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Similarly, a k-isohedral tiling has k separate symmetry orbits (it may contain m different face shapes, for m = k, or only for some m < k). [ 6 ] ("1-isohedral" is the same as "isohedral".) A monohedral polyhedron or monohedral tiling ( m = 1) has congruent faces, either directly or reflectively, which occur in one or more symmetry positions.
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The problem of anisohedral tiling has been generalised by saying that the isohedral number of a tile is the lowest number orbits (equivalence classes) of tiles in any tiling of that tile under the action of the symmetry group of that tiling, and that a tile with isohedral number k is k-anisohedral.
An example is the sphinx tiling, a periodic tiling formed by a pentagonal rep-tile. [20] The sphinx may also tile the plane periodically, by fitting two sphinx tiles together to form a parallelogram and then tiling the plane by translation of this parallelogram, [ 20 ] a pattern that can be extended to any non-convex pentagon that has two ...
The snub square tiling is an Archimedean tiling, and as the dual to an Archimedean tiling this form of the Cairo pentagonal tiling is a Catalan tiling or Laves tiling. [14] It is one of two monohedral pentagonal tilings that, when the tiles have unit area, minimizes the perimeter of the tiles.
The tile used in this tiling is a type 1 tile - it has two parallel sides. In order for it to be able to create this particular tiling, this tile is more restricted than the normal type 1 tile, in that on top of the two parallel sides (i.e. C+D=180), it also has one angle equal to 90 and another equation on the angles (2B+C=360).
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7601 E Frontage Road, Overland Park, KS · Directions · (913) 218-2276
quizntales.com has been visited by 1M+ users in the past month