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In geometry, the Cairo pentagonal tiling is a dual semiregular tiling of the Euclidean plane. It is given its name because several streets in Cairo are paved in this design.〔.〕〔.〕 It is one of 15 known isohedral pentagon tilings. It is also called MacMahon's net〔.〕 after Percy Alexander MacMahon and his 1921 publication ''New Mathematical Pastimes''.〔. PDF () p.101〕 Conway calls it a 4-fold pentille.〔John H. Conway, Heidi Burgiel, Chaim Goodman-Strass, ''The Symmetries of Things'' 2008, ISBN 978-1-56881-220-5 () (Chapter 21, Naming Archimedean and Catalan polyhedra and tilings, p288 table)〕 As a 2-dimensional crystal net, it shares a special feature with the honeycomb net. Both nets are examples of standard realization, the notion introduced by M. Kotani and T. Sunada for general crystal nets.〔T. Sunada, ''Topological Crystallography ---With a View Towards Discrete Geometric Analysis---'', Surveys and Tutorials in the Applied Mathematical Sciences, Vol. 6, Springer〕 == Geometry== These are not regular pentagons: their sides are not equal (they have four long ones and one short one in the ratio 1:sqrt(3)-1〔http://catnaps.org/islamic/geometry2.html〕), and their angles in sequence are 120°, 120°, 90°, 120°, 90°. It is represented by with face configuration V3.3.4.3.4. It is similar to the prismatic pentagonal tiling with face configuration V3.3.3.4.4, which has its right angles adjacent to each other. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Cairo pentagonal tiling」の詳細全文を読む スポンサード リンク
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