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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. 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 ...

5. 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.

6. Talk:Pentagonal tiling - Wikipedia

   en.wikipedia.org/wiki/Talk:Pentagonal_tiling

   All isohedral (=tile-transitive) tilings use tile types 1-5, usually with additional conditions necessary for the tiling. The statement that B. Grünbaum and G. C. Shephard 'have shown that there are exactly twenty-four distinct "types" of tile-transitive tilings by pentagons according to their classification scheme' is on page 33 of D ...

7. Aperiodic set of prototiles - Wikipedia

   en.wikipedia.org/wiki/Aperiodic_set_of_prototiles

   The best-known examples of an aperiodic set of tiles are the various Penrose tiles. [4] [5] The known aperiodic sets of prototiles are seen on the list of aperiodic sets of tiles. The underlying undecidability of the domino problem implies that there exists no systematic procedure for deciding whether a given set of tiles can tile the plane.