How to use skeleta in a sentence? Find typical usage patterns (collocations)/phrases/context for "skeleta" and check conjugation/comparative form for "skeleta". Mastering all the usages of "skeleta" from sentence examples published by news publications.
The skeleton is now displayed at the Whitby Museum. Skeleta of Steneosaurus brevior, another crocodile, have been found at the bay. Other skeleta found at Saltwick Bay have included the ichthyosaur and the plesiosaur. In 1914, the hospital ship SS Rohilla sank near Saltwick Nab in the bay; 146 of the 229 on board, including Captain Neilson and all the nurses, as well as Titanic survivor Mary Kezia Roberts, survived.
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It follows from Euler's formula that any simplicial 2-sphere with n vertices has 3n − 6 edges and 2n − 4 faces. The case of n = 4 is realized by the tetrahedron. By repeatedly performing the barycentric subdivision, it is easy to construct a simplicial sphere for any n ≥ 4. Moreover, Ernst Steinitz gave a characterization of 1-skeleta (or edge graphs) of convex polytopes in R3 implying that any simplicial 2-sphere is a boundary of a convex polytope.
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Along with investigating the numbers of faces of polytopes, researchers have studied other combinatorial properties of them, such as descriptions of the graphs obtained from the vertices and edges of polytopes (their 1-skeleta). Balinski's theorem states that the graph obtained in this way from any d-dimensional convex polytope is d-vertex-connected.; , pp. 95–96. In the case of three-dimensional polyhedra, this property and planarity may be used to exactly characterize the graphs of polyhedra: Steinitz's theorem states that G is the skeleton of a three-dimensional polyhedron if and only if G is a 3-vertex-connected planar graph.
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Thus the n-skeleton is the largest subcomplex of dimension n or less. A CW complex is often constructed by defining its skeleta inductively by 'attaching' cells of increasing dimension. By an 'attachment' of an n-cell to a topological space X one means an adjunction space B \cup_f X where f is a continuous map from the boundary of a closed n-dimensional ball B \subset R^n to X. To construct a CW complex, begin with a 0-dimensional CW complex, that is, a discrete space X_0. Attach 1-cells to X_0 to obtain a 1-dimensional CW complex X_1.
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Attach 2-cells to X_1 to obtain a 2-dimensional CW complex X_2. Continuing in this way, we obtain a nested sequence of CW complexes X_0 \subset X_1 \subset \cdots X_n \subset \cdots of increasing dimension such that if i\leq j then X_i is the i-skeleton of X_j . Up to isomorphism every n-dimensional CW complex can be obtained from its (n − 1)-skeleton via attaching n-cells, and thus every finite-dimensional CW complex can be built up by the process above. This is true even for infinite-dimensional complexes, with the understanding that the result of the infinite process is the direct limit of the skeleta: a set is closed in X if and only if it meets each skeleton in a closed set.
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