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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.
In geometry, a uniform polyhedron is a polyhedron which has regular polygons as faces and is vertex-transitive (transitive on its vertices, isogonal, i.e. there is an isometry mapping any vertex onto any other). It follows that all vertices are congruent, and the polyhedron has a high degree of reflectional and rotational symmetry.
2 Two dimensional (polygons) Toggle Two dimensional (polygons) subsection. 2.1 Star polygons. 2.2 Families. 2.3 Tilings. ... Print/export Download as PDF; Printable ...
The Archimedean solids. Two of them are chiral, with both forms shown, making 15 models in all.. The Archimedean solids are a set of thirteen convex polyhedra whose faces are regular polygons, but not all alike, and whose vertices are all symmetric to each other.
Peak, an (n-3)-dimensional element 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.
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.
For example, a cube has six faces in this sense. In more modern treatments of the geometry of polyhedra and higher-dimensional polytopes, a "face" is defined in such a way that it may have any dimension. The vertices, edges, and (2-dimensional) faces of a polyhedron are all faces in this more general sense. [1]
12 3-dimensional "pure" apeirohedra based on the structure of the cubic honeycomb, {4,3,4}. [22] A π petrie dual operator replaces faces with petrie polygons; δ is a dual operator reverses vertices and faces; φ k is a kth facetting operator; η is a halving operator, and σ skewing halving operator.
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