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. It is also called MacMahon's net[1] after Percy Alexander MacMahon, who depicted it in his 1921 publication New Mathematical Pastimes.[2] John Horton Conway called it a 4-fold pentille.[3]
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. 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.
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. It has also been studied as a crystal structure and appears in the art of M. C. Escher.
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In geometry, a Cairopentagonaltiling is a tessellation of the Euclidean plane by congruent convex pentagons, formed by overlaying two tessellations of...
geometry, a pentagonaltiling is a tiling of the plane where each individual piece is in the shape of a pentagon. A regular pentagonaltiling on the Euclidean...
into heptagons. The Cairopentagonaltiling is dual to the snub square tiling. This tiling is related to the elongated triangular tiling which also has 3...
tiling (m = 1) has congruent faces, either directly or reflectively, which occur in one or more symmetry positions. An m-hedral polyhedron or tiling has...
shows the tilings with a 45 degree rotation which also look a little different. Lower symmetry forms are related to the cairopentagonaltiling with axial...
carbon allotrope that utilizes the Cairopentagonaltiling. U carbon is predicted to consist of corrugated layers tiled with six- or 12-atom rings, linked...
episode, since it clashes against our prejudices. Cairopentagonaltiling, a tiling of the plane by pentagons also called "MacMahon's net" Stein, Paul R. (1979)...
Annalen der Naturphilosophie. Percy Alexander MacMahon depicts Cairopentagonaltiling. April–August – Nicolae Paulescu publishes papers on the preparation...
this way are based on tessellations, tiling the plane with a unit cell and leaving no gaps. Because the tiling makes use of translation and rotation...
coincide with the underlying construction lines of the tiling. The visible patterns and the underlying tiling represent a bridge linking the invisible to the...
as a pentagonal pyramid and a nine diagonal column. They can't change with each other, so their topology structure is different. But the pentagonal prism...
Laves tilings are unique except for the square tiling (1 degree of freedom), barn pentagonaltiling (1 degree of freedom), and hexagonal tiling (2 degrees...
For example, the Penrose tiles define extra rules for joining edges, resulting in interesting polyforms with a kind of pentagonal symmetry. When the base...
walls covered in geometrically patterned glazed tiles. Many traces of Fatimid architecture exist in Cairo today, the most defining examples include the...
rhombitrihexagonal tiling. A square symmetry projection forms two overlapping truncated square tiling, which combine together as a chamfered square tiling. The vertex...
that the Potsdam Declaration was no more than a rehash (yakinaoshi) of the Cairo Declaration, that the government intended to ignore it (mokusatsu, "kill...
religious structure in Surakhani, a suburb of greater Baku, Azerbaijan. The pentagonal complex, which has a courtyard surrounded by cells for monks and a tetrapillar-altar...
the original on February 3, 2022. Retrieved December 10, 2023. "Our Next Cairo Bureau Chief". The New York Times Company. April 17, 2020. Archived from...
Intel's silicon chips. In March 2011, Intel bought most of the assets of Cairo-based SySDSoft. In July 2011, Intel announced that it had agreed to acquire...
winter season. EgyptAir operates a Boeing 787–9 with nonstop service to Cairo three times a week year-round. TAP Air Portugal flies five times weekly...
sculpture. Khan's amazing insight – he was name-checked by Obama in his Cairo University speech last year – changed both the economics and the morphology...
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