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Parable of the Polygons is a 2014 explorable explanation created by Vi Hart and Nicky Case. The article focuses on a society of blue squares and yellow triangles which have slight personal biases against diversity, which leads to social segregation. It is based on game theorist Thomas Schelling's papers about residential segregation.
Star forms have either regular star polygon faces or vertex figures or both. This list includes these: all 75 nonprismatic uniform polyhedra; a few representatives of the infinite sets of prisms and antiprisms; one degenerate polyhedron, Skilling's figure with overlapping edges.
Here, a tiling is a covering of the plane by non-overlapping polygons or other shapes, and a tiling is aperiodic if it does not contain arbitrarily large periodic regions or patches. However, despite their lack of translational symmetry , Penrose tilings may have both reflection symmetry and fivefold rotational symmetry .
This notation represents (i) the number of vertices, (ii) the number of polygons around each vertex (arranged clockwise) and (iii) the number of sides to each of those polygons. For example: 3 6 ; 3 6 ; 3 4 .6, tells us there are 3 vertices with 2 different vertex types, so this tiling would be classed as a ‘3-uniform (2-vertex types)’ tiling.
Individual polygons are named (and sometimes classified) according to the number of sides, combining a Greek-derived numerical prefix with the suffix -gon, e.g. pentagon, dodecagon. The triangle , quadrilateral and nonagon are exceptions, although the regular forms trigon , tetragon , and enneagon are sometimes encountered as well.
Euler diagrams consist of simple closed shapes in a two-dimensional plane that each depict a set or category. How or whether these shapes overlap demonstrates the relationships between the sets. Each curve divides the plane into two regions or "zones": the interior, which symbolically represents the elements of the set, and the exterior, which ...
The regular complex polygons have been completely characterized, and can be described using a symbolic notation developed by Coxeter. A regular complex polygon with all 2-edges can be represented by a graph, while forms with k-edges can only be related by hypergraphs. A k-edge can be seen as a set of vertices, with no order implied. They may be ...
Some types of self-intersecting polygons are: the crossed quadrilateral, with four edges the antiparallelogram, a crossed quadrilateral with alternate edges of equal length the crossed rectangle, an antiparallelogram whose edges are two opposite sides and the two diagonals of a rectangle, hence having two edges parallel; Star polygons