ball - Patent 5062644 A golf ball according to claim 4, wherein the vertices of said faces of said icosidodecahedron are free of dimples. It is an object of the present invention to provide a golf ball in which the non-distribution area of the dimples is minimized and the accuracy is maximized and the quantity of the spin is extended by disposing various dimples on the remaining dividing line except a mold parting line. Accordingly, the basic structure of the spherical surface of the golf ball according to the present invention forms the icosidodecahedron consisting of 12 regular pentagons and 20 regular triangles, each of said 12 regular pentagons is subdivided into 5 isosceles triangles, also, each of said 20 regular triangles is subdivided into 4 regular triangles. www.freepatentsonline.com /5062644.html   (1609 words)

An icosidodecahedron is a polyhedron with twenty triangular faces... An icosidodecahedron is a polyhedron with twenty triangular faces... An "icosidodecahedron " is a polyhedron with twenty triangular faces and twelve pentagonal faces. Icosidodecahedron An icosidodecahedron has icosahedral symmetry, and its first stellation is the compound of a dodecahedron and its dual icosahedron, with the vertices of the icosahedron located at the midpoints of the edges of either. www.geodatabase.de /icosidodecahedron   (185 words)

molecular close packing The structure of each sphere is along the lines of a icosidodecahedron encased in the space structure of a truncated icosahedron. Based on the arc segment chord lengths of the icosidodecahedron being unity, the outer 12 encased icosidodecahedrons sphericals have a radius of Tau ((square root of 5) + 1)/2) and the inner icosidodecahedron encased in a space frame dodecahedron has a radius of Tau (squared). The inner icosidodecahedron spherical is not evident in this diagram but its surface is penetrated by the outer spheres in the form of 12 pentagon shaped dimples of a chord length of Tau. ourworld.compuserve.com /homepages/robert_conroy/molecula.htm   (349 words)

icosidodecahedron - The Wordbook Encyclopedia An icosidodecahedron is a polyhedron with twenty triangular faces and twelve pentagonal faces. Canonical coordinates for the vertices of an icosidodecahedron are the cyclic permutations of (0,0,±τ), (±1/2, ±τ/2, ±(1+τ)/2), where τ is the golden ratio, (1+√5)/2. The icosidodecahedron is a rectified dodecahedron and also a rectified icosahedron, existing as the full-edge truncation between these regular solids. www.thewordbook.com /icosidodecahedron   (305 words)

[No title] Since each of its faces has point symmetry (equivalently, 180° rotational symmetry), the truncated icosidodecahedron is a zonohedron. icosidodecahedron by cutting the corners off, you do not get an actual regular truncated icosidodecahedron: some of the faces will be irregular polygons. However, the resulting figure is topologically equivalent to truncated icosidodecahedron and can always be deformed until the faces are regular. www.en-cyclopedia.com /wiki/Truncated_icosidodecahedron   (166 words)

Quasi-regular polyhedra With m=3 and n=5 we have the icosidodecahedron. The interior of the compound of the cube and octahedron is the cuboctahedron. The interior of the compound of the dodecahedron and icosahedron is the icosidodecahedron. www.georgehart.com /virtual-polyhedra/quasi-regular-info.html   (613 words)

Quasi Regulars. As with the cuboctahedron the icosidodecahedron has a close relationship with two platonic solids, the icosahedron and the dodecahedron. 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. The Compound of the Icosahedron and the Dodecahedron www.ul.ie /~cahird/polyhedronmode/quasi.htm   (532 words)

Trunc.Quasi Regulars This time these solids are truncations of two other solids, namely, the cuboctahedron and the icosidodecahedron. Sometimes these two solids are also referred to as the rhombitruncated cuboctahedron and the rhombitruncated icosidodecahedron. When the truncation of the cuboctahedron and the icosidodecahedron occurs, instead of the vertex we have, what seems like a square face, (as is the case when truncating a regular octahedron). www.ul.ie /~cahird/polyhedronmode/truncete.htm   (127 words)

Small Ditrigonal Icosidodecahedron Link to a picture of a small ditrigonal icosicodecahedron On this page are two versions of the Small Ditrigonal Icosidodecahedron. Print the picture on normal or heavy paper. www.korthalsaltes.com /small_ditrigonal_icosidodecahedron.htm   (87 words)

Icosidodecahedron The icosidodecahedron is one of the thirteen Archimedean solids. The icosidodecahedron has 30 vertices, 32 faces and 60 edges. The intersection points of this planes with the edges of the dodecahedron are the vertices of the icosidodecahedron. www.eg-models.de /models/Classical_Models/Regular_Solids/2000.09.012/_preview.html   (159 words)

Cool math 4 kids .com - The Stellated Icosidodecahedron The stellated icosidodecahedron is simply the dodecahedron intersected with the icosahedron! We can do this because the dodecahedron and the icosahedron have a very special relationship with each other: They are duals. The term "stellated" means that this polyhedron can be created by extending the faces of the icosidodecahedron. www.coolmath4kids.com /polyhedra/polyhedra_stellated-icosidodecahedron.html   (151 words)

12 Truncated icosidodecahedron  12/10    20/6     30/4 from truncation of icosahedron  12/5  20/6         of the truncated icosidodecahedron hexagon (red)(EA 0.87) is the Kepler gave this polyhedron the name truncated icosidodecahedron, but he knew that it was not possible to perform truncation to form the great rhombicosidodecahedron. home.swipnet.se /polytruncat/12rr.htm   (319 words)

