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Any lemma on commutative diagrams. It can give relations between maps (as in the five lemma) or tell how to construct new diagrams from old ones (as in the snake lemma).

A heptahedron is a polyhedron with seven faces. Because there are 34 heptahedral graphs, there are 34 topologically distinct convex heptahedra. There are three semiregular ...

An identity is a mathematical relationship equating one quantity to another (which may initially appear to be different).

A perfect ruler also called a complete ruler, is type of ruler considered by Guy (1994) which has k distinct marks spaced such that the distances between marks can be used to ...

Sprague (1963) considered the problem of "rolling" five cubes, each which an upright letter "A" on its top, on a chessboard. Here "rolling" means the cubes are moved from ...

In celestial mechanics, the fixed path a planet traces as it moves around the sun is called an orbit. When a group G acts on a set X (this process is called a group action), ...

Transitivity is a result of the symmetry in the group. A group G is called transitive if its group action (understood to be a subgroup of a permutation group on a set Omega) ...

Geometry

One would think that by analogy with the matching-generating polynomial, independence polynomial, etc., a cycle polynomial whose coefficients are the numbers of cycles of ...

The tesseract is the hypercube in R^4, also called the 8-cell or octachoron. It has the Schläfli symbol {4,3,3}, and vertices (+/-1,+/-1,+/-1,+/-1). The figure above shows a ...