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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.
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.
John Skilling discovered an overlooked degenerate example, by relaxing the condition that only two faces may meet at an edge. This is a degenerate uniform polyhedron rather than a uniform polyhedron, because some pairs of edges coincide. Not included are: The uniform polyhedron compounds.
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.
Compound of two great inverted snub icosidodecahedra; Compound of two great retrosnub icosidodecahedra; Compound of two great snub icosidodecahedra; Compound of two icosahedra; Compound of two inverted snub dodecadodecahedra; Compound of two small stellated dodecahedra; Compound of two snub cubes; Compound of two snub dodecadodecahedra
A surface is a two-dimensional object, such as a sphere or paraboloid. [55] In differential geometry [53] and topology, [49] surfaces are described by two-dimensional 'patches' (or neighborhoods) that are assembled by diffeomorphisms or homeomorphisms, respectively. In algebraic geometry, surfaces are described by polynomial equations. [54]
However, a mirror image could be called a different shape. For instance, a "b" and a "p" have a different shape, at least when they are constrained to move within a two-dimensional space like the page on which they are written. Even though they have the same size, there's no way to perfectly superimpose them by translating and rotating them ...
Examples include Circoporus octahedrus, Circogonia icosahedra, Lithocubus geometricus and Circorrhegma dodecahedra; the shapes of these creatures are indicated by their names. [5] The outer protein shells of many viruses form regular polyhedra. For example, HIV is enclosed in a regular icosahedron, as is the head of a typical myovirus. [6] [7]