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Order-8 Triangular Tiling
In geometry, the order-8 triangular tiling is a regular tiling of the hyperbolic plane. It is represented by Schläfli symbol of ', having eight regular triangles around each vertex. Uniform colorings The half symmetry +,8,3= 4,3,3)can be shown with alternating two colors of triangles: : Symmetry From 4,4,4)symmetry, there are 15 small index subgroups (7 unique) by mirror removal and alternation operators. Mirrors can be removed if its branch orders are all even, and cuts neighboring branch orders in half. Removing two mirrors leaves a half-order gyration point where the removed mirrors met. In these images fundamental domains are alternately colored black and white, and mirrors exist on the boundaries between colors. Adding 3 bisecting mirrors across each fundamental domains creates 832 symmetry. The subgroup index-8 group, 1+,4,1+,4,1+,4)(222222) is the commutator subgroup of 4,4,4) A larger subgroup is constructed 4,4,4*) index 8, as (2*2222) with gyration points re ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Geometry
Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is called a '' geometer''. Until the 19th century, geometry was almost exclusively devoted to Euclidean geometry, which includes the notions of point, line, plane, distance, angle, surface, and curve, as fundamental concepts. During the 19th century several discoveries enlarged dramatically the scope of geometry. One of the oldest such discoveries is Carl Friedrich Gauss' ("remarkable theorem") that asserts roughly that the Gaussian curvature of a surface is independent from any specific embedding in a Euclidean space. This implies that surfaces can be studied ''intrinsically'', that is, as stand-alone spaces, and has been expanded into the theory of manifolds and Riemannian geometry. Later in the 19th century, it appeared that geom ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
444 Symmetry Xxx
Year 444 ( CDXLIV) was a leap year starting on Saturday (link will display the full calendar) of the Julian calendar. At the time, it was known as the Year of the Consulship of Theodosius and Aginatius (or, less frequently, year 1197 ''Ab urbe condita''). The denomination 444 for this year has been used since the early medieval period, when the Anno Domini calendar era became the prevalent method in Europe for naming years. Events By place Europe * Flavius Aetius, Roman general (magister militum), settles the Alans around Valence and Orléans, to contain unrest in Brittany. * Eudocia, eldest daughter of Emperor Valentinian III, is betrothed to Huneric, son of Vandal King Genseric (hostage in Italy). * Attila the Hun establishes his residence along the Tisza River (modern Hungary), and plans the coming campaign in the Balkans. * A " pestilence" that is probably cyprian plague strikes the British Isles, and makes the country vulnerable to internal revolts. * The Irish ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
