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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.
Simple tiles are generated by Möbius triangles with whole numbers p,q,r, while Schwarz triangles allow rational numbers p,q,r and allow star polygon faces, and have overlapping elements. 7 generator points
Such tilings can be considered edge-to-edge as nonregular polygons with adjacent colinear edges. There are seven families of isogonal figures, each family having a real-valued parameter determining the overlap between sides of adjacent tiles or the ratio between the edge lengths of different tiles. Two of the families are generated from shifted ...
Any one of these three shapes can be duplicated infinitely to fill a plane with no gaps. [6] Many other types of tessellation are possible under different constraints. For example, there are eight types of semi-regular tessellation, made with more than one kind of regular polygon but still having the same arrangement of polygons at every corner ...
Seeing a regular star polygon as a nonconvex isotoxal simple polygon with twice as many (shorter) sides but alternating the same outer and "inner" internal angles allows regular star polygons to be used in a tiling, and seeing isotoxal simple polygons as "regular" allows regular star polygons to (but not all of them can) be used in a "uniform ...
A Penrose tiling with rhombi exhibiting fivefold symmetry. A Penrose tiling is an example of an aperiodic tiling.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.
In hyperbolic geometry, a uniform hyperbolic tiling (or regular, quasiregular or semiregular hyperbolic tiling) is an edge-to-edge filling of the hyperbolic plane 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).
Clipping is defined as the interaction of subject and clip polygons. While clipping usually involves finding the intersections (regions of overlap) of subject and clip polygons, clipping algorithms can also be applied with other boolean clipping operations: difference, where the clipping polygons remove overlapping regions from the subject; union, where clipping returns the regions covered by ...