Build regular convex polyhedra with faces that are regular polygons.
Build Archimedean Solids

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What does vertex-transitive mean? How many Archimedean solids are there? How do you know there are no more?
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Who are Archimedes, Johannes Kepler, and John Conway? How did they name and document these shapes?
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What rule defines the relationship between faces, vertices and edges for these shapes? Does the rule apply to all polyhedra?
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Which Archimedean Solid model a Carbon allotrope?
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How can you depict 3D shapes in 2 dimensions? For each method, what information is lost?