![]() These pentagons and their tiling are often listed as "type 4" in the listing of types of pentagon that can tile. The result is an isohedral tiling, meaning that any pentagon in the tiling can be transformed into any other pentagon by a symmetry of the tiling. At the pentagon sides that are not adjacent to one of these two right angles, two tiles meet, rotated by a 180° angle with respect to each other. Any pentagon meeting these requirements tiles the plane by copies that, at the chosen right angled corners, are rotated by a right angle with respect to each other. One of these two families consists of pentagons that have two non-adjacent right angles, with a pair of sides of equal length meeting at each of these right angles. The pentagons that form these tilings can be grouped into two different infinite families, drawn from the 15 families of convex pentagons that can tile the plane, and the five families of pentagon found by Karl Reinhardt in 1918 that can tile the plane isohedrally (all tiles symmetric to each other). Infinitely many different pentagons can form Cairo tilings, all with the same pattern of adjacencies between tiles and with the same decomposition into hexagons, but with varying edge lengths, angles, and symmetries. Each hexagon of one tiling surrounds two vertices of the other tiling, and is divided by the hexagons of the other tiling into four of the pentagons in the Cairo tiling. The union of all edges of a Cairo tiling is the same as the union of two tilings of the plane by hexagons. It has also been studied as a crystal structure and appears in the art of M. In architecture, beyond Cairo, the Cairo tiling has been used in Mughal architecture in 18th-century India, in the early 20th-century Laeiszhalle in Germany, and in many modern buildings and installations. Another, overlaying two flattened tilings by regular hexagons, is the form used in Cairo and has the property that every edge is collinear with infinitely many other edges. One particular form of the tiling, dual to the snub square tiling, has tiles with the minimum possible perimeter among all pentagonal tilings. Their tilings have varying symmetries all are face-symmetric. Infinitely many different pentagons can form this pattern, belonging to two of the 15 families of convex pentagons that can tile the plane. John Horton Conway called it a 4-fold pentille. It is also called MacMahon's net after Percy Alexander MacMahon, who depicted it in his 1921 publication New Mathematical Pastimes. For more information, see our Application and Use Guidelines.In geometry, a Cairo pentagonal tiling is a tessellation of the Euclidean plane by congruent convex pentagons, formed by overlaying two tessellations of the plane by hexagons and named for its use as a paving design in Cairo. This tile is rated for the following applications. We show a single tile for the sample image. The rug layout reveals a grouping of 16 tiles. Mission colors used in this pattern: White (S100), Sage (S114), Jaune Clair (S907)Ī group of four (4) tiles are shown in the product photo. Cement tiles are handmade and expect to see variation in color, shade, and size. For a coordinated look, use plain tiles with colors from this pattern found in the Mission Solid Color cement tiles. Allow about 3 weeks for custom strike-off samples. Mission cement tiles patterns can be customized using any of the 60 colors in the Mission Palette. A 20% surcharge added to orders less than 100 sq ft.Minimum order: 100 sq ft (19 boxes or 228 tiles). ![]() ![]() Coverage: 2.3 tiles per sq ft / 5.2 sq ft per box (12 pcs per box).Seal with a penetrating sealer after installation.Tile is shipped pre-sealed so a grout release is not required.Inspired by Morrocan Latti, this lattice border pattern in a summer palette of sage green with accents of light yellow makes a great garden accent wall or patio floor. ![]()
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