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  2. Isohedral figure - Wikipedia

    en.wikipedia.org/wiki/Isohedral_figure

    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.

  3. List of isotoxal polyhedra and tilings - Wikipedia

    en.wikipedia.org/wiki/List_of_isotoxal_polyhedra...

    In geometry, isotoxal polyhedra and tilings are defined by the property that they have symmetries taking any edge to any other edge. [1] Polyhedra with this property can also be called "edge-transitive", but they should be distinguished from edge-transitive graphs, where the symmetries are combinatorial rather than geometric.

  4. Lists of uniform tilings on the sphere, plane, and hyperbolic ...

    en.wikipedia.org/wiki/Lists_of_uniform_tilings...

    A few of the infinitely many such patterns in the hyperbolic plane are also listed. (Increasing any of the numbers defining a hyperbolic or Euclidean tiling makes another hyperbolic tiling.) Point groups: (p 2 2) dihedral symmetry, =,, … (order ) (3 3 2) tetrahedral symmetry (order 24)

  5. Tilings and patterns - Wikipedia

    en.wikipedia.org/wiki/Tilings_and_patterns

    The last five chapters survey a variety of advanced topics in tiling theory: colored patterns and tilings, polygonal tilings, aperiodic tilings, Wang tiles, and tilings with unusual kinds of tiles. Each chapter open with an introduction to the topic, this is followed by the detailed material of the chapter, much previously unpublished, which is ...

  6. Category:Isohedral tilings - Wikipedia

    en.wikipedia.org/wiki/Category:Isohedral_tilings

    Pages in category "Isohedral tilings" The following 76 pages are in this category, out of 76 total. ... Octagonal tiling; Order-1 digonal tiling; Order-2 apeirogonal ...

  7. Tessellation - Wikipedia

    en.wikipedia.org/wiki/Tessellation

    A normal tiling is a tessellation for which every tile is topologically equivalent to a disk, the intersection of any two tiles is a connected set or the empty set, and all tiles are uniformly bounded. This means that a single circumscribing radius and a single inscribing radius can be used for all the tiles in the whole tiling; the condition ...

  8. Pentagonal tiling - Wikipedia

    en.wikipedia.org/wiki/Pentagonal_tiling

    There are also 2-isohedral tilings by special cases of type 1, type 2, and type 4 tiles, and 3-isohedral tilings, all edge-to-edge, by special cases of type 1 tiles. There is no upper bound on k for k-isohedral tilings by certain tiles that are both type 1 and type 2, and hence neither on the number of tiles in a primitive unit.

  9. List of k-uniform tilings - Wikipedia

    en.wikipedia.org/wiki/List_of_k-uniform_tilings

    Such periodic tilings of convex polygons may be classified by the number of orbits of vertices, edges and tiles. If there are k orbits of vertices, a tiling is known as k-uniform or k-isogonal; if there are t orbits of tiles, as t-isohedral; if there are e orbits of edges, as e-isotoxal.