Nested Dodecahedra, Russian Dolls
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Nested Polyhedra Nested structures are ubiquitous in mathematics - recursive algorithms that unfold like Russian dolls. Consider a sequence of 15 nested dodecahedron shells, each with an exterior edge length ranging from 48mm to 6mm. You can choose any number from this set and create a unique nested structure. It takes two halves to form a complete whole, after all. Each shell measures 2mm in thickness, with its edge length decreasing by 3mm as you progress through the sequence. But here's the fascinating question: how does the volume of each dodecahedron change when the side length drops by 3mm?
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