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Given three noncollinear points, construct three tangent circles such that one is centered at each point and the circles are pairwise tangent to one another. Then there exist ...

A polyhex consisting of hexagons arranged along a line.

If p divides the numerator of the Bernoulli number B_(2k) for 0<2k<p-1, then (p,2k) is called an irregular pair. For p<30000, the irregular pairs of various forms are p=16843 ...

A distinct (including reflections and rotations) arrangement of adjacent squares on a grid, also called a fixed polyomino.

Polycairos are polyforms obtained from the Cairo tessellation, illustrated above. The numbers of polycairos with n=1, 2, ... components are 1, 2, 5, 17, 55, 206, 781, 3099, ...

Polyrects are polyforms obtained from a rectangular grid, illustrated above. The numbers of polyrects with n=1, 2, ... components are 1, 2, 3, 9, 21, 68, 208, ... (OEIS ...

Polyrhombs are polyforms obtained from a rhombic grid, illustrated above. The numbers of polyrhombs with n=1, 2, ... components are 1, 1, 3, 7, 20, 62, 204, ... (OEIS ...

Assemble six 1×2×2 blocks and three 1×1×1 blocks into a 3×3×3 cube.

Let S be a set of simple polygonal obstacles in the plane, then the nodes of the visibility graph of S are just the vertices of S, and there is an edge (called a visibility ...

The 6-polyiamond illustrated above.