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An object created by folding a piece of paper along certain lines to form loops. The number of states possible in an n-flexagon is a Catalan number. By manipulating the ...

A flexagon made by folding a strip into adjacent equilateral triangles. The number of states possible in a hexaflexagon is the Catalan number C_5=42.

The Maltese cross is a symbol identified with the Christian warrior whose outward points form an octagon (left figure). Another class of cross sometimes (incorrectly) known ...

A pandiagonal perfect magic cube is a perfect magic cube that remains perfect when any single orthogonal section is "restacked" cyclically so that the ordering of any set of ...

A polygon that can be dissected into n smaller copies of itself is called a rep-n-tile. The triangular polygonal spiral is also a rep-tile. The above figure shows the zeroth ...

By a suitable rearrangement of terms, a conditionally convergent series may be made to converge to any desired value, or to diverge. For example, S = 1-1/2+1/3-1/4+1/5+... ...

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 algebraic topology, a p-skeleton is a simplicial subcomplex of K that is the collection of all simplices of K of dimension at most p, denoted K^((p)). The graph obtained ...

A figure formed by taking a series of steps of length 1, 2, ..., n, with an angle theta turn after each step. The symbol for a spirolateral is ^(a_1,...,a_k)n_theta, where ...

The Szilassi polyhedron is a heptahedron that is topologically equivalent to a torus and for which every pair of faces has a polygon edge in common. The Szilassi polyhedron ...