Self-folding origami animation of a samurai helmet

Build a self-folding origami animation in a single self-contained HTML file. A flat square sheet of paper with a printed pattern folds step by step into a recognizable traditional figure, such as a samurai helmet, then unfolds back to flat and repeats. Model every fold as a rotation around a crease line, keep track of which paper layers are on top and which faces are visible, and update the 3D shape after each step. Show a soft shadow under the paper on a dark, starry stage. Add a small caption naming the current step and the figure, plus a minimal editorial-style UI with play, pause and restart controls and a step progress bar. Use a warm red paper with a subtle pattern and a cream reverse side. Done means the full fold sequence plays smoothly without layers clipping, the figure is clearly identifiable at the end, and the loop restarts cleanly.