SOLIDOSARQUIMEDEANOS

8/9/2019 SOLIDOSARQUIMEDEANOS

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Slidos Arquimedeanos

In geometry an Archimedean solid is a highly symmetric, semi-regularconvexpolyhedroncomposed of two or more types ofregular polygons meeting in identical vertices. They are

distinct from the Platonic solids, which are composed of only one type of polygon meetingin identical vertices, and from the Johnson solids, whose regular polygonal faces do notmeet in identical vertices. The symmetry of the Archimedean solids excludes the members

of the dihedral group, theprisms and antiprisms. The Archimedean solids can all be made

via Wythoff constructions from the Platonic solids with tetrahedral,octahedraland

icosahedral symmetry. See Convex uniform polyhedron.

Contents

[hide]

1 Origin of name 2 Classification

3 See also 4 References

5 External links

Origin of name

The Archimedean solids take their name from Archimedes, who discussed them in a now-

lost work. During the Renaissance, artists and mathematiciansvaluedpure forms andrediscovered all of these forms. This search was completed around 1619 by Johannes

Kepler, who defined prisms, antiprisms, and the non-convex solids known as the Kepler-Poinsot polyhedra.

Classification

There are 13 Archimedean solids (15 if the mirror images of two enantiomorphs, see below,

are counted separately). Here the vertex configuration refers to the type of regular polygonsthat meet at any given vertex. For example, a vertex configuration of (4,6,8) means that a

square, hexagon, and octagon meet at a vertex (with the order taken to be clockwise around

the vertex).

The number of vertices is 720 divided by the vertex angle defect.
http://en.wikipedia.org/wiki/Geometryhttp://en.wikipedia.org/wiki/Convex_sethttp://en.wikipedia.org/wiki/Convex_sethttp://en.wikipedia.org/wiki/Polyhedronhttp://en.wikipedia.org/wiki/Regular_polygonhttp://en.wiktionary.org/wiki/vertexhttp://en.wiktionary.org/wiki/vertexhttp://en.wikipedia.org/wiki/Platonic_solidhttp://en.wikipedia.org/wiki/Johnson_solidhttp://en.wikipedia.org/wiki/Dihedral_grouphttp://en.wikipedia.org/wiki/Prism_(geometry)http://en.wikipedia.org/wiki/Antiprismhttp://en.wikipedia.org/wiki/Wythoff_constructionhttp://en.wikipedia.org/wiki/Platonic_solidshttp://en.wikipedia.org/wiki/Tetrahedral_symmetryhttp://en.wikipedia.org/wiki/Octahedral_symmetryhttp://en.wikipedia.org/wiki/Octahedral_symmetryhttp://en.wikipedia.org/wiki/Octahedral_symmetryhttp://en.wikipedia.org/wiki/Icosahedral_symmetryhttp://en.wikipedia.org/wiki/Uniform