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I42 Symmetry
In geometry, the truncated tetraapeirogonal tiling is a semiregular tiling of the hyperbolic plane. There are one square, one octagon, and one apeirogon on each vertex. It has Schläfli symbol of tr. Related polyhedra and tilings Symmetry The dual of this tiling represents the fundamental domains of ��,4 (*∞42) symmetry. There are 15 small index subgroups constructed from ��,4by mirror removal and alternation. 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. The subgroup index-8 group, +,∞,1+,4,1+(∞2∞2) is the commutator subgroup of ��,4 A larger subgroup is constructed as ��,4* index 8, as ��,4+ (4*∞) with gyration points removed, becomes (*∞∞∞∞) or (*∞4), and another ��*,4 inde ... [...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] |
I44 Symmetry
In geometry, the truncated infinite-order square tiling is a uniform tiling of the hyperbolic plane. It has Schläfli symbol of t. Uniform color In (*∞44) symmetry this tiling has 3 colors. Bisecting the isosceles triangle domains can double the symmetry to *∞42 symmetry. : Symmetry The dual of the tiling represents the fundamental domains of (*∞44) orbifold symmetry. From ∞,4,4)(*∞44) symmetry, there are 15 small index subgroup (11 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. The symmetry can be doubled to *∞42 by adding a bisecting mirror across the fundamental domains. The subgroup index-8 group, 1+,∞,1+,4,1+,4)(∞22∞22) is the com ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
I42 Symmetry Abc
I4, i4, I 4 or I-4 may refer to: Arts, entertainment, and media * '' I-4: Loafing and Camouflage'', a Greek film Military * 1st Life Grenadier Regiment (Sweden) (1816–1927), a Swedish infantry regiment * , a World War II Type J1 submarine of the Imperial Japanese Navy * Life Grenadier Regiment (Sweden) (1928–1997), a Swedish infantry regiment * Tupolev I-4, a 1927 Soviet aircraft Science and technology * I-4 satellite * i4, an integer in XML-RPC Transportation * I4 engine, a piston engine * Interstate 4, an interstate highway in Florida * BMW i4 The BMW i4 (model code G26) is a battery electric compact executive car produced by BMW since 2021. It adopts a five-door liftback body style and is marketed as a four-door coupé. The initial concept version, named BMW i Vision Dynamics, debu ..., a German mid-size electric sedan * Interstate Airlines, by IATA airline designator * LB&SCR I4 class, a British locomotive See also * iPhone 4, a smartphone {{Lett ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
