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Special cases are right triangles (p q 2). Uniform solutions are constructed by a single generator point with 7 positions within the fundamental triangle, the 3 corners, along the 3 edges, and the triangle interior. All vertices exist at the generator, or a reflected copy of it. Edges exist between a generator point and its image across a mirror.
Menger sphere, rendered in SunFlow; Post-It Menger Sponge – a level-3 Menger sponge being built from Post-its; The Mystery of the Menger Sponge. Sliced diagonally to reveal stars; OEIS sequence A212596 (Number of cards required to build a Menger sponge of level n in origami) Woolly Thoughts Level 2 Menger Sponge by two "Mathekniticians"
The Hopf fibration is a nontrivial mapping of the 3-sphere to the 2-sphere, and generates the third homotopy group of the 2-sphere. This picture mimics part of the Hopf fibration, an interesting mapping from the three-dimensional sphere to the two-dimensional sphere. This mapping is the generator of the third homotopy group of the 2-sphere.
A skybox is a method of creating backgrounds to make a video game level appear larger than it really is. [1] When a skybox is used, the level is enclosed in a cuboid.The sky, distant mountains, distant buildings, and other unreachable objects are projected onto the cube's faces (using a technique called cube mapping), thus creating the illusion of distant three-dimensional surroundings.
Let be a metric space with distance function .Let be a set of indices and let () be a tuple (indexed collection) of nonempty subsets (the sites) in the space .The Voronoi cell, or Voronoi region, , associated with the site is the set of all points in whose distance to is not greater than their distance to the other sites , where is any index different from .
The quotient map from the sphere onto the real projective plane is in fact a two sheeted (i.e. two-to-one) covering map. It follows that the fundamental group of the real projective plane is the cyclic group of order 2; i.e., integers modulo 2. One can take the loop AB from the figure above to be the generator.
David A. Plotz [2] (born January 31, 1970) [3] is an American journalist and former CEO of Atlas Obscura, an online magazine devoted to discovery and exploration. [4] A writer with Slate since its inception in 1996, Plotz was the online magazine's editor from June 2008 until July 2014, [ 5 ] succeeding Jacob Weisberg . [ 6 ]
A generator for the fundamental group is the closed curve obtained by projecting any curve connecting antipodal points in down to . The projective n {\displaystyle n} -space is compact, connected, and has a fundamental group isomorphic to the cyclic group of order 2: its universal covering space is given by the antipody ...
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