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  2. Cairo pentagonal tiling - Wikipedia

    en.wikipedia.org/wiki/Cairo_pentagonal_tiling

    Infinitely many different pentagons can form this pattern, belonging to two of the 15 families of convex pentagons that can tile the plane. Their tilings have varying symmetries; all are face-symmetric. One particular form of the tiling, dual to the snub square tiling, has tiles with the minimum possible perimeter among all pentagonal tilings ...

  3. Euclidean tilings by convex regular polygons - Wikipedia

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

    Convex regular polygons can also form plane tilings that are not edge-to-edge. Such tilings can be considered edge-to-edge as nonregular polygons with adjacent colinear edges. There are seven families of isogonal figures , each family having a real-valued parameter determining the overlap between sides of adjacent tiles or the ratio between the ...

  4. Regular icosahedron - Wikipedia

    en.wikipedia.org/wiki/Regular_icosahedron

    In geometry, the regular icosahedron (or simply icosahedron) is a convex polyhedron that can be constructed from pentagonal antiprism by attaching two pentagonal pyramids with regular faces to each of its pentagonal faces, or by putting points onto the cube.

  5. Entasis - Wikipedia

    en.wikipedia.org/wiki/Entasis

    In architecture, entasis is the application of a convex curve to a surface for aesthetic purposes, or increasing strength. Its best-known use is in certain orders of Classical columns that diminish in a very gentle curve, rather than in a straight line as they narrow going upward. The human eye would believe that the middle of the column was ...

  6. Convex hull - Wikipedia

    en.wikipedia.org/wiki/Convex_hull

    In geometry, the convex hull, convex envelope or convex closure [1] of a shape is the smallest convex set that contains it. The convex hull may be defined either as the intersection of all convex sets containing a given subset of a Euclidean space, or equivalently as the set of all convex combinations of points in the subset.

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