Geometry

1. Solid Geometry
   1. Three-dimensional Shapes
      1. Polyhedra
         1. Definition and Characteristics
            1. Definition of polyhedra
            2. Convex vs. non-convex polyhedra
            3. Regular polyhedra (Platonic solids)
            4. Semi-regular polyhedra (Archimedean solids)
            5. Other classifications (Kepler–Poinsot polyhedra, Johnson solids)
         2. Prisms
            1. Definition and identification of prisms
            2. Types of prisms (rectangular, triangular)
            3. Lateral faces and bases
            4. Volume calculation (base area × height)
            5. Surface area calculation (sum of lateral area and base area)
         3. Pyramids
            1. Definition and properties of pyramids
            2. Right vs. oblique pyramids
            3. Types (triangular, square)
            4. Volume calculation (1/3 × base area × height)
            5. Surface area computation (base area + 1/2 × perimeter × slant height)
         4. Euler's Formula
            1. Explanation of Euler's formula (V - E + F = 2)
            2. Application to different polyhedral shapes
            3. Derivation and proof
      2. Non-polyhedra
         1. Spheres
            1. Characteristics of a sphere
            2. Great circles and spheres
            3. Volume formula derivation (4/3 × π × r³)
            4. Surface area formula derivation (4 × π × r²)
         2. Cylinders
            1. Definition and parts (base, height, lateral surface)
            2. Types (right, oblique)
            3. Volume calculation (π × r² × h)
            4. Surface area computation (2 × π × r × h + 2 × π × r²)
         3. Cones
            1. Elements of a cone (base, height, slant height)
            2. Types (right circular, oblique)
            3. Volume calculation (1/3 × π × r² × h)
            4. Surface area calculation (π × r × l + π × r²)
      3. Solids of Revolution
         1. Definition and creation process
            1. Generation through rotation
            2. Examples (sphere, cylinder, cone)
         2. Method of Disks
            1. Explanation of the disk method for volume
            2. Application to obtaining volumes of rotational solids
         3. Method of Shells
            1. Explanation of the shell method
            2. Use in calculating volumes of revolution
         4. Volume and Surface Area Calculations
            1. Integration techniques for volume calculation
            2. Surface area integrals for solids of revolution
   2. Properties and Theorems
      1. Relationship between edges, vertices, and faces in polyhedra
      2. Symmetries in three-dimensional shapes
      3. Dual polyhedra concepts
      4. Intersection of solids
   3. Measurement in Solid Geometry
      1. Units and conversions for volume and area
      2. Measuring angles in three-dimensional structures
      3. Importance of dimensional analysis
   4. Applications of Solid Geometry
      1. Real-world use in architecture and engineering
      2. Modeling and visualization in computer graphics
      3. Applications in physics, e.g., determining moments of inertia
      4. Role in product design and industrial applications