Example: the Cube is a Platonic Solid. each face is the same-sized square. 3 squares meet at each cornerThere are only five platonic solids.
The Platonic SolidsFor each solid we have two printable nets (with and without tabs). You can make with them!Print them on a piece of card, cut them out, tape the edges, and you will have your own platonic solids.Tetrahedron. 3 triangles meet at each vertex.
4 Faces. 4 Vertices. 6 Edges.Cube. 3 squares meet at each vertex. 6 Faces. 8 Vertices.
12 Edges.Octahedron. 4 triangles meet at each vertex. 8 Faces. 6 Vertices. 12 Edges.Dodecahedron.
3 pentagons meet at each vertex. 12 Faces.
The dual of a cube is an octahedron. Vertices of one correspond to faces of the other, and edges correspond to each other. In geometry, any polyhedron is associated with a second dual figure. More generally, an octahedron can be any polyhedron with eight faces. The regular octahedron has 6 vertices and 12 edges, the minimum for an octahedron; irregular octahedra may have as many as 12 vertices and 18 edges.
20 Vertices. 30 Edges.Icosahedron. 5 triangles meet at each vertex. 20 Faces.
12 Vertices. 30 Edges.
.SphericalEuclid.Compact hyper.Paraco.Noncompact hyperbolic3 12i3 9i3 6i3 3iTetratetrahedronThe regular octahedron can also be considered a tetrahedron – and can be called a tetratetrahedron. This can be shown by a 2-color face model. With this coloring, the octahedron has.Compare this truncation sequence between a tetrahedron and its dual::, (.332)3,3 +, (332)Duals to uniform polyhedraThe above shapes may also be realized as slices orthogonal to the long diagonal of a. If this diagonal is oriented vertically with a height of 1, then the first five slices above occur at heights r, 3 / 8, 1 / 2, 5 / 8, and s, where r is any number in the range 0.
Finbow, Arthur S.; Hartnell, Bert L.; Nowakowski, Richard J.; (2010). 'On well-covered triangulations. Discrete Applied Mathematics.
158 (8): 894–912.: doi: 10.1016/j.dam.2009.08.002. Archived from on 17 November 2014. Retrieved 14 August 2016. CS1 maint: archived copy as title. Klein, Douglas J. Croatica Chemica Acta. 75 (2): 633–649.
Retrieved 30 September 2006., Third edition, (1973), Dover edition, (Chapter V: The Kaleidoscope, Section: 5.7 Wythoff's construction).External links. 19 (11th ed.). 1911.
Klitzing, Richard. The Encyclopedia of Polyhedra. Try: dP4.
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