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An n-he (a term coined by Brendan Owen) is a shape formed from a polyhex by removing half of each hexagon in such a way that the remaining pieces are connected (Clarke). The ...

A packing of polyhedron in three-dimensional space. A polyhedron which can pack with no holes or gaps is said to be a space-filling polyhedron. Betke and Henk (2000) present ...

There are no tilings of the equilateral triangle of side length 7 by all the polyhexes of order n=4. There are nine distinct solutions of all the polyhexes of order n=4 which ...

Polykites are polyforms obtained from a regular triangular grid superposed on a regular hexagonal grid (its dual), illustrated above. The monokite is therefore a ...

A polyomino-like object made by attaching squares joined either at sides or corners. Because neighboring squares can be in relation to one another as kings may move on a ...

Polysticks, sometimes also known as polyedges, are polyforms obtained from the edges of a regular grid. Square polysticks are polyforms obtained from the edges of a regular ...

In a plane, consider a sum of N two-dimensional vectors with random orientations. Use phasor notation, and let the phase of each vector be random. Assume N unit steps are ...

On a three-dimensional lattice, a random walk has less than unity probability of reaching any point (including the starting point) as the number of steps approaches infinity. ...

Define the packing density eta of a packing of spheres to be the fraction of a volume filled by the spheres. In three dimensions, there are three periodic packings for ...

A tetromino is a 4-polyomino. There are five free tetrominoes, seven one-sided tetrominoes, and 19 fixed tetrominoes. The free tetrominoes are known as the T-tetromino, ...