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Tessellation in two dimensions, also called planar tiling, is a topic in geometry that studies how shapes, known as tiles, can be arranged to fill a plane without any gaps, according to a given set of rules. These rules can be varied.
Flood fill, also called seed fill, is a flooding algorithm that determines and alters the area connected to a given node in a multi-dimensional array with some matching attribute. It is used in the "bucket" fill tool of paint programs to fill connected, similarly colored areas with a different color, and in games such as Go and Minesweeper for ...
The cube is the only Platonic solid that can fill space, although a tiling that combines tetrahedra and octahedra (the tetrahedral-octahedral honeycomb) is possible. Although the regular tetrahedron cannot fill space, other tetrahedra can, including the Goursat tetrahedra derived from the cube, and the Hill tetrahedra.
(Alternatively, we could use the theorem that every compact metric space is a continuous image of the Cantor set to get the function .) Finally, one can extend f {\displaystyle f} to a continuous function F {\displaystyle F} whose domain is the entire unit interval [ 0 , 1 ] {\displaystyle [0,\,1]} .
It is possible to fill the plane with polygons which do not meet at their corners, for example using rectangles, as in a brick wall pattern: this is not a proper tiling because corners lie part way along the edge of a neighbouring polygon. Similarly, in a proper honeycomb, there must be no edges or vertices lying part way along the face of a ...
Animation of the missing square puzzle, showing the two arrangements of the pieces and the "missing" square Both "total triangles" are in a perfect 13×5 grid; and both the "component triangles", the blue in a 5×2 grid and the red in an 8×3 grid.
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mapframe-shape-fill-opacity – Opacity level of shape fill, a number between 0 and 1. Default: 0.5; mapframe-stroke-color or mapframe-stroke-colour – Color of line features, and outlines of shape features. Default: #ff0000; mapframe-stroke-width – Width of line features, and outlines of shape features; default is "5". Default: 5