# Questions tagged [tiling]

Use this tag for questions about (not necessarily periodic) tilings of metric spaces, their combinatorial, topological and dynamical properties, as well as basic definitions and concepts.

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### Which repeated shape covers a circle most efficiently

Imagine you have a ring and you want to fill as much of this ring as possible with one type of shape (triangle, square, hexagon, must be the entire shape repeated within the ring no overlaps). To be ...
• 31
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### Find the number of ways of tiling a $3\times n$ rectangular grid with $2\times 1$ dominoes

I'm trying to find the number of ways $(a_n)$ of tiling a $3\times n$ rectangular grid with $2\times 1$ dominoes, where rotation is allowed. I want to find a recurrence relation for $(a_n)$ and an ...
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• 331
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### Cutting a polygon into 2 or 3 smaller, rationally-scaled copies of itself?

I've noticed that many 2D geometric figures can be tiled using four smaller copies of themselves. For example, here's how to subdivide a rectangle, equilateral triangle, and right triomino into four ...
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