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A torus with a hole that can eat another torus. The transformation is continuous, and so can be achieved by stretching only without tearing or making new holes in the tori.

The truncated icosahedron is the 32-faced Archimedean solid with 60 vertices corresponding to the facial arrangement 20{6}+12{5}. It is also the uniform polyhedron with ...

Let a number n be written in binary as n=(epsilon_kepsilon_(k-1)...epsilon_1epsilon_0)_2, (1) and define b_n=sum_(i=0)^(k-1)epsilon_iepsilon_(i+1) (2) as the number of digits ...

The regular heptagon is the seven-sided regular polygon illustrated above, which has Schläfli symbol {7}. According to Bankoff and Garfunkel (1973), "since the earliest days ...

An origami configuration that can be pressed to a plane figure without crumpling it or adding new creases.

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.

If one looks inside a flat origami without unfolding it, one sees a zigzagged profile, determined by an alternation of "mountain-creases" and "valley-creases." The numbers of ...

A theorem giving a criterion for an origami construction to be flat. Kawasaki's theorem states that a given crease pattern can be folded to a flat origami iff all the ...

The word net has several meanings in mathematics. It refers to a plane diagram in which the polyhedron edges of a polyhedron are shown, a point set satisfying certain ...

An unfolding is the cutting along edges and flattening out of a polyhedron to form a net. Determining how to unfold a polyhedron into a net is tricky. For example, cuts ...