https://github.com/pushtogithub23/cube_rotational_symmetry

https://github.com/pushtogithub23/cube_rotational_symmetry

Last synced: 11 months ago
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• Host: GitHub
• URL: https://github.com/pushtogithub23/cube_rotational_symmetry
• Owner: Pushtogithub23
• Created: 2025-03-29T15:40:05.000Z (about 1 year ago)
• Default Branch: main
• Last Pushed: 2025-03-29T16:14:34.000Z (about 1 year ago)
• Last Synced: 2025-04-10T20:18:37.579Z (about 1 year ago)
• Language: Jupyter Notebook
• Size: 21 MB
• Stars: 0
• Watchers: 1
• Forks: 0
• Open Issues: 0
• Metadata Files:
  • Readme: README.md

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README

          
# Cube Rotational Symmetry Visualization

This repository uses Python to explore and visualise the rotational symmetry elements of a cube. The project demonstrates how a cube remains invariant when rotated about specific symmetry axes by certain angles.

![cube_rotation_symmetry_1](https://github.com/user-attachments/assets/80ab2f6c-79b2-418b-9aa1-9dedbe654697)

## Overview

The project visualizes three main types of rotational symmetry axes in a cube:

1. **4-fold Axis of Symmetry(Tetrad)**: (3 axes)

   - Passing through centres of opposite faces

   - 90°, 180°, 270° rotations

2. **2-fold Axis of Symmetry(Diad)**: (6 axes)

   - Passing through midpoints of opposite edges

   - 180° rotations

3. **3-fold Axis of Symmetry(Triad)**: (4 axes)

   - Passing through opposite vertices

   - 120° and 240° rotations

## Features

- 3D visualization of a cube and its symmetry axes

- Interactive rotations about different symmetry axes

- Animated demonstrations of cube rotations

- Detailed mathematical explanations of symmetry operations

## Requirements

- Python 3.x

- NumPy

- Scipy

- Matplotlib

- IPython

- Jupyter Notebook

## Usage

1. Clone the repository

2. Open `CubeSymmetryAxes.ipynb` in Jupyter Notebook

3. Run the cells to visualize:

   - Static cube representations

   - Symmetry axes visualization

   - Rotation animations

## Visualizations

The repository includes:

- Static images showing symmetry axes

- GIF animations demonstrating rotations

- 3D interactive plots

## Acknowledgments

This project was created to explore geometric symmetry in 3D objects using Python visualization tools.