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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.
A vertex of an angle is the endpoint where two lines or rays come together. In geometry, a vertex (pl.: vertices or vertexes) is a point where two or more curves, lines, or edges meet or intersect. As a consequence of this definition, the point where two lines meet to form an angle and the corners of polygons and polyhedra are vertices. [1] [2] [3]
The truncated cubic honeycomb has two edge types, one with four truncated cubes, and the others with one octahedron, and two truncated cubes. These can be seen as two types of edge figures. These are seen as the vertices of the vertex figure. Related to the vertex figure, an edge figure is the vertex figure of a vertex figure. [3]
Tessellations of euclidean and hyperbolic space may also be considered regular polytopes. Note that an 'n'-dimensional polytope actually tessellates a space of one dimension less. For example, the (three-dimensional) platonic solids tessellate the 'two'-dimensional 'surface' of the sphere.
Many two-dimensional geometric shapes can be defined by a set of points or vertices and lines connecting the points in a closed chain, as well as the resulting interior points. Such shapes are called polygons and include triangles , squares , and pentagons .
In geometry, a bigon, [1] digon, or a 2-gon, is a polygon with two sides and two vertices.Its construction is degenerate in a Euclidean plane because either the two sides would coincide or one or both would have to be curved; however, it can be easily visualised in elliptic space.
This maximum is attained for simple arrangements, those in which each two lines cross at a vertex that is disjoint from all the other lines. The number of vertices is smaller when some lines are parallel, or when some vertices are crossed by more than two lines. [4] An arrangement can be rotated, if necessary, to avoid axis-parallel lines.
A geodesic triangle is a region of a general two-dimensional surface enclosed by three sides that are straight relative to the surface . A curvilinear triangle is a shape with three curved sides, for instance, a circular triangle with circular-arc sides. (This article is about straight-sided triangles in Euclidean geometry, except where ...