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3D Geometry

Math Experiment Details

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📖 About This Experiment

Explore the five Platonic solids - the only regular convex polyhedra in 3D space. Each face is the same regular polygon, and the same number of faces meet at each vertex. This experiment demonstrates Euler's formula: V - E + F = 2 for all convex polyhedra.

💡 Key Concepts

  • •Platonic Solids: Five regular convex polyhedra
  • •Euler's Formula: V - E + F = 2 for convex polyhedra
  • •Regular Polyhedron: All faces are congruent regular polygons
  • •Dual Solids: Cube ↔ Octahedron, Dodecahedron ↔ Icosahedron

🔢 Key Formulas

Euler's Characteristic
χ = V - E + F = 2
Dihedral Angle
cos(θ/2) = sin(π/n) / sin(π/m)
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