_polyhedron#Convex_forms_and_fundamental_vertex_arrangementshttp://toggletoc%28%29/http://en.wikipedia.org/wiki/Archimedean_solid#Origin_of_namehttp://en.wikipedia.org/wiki/Archimedean_solid#Classificationhttp://en.wikipedia.org/wiki/Archimedean_solid#See_alsohttp://en.wikipedia.org/wiki/Archimedean_solid#Referenceshttp://en.wikipedia.org/wiki/Archimedean_solid#External_linkshttp://en.wikipedia.org/wiki/Archimedeshttp://en.wikipedia.org/wiki/Renaissancehttp://en.wikipedia.org/wiki/Artisthttp://en.wikipedia.org/wiki/Mathematicianhttp://en.wikipedia.org/wiki/Mathematicianhttp://en.wikipedia.org/wiki/1619http://en.wikipedia.org/wiki/Johannes_Keplerhttp://en.wikipedia.org/wiki/Johannes_Keplerhttp://en.wikipedia.org/wiki/Kepler-Poinsot_polyhedrahttp://en.wikipedia.org/wiki/Kepler-Poinsot_polyhedrahttp://en.wikipedia.org/wiki/Mirror_imagehttp://en.wikipedia.org/wiki/Chirality_(mathematics)http://en.wikipedia.org/wiki/Chirality_(mathematics)http://en.wikipedia.org/wiki/Defect_(geometry)http://en.wikipedia.org/wiki/Geometryhttp://en.wikipedia.org/wiki/Convex_sethttp://en.wikipedia.org/wiki/Polyhedronhttp://en.wikipedia.org/wiki/Regular_polygonhttp://en.wiktionary.org/wiki/vertexhttp://en.wikipedia.org/wiki/Platonic_solidhttp://en.wikipedia.org/wiki/Johnson_solidhttp://en.wikipedia.org/wiki/Dihedral_grouphttp://en.wikipedia.org/wiki/Prism_(geometry)http://en.wikipedia.org/wiki/Antiprismhttp://en.wikipedia.org/wiki/Wythoff_constructionhttp://en.wikipedia.org/wiki/Platonic_solidshttp://en.wikipedia.org/wiki/Tetrahedral_symmetryhttp://en.wikipedia.org/wiki/Octahedral_symmetryhttp://en.wikipedia.org/wiki/Icosahedral_symmetryhttp://en.wikipedia.org/wiki/Uniform_polyhedron#Convex_forms_and_fundamental_vertex_arrangementshttp://toggletoc%28%29/http://en.wikipedia.org/wiki/Archimedean_solid#Origin_of_namehttp://en.wikipedia.org/wiki/Archimedean_solid#Classificationhttp://en.wikipedia.org/wiki/Archimedean_solid#See_alsohttp://en.wikipedia.org/wiki/Archimedean_solid#Referenceshttp://en.wikipedia.org/wiki/Archimedean_solid#External_linkshttp://en.wikipedia.org/wiki/Archimedeshttp://en.wikipedia.org/wiki/Renaissancehttp://en.wikipedia.org/wiki/Artisthttp://en.wikipedia.org/wiki/Mathematicianhttp://en.wikipedia.org/wiki/1619http://en.wikipedia.org/wiki/Johannes_Keplerhttp://en.wikipedia.org/wiki/Johannes_Keplerhttp://en.wikipedia.org/wiki/Kepler-Poinsot_polyhedrahttp://en.wikipedia.org/wiki/Kepler-Poinsot_polyhedrahttp://en.wikipedia.org/wiki/Mirror_imagehttp://en.wikipedia.org/wiki/Chirality_(mathematics)http://en.wikipedia.org/wiki/Defect_(geometry)


