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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...

    Regular polyhedra are isohedral (face-transitive), isogonal (vertex-transitive), and isotoxal (edge-transitive). Quasiregular polyhedra are isogonal and isotoxal, but not isohedral; their duals are isohedral and isotoxal, but not isogonal. The dual of an isotoxal polyhedron is also an isotoxal polyhedron. (See the Dual polyhedron article.)

  4. Tilings and patterns - Wikipedia

    en.wikipedia.org/wiki/Tilings_and_patterns

    §6.2 Isohedral tiling, §6.3 isogonal tiling, §6.4 isotoxal tiling, list of isotoxal tilings, §6.5 striped pattern, §6.6 Evgraf Fedorov, Alexei Vasilievich Shubnikov, planigon, Boris Delone: 7: Classification with respect to symmetries §7.1 Conjugate element, §7.7 arrangement of lines, §7.8 Circle packing: 8: Colored patterns and tilings

  5. 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 ...

  6. Pentagonal tiling - Wikipedia

    en.wikipedia.org/wiki/Pentagonal_tiling

    An example is the sphinx tiling, an aperiodic 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 ...

  7. Isogonal figure - Wikipedia

    en.wikipedia.org/wiki/Isogonal_figure

    In geometry, a polytope (e.g. a polygon or polyhedron) or a tiling is isogonal or vertex-transitive if all its vertices are equivalent under the symmetries of the figure. This implies that each vertex is surrounded by the same kinds of face in the same or reverse order, and with the same angles between corresponding faces.

  8. Cairo pentagonal tiling - Wikipedia

    en.wikipedia.org/wiki/Cairo_pentagonal_tiling

    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.

  9. Euclidean tilings by convex regular polygons - Wikipedia

    en.wikipedia.org/wiki/Euclidean_tilings_by...

    Following Grünbaum and Shephard (section 1.3), a tiling is said to be regular if the symmetry group of the tiling acts transitively on the flags of the tiling, where a flag is a triple consisting of a mutually incident vertex, edge and tile of the tiling. This means that, for every pair of flags, there is a symmetry operation mapping the first ...