examples/README.md

Examples Directory

This directory contains organized example scripts demonstrating the use of the ideal polyhedra volume toolkit.

Directory Structure

distributions/

Analysis of volume distributions for various polyhedra:

• tetrahedron/ - 4-vertex polyhedra volume distributions (10 files)
• five_vertex/ - 5-vertex polyhedra distributions
• six_vertex/ - 6-vertex polyhedra distributions
• euclidean/ - Euclidean tetrahedra analysis and fitting

optimization/

Optimization scripts organized by vertex count:

• 7vertex/ - 7-vertex optimization (octahedron with stellated face hypothesis) - 9 scripts
• 12vertex/ - 12-vertex optimization - 3 scripts
• 20vertex/ - 20-vertex optimization (icosahedron-like) - 6 scripts
• platonic/ - Platonic solid analysis and perturbations

visualization/

Visualization scripts (5 scripts):

• Sphere projection visualizations
• Golden ratio configurations
• Maximal volume configurations
• Volume landscapes

analysis/

Statistical and theoretical analysis scripts (14 scripts):

• Beta distribution theory
• Central limit theorem analysis
• Combinatorial mixture analysis
• Special configuration analysis

Running Examples

All examples can be run from their respective directories:

cd examples/optimization/7vertex
python optimize_7vertex.py

Or from the project root using absolute imports (package must be installed with pip install -e .).