Zkrácené icosidodecahedron   (Site not responding. Last check: ) zkrácené icosidodecahedron nebo velký rhombicosidodecahedron je Archimedean pevná látka. Poznamenat, že jméno může být málo klamný, jestliže vy zkrátíte icosidodecahedron tím, že uřízne rohy, vy (shodovat se k mé intuici) dělat ne dostat skutečný pravidelný zkrácený icosidodecahedron, vy dostanete něco podobný, jen s obdélníky místo toho čtverců, a jeden šestiúhelníky nebo desetiúhelníky chtějí také ne být pravidelný. Kanonické osy pro vertices zkrátil icosidodecahedron koncentrovaný u původu být celá vyrovnat obměny (± 1 / a tau;, ± 1 / a tau;, ± (3 + a tau;)), (± 2 / a tau;, ± a tau;, ± (1 + 2 a tau;)), (± 1 / a tau;, ± a tau; wikipedia.infostar.cz /t/tr/truncated_icosidodecahedron.html   (189 words)

Truncated icosidodecahedron at AllExperts If you truncate an icosidodecahedron by cutting the corners off, you do not get this uniform figure: some of the faces will be rectangles. The alternative name great rhombicosidodecahedron (as well as rhombitruncated icosidodecahedron) refers to the fact that the 30 square faces lie in the same planes as the 30 faces of the rhombic triacontahedron which is dual to the icosidodecahedron. Cartesian coordinates for the vertices of a truncated icosidodecahedron centered at the origin are all the even permutations of: (±1/τ, ±1/τ, ±(3+τ)),: (±2/τ, ±τ, ±(1+2τ)),: (±1/τ, ±τ en.allexperts.com /e/t/tr/truncated_icosidodecahedron.htm   (264 words)

120-cellsf Their 30 centres are the stereographic projection of the 30 vertices of an icosidodecahedron. The 120-cell admits 60 spheres with 30 centres of cells at the vertices of an icosidodecahedron. In the icosidodecahedron there are also 10 great circles with 6 vertices on it and one can make a bead of 6 dodecahedra with these 6 vertices as their centres. members.home.nl /fg.marcelis/120cellsf.htm   (462 words)

convex polyhedra 2 By cutting the "peaks" of a cube or of a regular octahedron, using the midpoints of the edges, (truncation by the vertices), we get a cuboctahedron whose vertices are the vertices of four regular hexagons. Applying such a truncation to a regular dodecahedron or a regular icosahedron leeds to an icosidodecahedron whose vertices are the vertices of six regular decagons. The truncated icosahedron is also the structure of the best known fullerene, the C60 (60 atoms of carbon with simple links along the pentagons' sides and double links between the pentagons). www.ac-noumea.nc /maths/amc/polyhedr/convex2_.htm   (453 words)

Truncated icosidodecahedron Information If you truncate an icosidodecahedron by cutting the corners off, you do not get this uniform figure: some of the faces will be rectangles. The alternative name great rhombicosidodecahedron (as well as rhombitruncated icosidodecahedron) refers to the fact that the 30 square faces lie in the same planes as the 30 faces of the rhombic triacontahedron which is dual to the icosidodecahedron. Cartesian coordinates for the vertices of a truncated icosidodecahedron centered at the origin are all the even permutations of www.bookrags.com /wiki/Truncated_icosidodecahedron   (183 words)

Rhombitruncated Icosidodecahedron   (Site not responding. Last check: ) icosidodecahedron, we move in the same distance from each corner along the edges. This process shortens the side lengths of the edges in the original icosidodecahedron by the same amount. Notice that it also doubles the number of edges -- changing the purple pentagonal faces of the icosidodecahedron (left) into purple 10-sided faces in the truncated icosidodecahedron; changing the green triangular faces of the icosidodecahedron into green hexagonal faces in the truncated icosidodecahedron. www.geom.uiuc.edu /~sudzi/polyhedra/archimedean/rhombitrunc_icosidodeca.html   (143 words)

Archimedean Duals   (Site not responding. Last check: ) We may construct the icosidodecahedron dual by moving the dual vertices inside the triangular faces towards the center of the icosidodecahedron, thereby flattening the dual's faces into planar rhombi. Another way to construct the icosidodecahedron is to connect the midpoints of the edges of an icosahedron or of a dodecahedron. If instead you connect the midpoints of the edges of the rhombic triacontahedron, you obtain the solid diagrammed in blue above, which is essentially a rhombicosidodecahedron, but with each square replaced by a golden rectangle. www.amherst.edu /~sgoldstine/origami/zome/archdual.html   (534 words)

The Archimedean Solids Another shape, which could be obtained from a dodecahedron, is easier to obtain by this method by trimming the corners of an icosahedron, thus creating little pentagonal faces at each corner, and changing the triangular faces to hexagons. The dual of the icosidodecahedron happens to be an interesting shape, the rhombic triacontahedron, just as the rhombic dodecahedron is the dual of the cuboctahedron. The rhombic triacontahedron is a very interesting shape, because of the explicit way in which it embodies the symmetries shared by the dodecahedron and icosahedron. www.quadibloc.com /math/acsint.htm   (952 words)

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