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An attractive tiling of the square composed of two types of triangular tiles. It consists of 16 equilateral triangles and 32 15 degrees-15 degrees-150 degrees isosceles ...

A Greek cross, also called a square cross, is a cross in the shape of a plus sign. It is a non-regular dodecagon. A square cross appears on the flag of Switzerland, and also ...

Fuglede (1974) conjectured that a domain Omega admits an operator spectrum iff it is possible to tile R^d by a family of translates of Omega. Fuglede proved the conjecture in ...

Two rectangles, neither of which will fit inside the other, are said to be incomparable. This is equivalent to one rectangle being both longer and narrower. At least seven ...

A space-filling polyhedron is a polyhedron which can be used to generate a tessellation of space. Although even Aristotle himself proclaimed in his work On the Heavens that ...

A tiling of regular polygons (in two dimensions), polyhedra (three dimensions), or polytopes (n dimensions) is called a tessellation. Tessellations can be specified using a ...

If a discrete group of displacements in the plane has more than one center of rotation, then the only rotations that can occur are by 2, 3, 4, and 6. This can be shown as ...

The Gosper island (Mandelbrot 1977), also known as a flowsnake (Gardner 1989, p. 41), is a fractal that is a modification of the Koch snowflake. The term "Gosper island" was ...

Every Möbius strip dissection of unequal squares can be glued along its edge to produce a dissection of the Klein bottle. There are no other ways to tile a Klein bottle with ...

The perspective image of an infinite checkerboard. It can be constructed starting from any triangle DeltaOXY, where OX and OY form the near corner of the floor, and XY is the ...