Planar Tilings
21 aperiodic tiling families with displacement vector variants
3D Icosahedra
Three icosahedral model types with full 3D rotation and slice plane
Analysis
Area/volume metrics, equal-tile detection, tile selection and video export
Planar Tilings
Infinite patterns
without repetition
Aperiodic tilings fill the plane completely — yet the pattern never repeats. Starting from the Penrose tiling's fivefold symmetry (D5), the visualizer supports every dihedral group up to D27, generating rich quasiperiodic structures from simple substitution rules.
Each model is computed from a displacement-vector matrix, inflated iteratively to produce arbitrarily large patches. Adjust iterations, explore displacement variants, and watch complex long-range order emerge in real time.
3D Icosahedra
Quasicrystals
in three dimensions
Nature's most elegant aperiodic structures are three-dimensional. Icosahedral symmetry group Ih — with its 120 symmetry operations — underlies real quasicrystals discovered in metallic alloys and even meteorites. The visualizer renders all three icosahedral model types as fully interactive 3D objects.
Rotate freely, engage the slice-plane to section through the interior, and toggle individual tile layers. The same displacement matrix algebra that governs planar tilings extends naturally into six-dimensional superspace.
Analysis Tools
Built for deep
geometric exploration
Beyond rendering, the tool gives you interactive analysis capabilities that let you interrogate the mathematics behind each pattern.
Tile Selection
Click any tile in the pattern to highlight and inspect it. View area, vertex count, face indices, and the tile's position within the substitution hierarchy.
- Click-to-select individual tiles
- Geometric metrics per tile
- Highlight connected faces
Equal Tile Detection
Automatically identify all tiles that are congruent — same shape and size, possibly rotated or reflected — and color them consistently across the entire pattern.
- Congruence up to rotation & reflection
- Consistent color-coding across pattern
- Tile-type frequency statistics
Video Export
Record any animation as a downloadable video. Capture slow rotations, parameter sweeps, or slice-plane animations and export them directly from the browser — no plugins required.
- Browser-native MediaRecorder API
- Configurable frame rate & duration
- WebM download, ready to share
Get Started
Ready to explore?
21 tiling models. 3D icosahedra. Real-time analysis.
All in your browser — no installation needed.