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Two-dimensionalWhich fits best - a square peg in a round hole, or a round peg in a square hole? To be more precise, if you take a circle and fit inside it the largest possible square, and then take a square and fit inside it the largest possible circle, which leaves proportionally least space?
Which fits best?
Three-dimensionalWhich fits best in a sphere - a dodecahedron or an icosahedron? That is, if you fit the largest possible dodecahedron and icosahedron inside a given sphere, which leaves least space?
(Both images copyright by Rüdiger Appel)
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