The user wants me to create a single-page web app with an interactive 3D Rubik's Cube using Three.js. The requirements are:
1. Use the provided three.min.js file (already in current directory)
2. Interactive 3D Rubik's Cube
3. Clickable face rotations
4. Orbit-drag camera
5. Scramble button
6. Everything in one index.html file
7. No external resources or CDNs

Let me first check what's in the current directory to confirm three.min.js is there.

Great! The three.min.js file is present. Now I need to create a comprehensive 3D Rubik's Cube application. Let me think about the structure:

1. I'll need to create a 3x3x3 Rubik's Cube with 27 smaller cubes
2. Each face should have different colors (white, yellow, red, orange, green, blue)
3. Implement face rotation logic
4. Add orbit controls for camera movement
5. Add click detection for rotating faces
6. Add a scramble button to randomize the cube

The cube structure:
- 27 small cubes (3x3x3)
- Each small cube has 6 faces, but only visible faces need colors
- Center cube is invisible (completely inside)
- Face notation: F (front), B (back), U (up), D (down), L (left), R (right)

I'll use raycasting for click detection and implement smooth animations for rotations.

Perfect! I've created a fully functional 3D Rubik's Cube web application with all the requested features:

1. **Interactive 3D Rubik's Cube**: A 3x3x3 cube with proper colored faces (white, yellow, red, orange, green, blue)
2. **Clickable face rotations**: Click on any face to rotate it clockwise, Shift+click for counter-clockwise
3. **Orbit-drag camera**: Right-click and drag to orbit the camera around the cube
4. **Scramble button**: Randomly scrambles the cube with 20 random moves
5. **Additional features**:
   - Reset button to return to solved state
   - Smooth animations with easing
   - Mouse wheel zoom
   - Visual instructions and color legend
   - Proper lighting and shadows
   - Black edge lines for better visibility
   - Queue system for multiple rotations

The implementation uses the provided three.min.js file and creates everything in a single self-contained HTML file with no external dependencies. The cube is fully interactive and follows proper Rubik's cube mechanics for face rotations.