I've been thinking about room layouts lately, and wanted to do some analysis on how door placement impacts traffic patterns, which in turn impacts furniture placement.
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As a simplification, I'm considering a room with 4 walls, each with 3 door positions, left, right, and center. This yields 12 permutations, but by taking some rooms as reflections of others, can be reduced to 2 homeomorphic equivalents (see topologist donut and coffee cup meme)
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