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To inscribe an equilateral triangle in an ellipse, place the top polygon vertex at (0,b), then solve to find the (x,y) coordinate of the other two vertices. ...

A column-convex polyomino is a self-avoiding convex polyomino such that the intersection of any vertical line with the polyomino has at most two connected components. ...

1. A fixed polyomino. 2. The set of points obtained by taking the centers of a fixed polyomino.

The 4-polyhex illustrated above (Gardner 1978, p. 147).

A polyhex consisting of hexagons arranged along a line.

A polyiamond consisting of equilateral triangles arranged along a line.

The 4-polyhex illustrated above.

The 6-polyiamond illustrated above.

The 6-polyiamond illustrated above.

Compass and straightedge geometric constructions dating back to Euclid were capable of inscribing regular polygons of 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, ...