Search results
Results from the WOW.Com Content Network
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
Vector overlay is an operation (or class of operations) in a geographic information system (GIS) for integrating two or more vector spatial data sets. Terms such as polygon overlay, map overlay, and topological overlay are often used synonymously, although they are not identical in the range of operations they include.
There are 17 combinations of regular convex polygons that form 21 types of plane-vertex tilings. [6] [7] Polygons in these meet at a point with no gap or overlap. Listing by their vertex figures, one has 6 polygons, three have 5 polygons, seven have 4 polygons, and ten have 3 polygons. [8]
The vertex figures for the six tilings with convex regular polygon and apeirogon faces. (The Wythoff symbol is given in red.) Vertex figures for 21 uniform tilings. There are several ways the list of uniform tilings can be expanded: Vertex figures can have retrograde faces and turn around the vertex more than once. Star polygon tiles can be ...
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 ...
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 .
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.