Archimedean solid

In geometry, an Archimedean solid is a convex shape which is composed of polygons. It is a polyhedron, with the following properties:
 Each face is made of a regular polygon
 All the corners of the shape look the same
 The shape is neither a platonic solid, nor a prism, nor an antiprism.
Depending on the way there are counted, there are thirteen or fifteen such shapes.  Of two of these shapes, there are two versions, which cannot be made congruent using rotation. The Archimedean solids are named after the Ancient Greek mathematician Archimedes, who probably discovered them in the 3rd century BC. The writings of Archimedes have been lost, but  Pappus of Alexandria summarized them in the 4th century.Grünbaum, Branko 2009. An enduring error. Elemente der Mathematik 64 (3): 89–101. Reprinted in Pitici, Mircea, ed. 2011. The best writing on mathematics, 2010. Princeton University Press, pp. 18–31. During the Renaissance, artists and mathematicians valued pure forms and rediscovered all of these forms.  Johannes Kepler probably completed this search around 1620.Field J. 1997. Rediscovering the Archimedean Polyhedra: Piero della Francesca, Luca Pacioli, Leonardo da Vinci, Albrecht Dürer, Daniele Barbaro, and Johannes Kepler. Archive for History of Exact Sciences. 50, 227.

Constructing an Archimedean solid takes at least two different polygons.

 Properties 
 Archimedean solids are made of regular polygons, therefore all edges have the same length.
 All Archimedean solids can be produced from Platonic solids, by "cutting the edges" of the platonic solid.
 The type of polygons meting at a corner ("vertex") characterizes both the archimedean and platonic solid

 Relationship with Platonic solids 

Platonic solids can be turned into Archimedean solids by following a series of rules for their construction.

 Listing of Archimedean solids 
The following is a listing of all Archimedean solids
ImageNameFacesTypeEdgesVertices60px|8Truncated tetrahedron84 triangles
4 hexagons181260px|14Cuboctahedron148 triangles
6 squares241260px|14Truncated cube148 triangles
6 octagons362460px|14Truncated octahedron146 squares
8 hexagons362460px|26Rhombicuboctahedron268 triangles
18 squares482460px|26Truncated cuboctahedron2612 squares
8 hexagons

6 octagons724860px|3860px|38Snub cube (2 mirrored versions)3832 triangles
6 squares602460px|32Icosidodecahedron3220 triangles
12 pentagons603060px|32Truncated dodecahedron3220 triangles
12 decagons906060px|32Truncated icosahedron3212 pentagons
20 hexagons906060px|62Rhombicosidodecahedron6220 triangles30 squares12 pentagons1206060px|62Truncated icosidodecahedron6230 squares
20 hexagons

12 decagons18012060px|9260px|92Snub dodecahedron (2 mirrored versions)9280 triangles
12 pentagons15060

 References 


Category:Archimedes