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A polygon is a 2-dimensional example of the more general polytope in any number of dimensions. A circle is a simple shape of two-dimensional geometry that is the set of all points in a plane that are at a given distance from a given point, the center .The distance between any of the points and the center is called the radius .
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 ...
The elements of a polytope can be considered according to either their own dimensionality or how many dimensions "down" they are from the body. Vertex, a 0-dimensional element; Edge, a 1-dimensional element; Face, a 2-dimensional element; Cell, a 3-dimensional element; Hypercell or Teron, a 4-dimensional element; Facet, an (n-1)-dimensional element
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 ),
A two-dimensional space is a mathematical space with two dimensions, meaning points have two degrees of freedom: their locations can be locally described with two coordinates or they can move in two independent directions. Common two-dimensional spaces are often called planes, or, more generally, surfaces. These include analogs to physical ...
The square is in two families of polytopes in two dimensions: hypercube and the cross-polytope. The Schläfli symbol for the square is {4}. The square is a highly symmetric object. There are four lines of reflectional symmetry and it has rotational symmetry of order 4 (through 90°, 180° and 270°). Its symmetry group is the dihedral group D 4.
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