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For example, in a polyhedron (3-dimensional polytope), a face is a facet, an edge is a ridge, and a vertex is a peak. Vertex figure: not itself an element of a polytope, but a diagram showing how the elements meet.
Lists of shapes cover different types of geometric shape and related topics. They include mathematics topics and other lists of shapes, such as shapes used by drawing or teaching tools. They include mathematics topics and other lists of shapes, such as shapes used by drawing or teaching tools.
The basic quantities describing a sphere (meaning a 2-sphere, a 2-dimensional surface inside 3-dimensional space) will be denoted by the following variables r {\displaystyle r} is the radius, C = 2 π r {\displaystyle C=2\pi r} is the circumference (the length of any one of its great circles ),
This is a list of two-dimensional geometric shapes in Euclidean and other geometries. For mathematical objects in more dimensions, see list of mathematical shapes. For a broader scope, see list of shapes.
In geometry, many uniform tilings on sphere, euclidean plane, and hyperbolic plane can be made by Wythoff construction within a fundamental triangle, (p q r), defined by internal angles as π/p, π/q, and π/r. Special cases are right triangles (p q 2).
In general, for any natural number n, there are regular n-pointed stars with Schläfli symbols {n/m} for all m such that m < n/2 (strictly speaking {n/m} = {n/(n − m)}) and m and n are coprime (as such, all stellations of a polygon with a prime number of sides will be regular stars).
For example, the unit sphere is an algebraic surface, as it may be defined by the implicit equation x 2 + y 2 + z 2 − 1 = 0. {\displaystyle x^{2}+y^{2}+z^{2}-1=0.} A surface may also be defined as the image , in some space of dimension at least 3, of a continuous function of two variables (some further conditions are required to ensure that ...
This sphere was a fused quartz gyroscope for the Gravity Probe B experiment, and differs in shape from a perfect sphere by no more than 40 atoms (less than 10 nm) of thickness. It was announced on 1 July 2008 that Australian scientists had created even more nearly perfect spheres, accurate to 0.3 nm, as part of an international hunt to find a ...