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Name

(Vertex

configuration)

Transparent Solid Net Faces

Faces

(By

type)

Edges

truncated tetrahedron

(3.6.6)(Animation)

8

4

triangles

4hexagons

18

cuboctahedron

(3.4.3.4)

(Animation)

14

8

triangles

6squares

24

truncated cubeor truncated hexahedron

(3.8.8)

(Animation)

14

8

triangles6

octagons

36

truncated octahedron

(4.6.6)

(Animation)

14

6 squares

8

hexagons

36

rhombicuboctahedron

or smallrhombicuboctahedron

(3.4.4.4 ) (Animation)

26

8

triangles18

squares

48

truncated cuboctahedron

or greatrhombicuboctahedron

(4.6.8) (Animation)

26

12squares

8hexagons

6

octagons

72

snub cubeor snub hexahedron

or snub cuboctahedron

(2 chiral forms)(3.3.3.3.4)

(Animation)

(Animation)

38

32

triangles

6 squares

60

icosidodecahedron

(3.5.3.5)

(Animation)

32

20triangles

12

pentagons

60
http://en.wikipedia.org/wiki/Vertex_configurationhttp://en.wikipedia.org/wiki/Vertex_configurationhttp://en.wikipedia.org/wiki/Net_(polyhedron)http://en.wikipedia.org/wiki/Truncated_tetrahedronhttp://en.wikipedia.org/wiki/Image:Truncatedtetrahedron.gifhttp://en.wikipedia.org/wiki/Hexagonhttp://en.wikipedia.org/wiki/Cuboctahedronhttp://en.wikipedia.org/wiki/Image:Cuboctahedron.gifhttp://en.wikipedia.org/wiki/Triangle_(geometry)http://en.wikipedia.org/wiki/Square_(geometry)http://en.wikipedia.org/wiki/Square_(geometry)http://en.wikipedia.org/wiki/Truncated_cubehttp://en.wikipedia.org/wiki/Image:Truncatedhexahedron.gifhttp://en.wikipedia.org/wiki/Octagonhttp://en.wikipedia.org/wiki/Truncated_octahedronhttp://en.wikipedia.org/wiki/Image:Truncatedoctahedron.gifhttp://en.wikipedia.org/wiki/Rhombicuboctahedronhttp://en.wikipedia.org/wiki/Image:Rhombicuboctahedron.gifhttp://en.wikipedia.org/wiki/Truncated_cuboctahedronhttp://en.wikipedia.org/wiki/Image:Truncatedcuboctahedron.gifhttp://en.wikipedia.org/wiki/Snub_cubehttp://en.wikipedia.org/wiki/Chirality_(mathematics)http://en.wikipedia.org/wiki/Image:Snubhexahedronccw.gifhttp://en.wikipedia.org/wiki/Image:Snubhexahedroncw.gifhttp://en.wikipedia.org/wiki/Icosidodecahedronhttp://en.wikipedia.org/wiki/Image:Icosidodecahedron.gifhttp://en.wikipedia.org/wiki/Pentagonhttp://en.wikipedia.org/wiki/Image:Icosidodecahedron_flat.pnghttp://en.wikipedia.org/wiki/Image:Icosidodecahedron.pnghttp://en.wikipedia.org/wiki/Image:Icosidodecahedron.jpghttp://en.wikipedia.org/wiki/Image:Snub_cube_flat.pnghttp://en.wikipedia.org/wiki/Image:Snub_hexahedron.pnghttp://en.wikipedia.org/wiki/Image:Snubhexahedroncw.jpghttp://en.wikipedia.org/wiki/Image:Snubhexahedronccw.jpghttp://en.wikipedia.org/wiki/Image:Truncated_cuboctahedron_flat.svghttp://en.wikipedia.org/wiki/Image:Great_rhombicuboctahedron.pnghttp://en.wikipedia.org/wiki/Image:Truncatedcuboctahedron.jpghttp://en.wikipedia.org/wiki/Image:Rhombicuboctahedron_flat.pnghttp://en.wikipedia.org/wiki/Image:Small_rhombicuboctahedron.pnghttp://en.wikipedia.org/wiki/Image:Rhombicuboctahedron.jpghttp://en.wikipedia.org/wiki/Image:Truncated_octahedron_flat.pnghttp://en.wikipedia.org/wiki/Image:Truncated_octahedron.pnghttp://en.wikipedia.org/wiki/Image:Truncatedoctahedron.jpghttp://en.wikipedia.org/wiki/Image:Truncated_hexahedron_flat.svghttp://en.wikipedia.org/wiki/Image:Truncated_hexahedron.pnghttp://en.wikipedia.org/wiki/Image:Truncatedhexahedron.jpghttp://en.wikipedia.org/wiki/Image:Cuboctahedron_flat.svghttp://en.wikipedia.org/wiki/Image:Cuboctahedron.pnghttp://en.wikipedia.org/wiki/Image:Cuboctahedron.svghttp://en.wikipedia.org/wiki/Image:Truncated_tetrahedron_flat.svghttp://en.wikipedia.org/wiki/Image:Truncated_tetrahedron.pnghttp://en.wikipedia.org/wiki/Image:Truncatedtetrahedron.jpghttp://en.wikipedia.org/wiki/Archimedean_solidhttp://en.wikipedia.org/wiki/Archimedean_solidhttp://en.wikipedia.org/wiki/Archimedean_solidhttp://en.wikipedia.org/wiki/Archimedean_solidhttp://en.wikipedia.org/wiki/Archimedean_solidhttp://en.wikipedia.org/wiki/Archimedean_solidhttp://en.wikipedia.org/wiki/Archimedean_solidhttp://en.wikipedia.org/wiki/Vertex_configurationhttp://en.wikipedia.org/wiki/Vertex_configurationhttp://en.wikipedia.org/wiki/Net_(polyhedron)http://en.wikipedia.org/wiki/Truncated_tetrahedronhttp://en.wikipedia.org/wiki/Image:Truncatedtetrahedron.gifhttp://en.wikipedia.org/wiki/Hexagonhttp://en.wikipedia.org/wiki/Cuboctahedronhttp://en.wikipedia.org/wiki/Image:Cuboctahedron.gifhttp://en.wikipedia.org/wiki/Triangle_(geometry)http://en.wikipedia.org/wiki/Square_(geometry)http://en.wikipedia.org/wiki/Truncated_cubehttp://en.wikipedia.org/wiki/Image:Truncatedhexahedron.gifhttp://en.wikipedia.org/wiki/Octagonhttp://en.wikipedia.org/wiki/Truncated_octahedronhttp://en.wikipedia.org/wiki/Image:Truncatedoctahedron.gifhttp://en.wikipedia.org/wiki/Rhombicuboctahedronhttp://en.wikipedia.org/wiki/Image:Rhombicuboctahedron.gifhttp://en.wikipedia.org/wiki/Truncated_cuboctahedronhttp://en.wikipedia.org/wiki/Image:Truncatedcuboctahedron.gifhttp://en.wikipedia.org/wiki/Snub_cubehttp://en.wikipedia.org/wiki/Chirality_(mathematics)http://en.wikipedia.org/wiki/Image:Snubhexahedronccw.gifhttp://en.wikipedia.org/wiki/Image:Snubhexahedroncw.gifhttp://en.wikipedia.org/wiki/Icosidodecahedronhttp://en.wikipedia.org/wiki/Image:Icosidodecahedron.gifhttp://en.wikipedia.org/wiki/Pentagon


