📘 Three-Dimensional Polyhedra

A polyhedron is a three-dimensional shape made up of flat polygonal faces, straight edges, and vertices. Common types of polyhedra include:

• Tetrahedron (4 triangular faces)
• Cube (6 square faces)
• Octahedron (8 triangular faces)
• Dodecahedron (12 pentagonal faces)
• Icosahedron (20 triangular faces)

📌 Euler’s Formula

For any convex polyhedron:

V - E + F = 2

where:

• $$V$$ is the number of vertices,
• $$E$$ is the number of edges,
• $$F$$ is the number of faces.

This formula is fundamental in topology and geometry, providing a relationship between the different components of a polyhedron.

⚜️ Applications of Polyhedra

• Architecture and Engineering: Used in structural designs like geodesic domes.
• Crystals and Molecular Structures: Many natural formations follow polyhedral arrangements.
• Computer Graphics and 3D Modeling: Polyhedra form the basis of 3D rendering and game design.