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For a smooth triangulation of a closed smooth manifold, the minimal number of edges in a homotopically non-trivial loop contained in the 1-skeleton gives an integer called the combinatorial systole. The number of top-dimensional simplices in the triangulation gives another integer called the combinatorial volume.

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A 3-manifold is said to be small if it is closed, irreducible and does not contain any incompressible surfaces. Orbifold Theorem. Let M be a small 3-manifold. Let φ be a non-trivial periodic orientation-preserving diffeomorphism of M. Then M admits a φ-invariant hyperbolic or Seifert fibered structure.

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Nov 05, 2005 · undirected edge labeled s α connecting vertices γ 1 and γ 2 if and only if γ 2 = γ 1s α in Γ v.Inparticular,C v has s 2 labeled edges corresponding to the reﬂection in F 2. Removing these s 2-edges decomposes C v into components, each of which is a copy of the Cayley graph C e for Γ e, with respect to the generating reﬂections. Take ...

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The manual shows that it is not necessary to remove the TB for cleaning, but you can do a much more thorough job if it is not on the car. If you decide to remove the TB, you must disconnect as many as 7 hoses, including the two water supply lines, the throttle cable, and two electrical connections. There is a disassembly list in the manual.

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Mi Mix 2 (And related TWRPs) to the Official Support; Added function to root the device if the TWRP is already flashed; Removed from Official support: LG G6 and all Huawei devices (The support for these devices will remain in older versions); General BugFixes and Improvements.

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Two-manifold topology polygons have a configuration such that the polygon mesh can be split along its various edges and subsequently unfolded so that the mesh lays flat without overlapping pieces. Non-manifold topology polygons have a configuration that cannot be unfolded into a continuous flat piece. Some tools and actions in Maya cannot work ...

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Select Open Edges: Displays Open edges. Select Non-manifold Edges: Displays Non-Manifold edges. Select Collapsed Facets: Displays Collapsed Facets. Select Duplicate Facets: Displays Duplicate Facets and asks if you want to remove them. On clicking "Yes", duplicate facets are removed.