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truncated dodecahedron(3.10.10)

(Animation)

32

20

triangles12

decagons

90

truncated icosahedronorbuckyballorfootball/soccer ball

(5.6.6 )(Animation)

3212pentagons20

hexagons

90

rhombicosidodecahedron

or smallrhombicosidodecahedron

(3.4.5.4) (Animation)

62

20

triangles

30squares

12

pentagons

120

truncatedicosidodecahedron

or greatrhombicosidodecahedron

(4.6.10)(Animation)

62

30

squares

20hexagons

12

decagons

180

snub dodecahedronor snub

icosidodecahedron

(2 chiral forms)

(3.3.3.3.5)

(Animation)

(Animation)

92

80triangles

12

pentagons

150

The cuboctahedron and icosidodecahedron are edge-uniform and are called quasi-regular.

The snub cube and snub dodecahedron are known as chiral, as they come in a left-handed

(Latin: levomorph or laevomorph) form and right-handed (Latin: dextromorph) form. When

something comes in multiple forms which are each other's three-dimensional mirror image,these forms may be called enantiomorphs. (This nomenclature is also used for the forms of

certain chemical compounds).

The duals of the Archimedean solids are called the Catalan solids. Together with the

bipyramids andtrapezohedra, these are the face-uniform solids with regular vertices.
http://en.wikipedia.org/wiki/Truncated_dodecahedronhttp://en.wikipedia.org/wiki/Image:Truncateddodecahedron.gifhttp://en.wikipedia.org/wiki/Decagonhttp://en.wikipedia.org/wiki/Truncated_icosahedronhttp://en.wikipedia.org/wiki/Fullerenehttp://en.wikipedia.org/wiki/Football_(ball)http://en.wikipedia.org/wiki/Image:Truncatedicosahedron.gifhttp://en.wikipedia.org/wiki/Rhombicosidodecahedronhttp://en.wikipedia.org/wiki/Image:Rhombicosidodecahedron.gifhttp://en.wikipedia.org/wiki/Truncated_icosidodecahedronhttp://en.wikipedia.org/wiki/Truncated_icosidodecahedronhttp://en.wikipedia.org/wiki/Image:Truncatedicosidodecahedron.gifhttp://en.wikipedia.org/wiki/Snub_dodecahedronhttp://en.wikipedia.org/wiki/Chirality_(mathematics)http://en.wikipedia.org/wiki/Image:Snubdodecahedronccw.gifhttp://en.wikipedia.org/wiki/Image:Snubdodecahedroncw.gifhttp://en.wikipedia.org/wiki/Quasiregular_polyhedronhttp://en.wikipedia.org/wiki/Mirror_imagehttp://en.wikipedia.org/wiki/Chemical_compoundhttp://en.wikipedia.org/wiki/Dual_polyhedronhttp://en.wikipedia.org/wiki/Catalan_solidhttp://en.wikipedia.org/wiki/Bipyramidhttp://en.wikipedia.org/wiki/Trapezohedronhttp://en.wikipedia.org/wiki/Trapezohedronhttp://en.wikipedia.org/wiki/Image:Snub_dodecahedron_flat.svghttp://en.wikipedia.org/wiki/Image:Snub_dodecahedron_ccw.pnghttp://en.wikipedia.org/wiki/Image:Snubdodecahedroncw.jpghttp://en.wikipedia.org/wiki/Image:Snubdodecahedronccw.jpghttp://en.wikipedia.org/wiki/Image:Truncated_icosidodecahedron_flat.pnghttp://en.wikipedia.org/wiki/Image:Great_rhombicosidodecahedron.pnghttp://en.wikipedia.org/wiki/Image:Truncatedicosidodecahedron.jpghttp://en.wikipedia.org/wiki/Image:Rhombicosidodecahedron_flat.pnghttp://en.wikipedia.org/wiki/Image:Small_rhombicosidodecahedron.pnghttp://en.wikipedia.org/wiki/Image:Rhombicosidodecahedron.jpghttp://en.wikipedia.org/wiki/Image:Truncated_icosahedron_flat.pnghttp://en.wikipedia.org/wiki/Image:Truncated_icosahedron.pnghttp://en.wikipedia.org/wiki/Image:Truncatedicosahedron.jpghttp://en.wikipedia.org/wiki/Image:Truncated_dodecahedron_flat.pnghttp://en.wikipedia.org/wiki/Image:Truncated_dodecahedron.pnghttp://en.wikipedia.org/wiki/Image:Truncateddodecahedron.jpghttp://en.wikipedia.org/wiki/Truncated_dodecahedronhttp://en.wikipedia.org/wiki/Image:Truncateddodecahedron.gifhttp://en.wikipedia.org/wiki/Decagonhttp://en.wikipedia.org/wiki/Truncated_icosahedronhttp://en.wikipedia.org/wiki/Fullerenehttp://en.wikipedia.org/wiki/Football_(ball)http://en.wikipedia.org/wiki/Image:Truncatedicosahedron.gifhttp://en.wikipedia.org/wiki/Rhombicosidodecahedronhttp://en.wikipedia.org/wiki/Image:Rhombicosidodecahedron.gifhttp://en.wikipedia.org/wiki/Truncated_icosidodecahedronhttp://en.wikipedia.org/wiki/Truncated_icosidodecahedronhttp://en.wikipedia.org/wiki/Image:Truncatedicosidodecahedron.gifhttp://en.wikipedia.org/wiki/Snub_dodecahedronhttp://en.wikipedia.org/wiki/Chirality_(mathematics)http://en.wikipedia.org/wiki/Image:Snubdodecahedronccw.gifhttp://en.wikipedia.org/wiki/Image:Snubdodecahedroncw.gifhttp://en.wikipedia.org/wiki/Quasiregular_polyhedronhttp://en.wikipedia.org/wiki/Mirror_imagehttp://en.wikipedia.org/wiki/Chemical_compoundhttp://en.wikipedia.org/wiki/Dual_polyhedronhttp://en.wikipedia.org/wiki/Catalan_solidhttp://en.wikipedia.org/wiki/Bipyramidhttp://en.wikipedia.org/wiki/Trapezohedron

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