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The non-orientable genus, demigenus, or Euler genus of a connected, non-orientable closed surface is a positive integer representing the number of cross-caps attached to a sphere. Alternatively, it can be defined for a closed surface in terms of the Euler characteristic χ, via the relationship χ = 2 − k , where k is the non-orientable genus.
A polyhedral torus can be constructed to approximate a torus surface, from a net of quadrilateral faces, like this 6x4 example. In geometry, a toroidal polyhedron is a polyhedron which is also a toroid (a g-holed torus), having a topological genus (g) of 1 or greater. Notable examples include the Császár and Szilassi polyhedra.
A g-holed toroid can be seen as approximating the surface of a torus having a topological genus, g, of 1 or greater. The Euler characteristic χ of a g holed toroid is 2(1-g). [2] The torus is an example of a toroid, which is the surface of a doughnut. Doughnuts are an example of a solid torus created by rotating a disk, and are not toroids.
As examples, a genus zero surface (without boundary) is the two-sphere while a genus one surface (without boundary) is the ordinary torus. The surfaces of higher genus are sometimes called n-holed tori (or, rarely, n-fold tori). The terms double torus and triple torus are also occasionally used.
Trump last week demanded that BRICS member countries commit to not creating a new currency or supporting another currency that would replace the U.S. dollar, saying they would otherwise face 100% ...
Jay-Z, the star rapper and entrepreneur whose real name is Shawn Carter, was accused in a lawsuit Sunday of raping a 13-year-old girl in 2000 allegedly along with Sean “Diddy” Combs.
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