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The term "homology group" usually means a singular homology group, which is an Abelian group which partially counts the number of holes in a topological space. In particular, ...

A number of attractive 10-compounds of the regular icosahedron can be constructed. The compound illustrated above will be implemented in a future version of the Wolfram ...

A number of attractive 11-compounds of the regular icosahedron can be constructed. The compound illustrated above will be implemented in a future version of the Wolfram ...

A number of attractive 2-compounds of the regular icosahedron can be constructed. The compounds illustrated above will be implemented in a future version of the Wolfram ...

A number of attractive 5-compounds of the regular icosahedron can be constructed. The compounds illustrated above will be implemented in a future version of the Wolfram ...

A number of attractive 6-compounds of the regular icosahedron can be constructed. The compounds illustrated above will be implemented in a future version of the Wolfram ...

A framework is called "just rigid" if it is rigid, but ceases to be so when any single bar is removed. Lamb (1928, pp. 93-94) proved that a necessary (but not sufficient) ...

Let Q_i denote anything subject to weighting by a normalized linear scheme of weights that sum to unity in a set W. The Kolmogorov axioms state that 1. For every Q_i in W, ...

If a compact manifold M has nonnegative Ricci curvature tensor, then its fundamental group has at most polynomial growth. On the other hand, if M has negative curvature, then ...

Multisection of a mathematical quantity or figure is division of it into a number of (usually) equal parts. Division of a quantity into two equal parts is known as bisection, ...