mathematics

Geometry & Spatial Structures

From Voronoi diagrams to hyperbolic tilings, explore the visual mathematics of space, symmetry, and shape through interactive simulations.

geometryVoronoihyperbolicPlatonic solidstessellationprojective

Geometry is the oldest branch of mathematics, yet it remains one of the most visually stunning and practically relevant. From the honeycomb patterns of Voronoi diagrams to the mind-bending curvature of hyperbolic space, geometric structures appear everywhere — in crystal lattices, city planning, computer graphics, and the fabric of spacetime itself.

These simulations let you manipulate geometric constructions in real time. Generate Voronoi diagrams and their dual Delaunay triangulations. Tile the Poincaré disk with hyperbolic polygons. Rotate Platonic solids in 3D wireframe. Create tessellations with various symmetry groups. Explore how projective transformations distort space.

5 interactive simulations

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Hyperbolic Geometry & Poincaré Disk Tiling

Explore hyperbolic tilings in the Poincaré disk model — visualize non-Euclidean geometry where parallel lines diverge and triangles have angle sums less than 180°

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Platonic Solids Wireframe Rotation

Rotate all five Platonic solids in 3D wireframe — tetrahedron, cube, octahedron, dodecahedron, and icosahedron — and explore their dual relationships

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Projective Geometry & Perspective

Explore projective transformations, vanishing points, and cross-ratios — the geometry behind perspective drawing, camera calibration, and algebraic geometry

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Tessellation & Tiling Patterns

Create tessellations with different polygon types and symmetry groups — explore how shapes tile the plane without gaps or overlaps

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Voronoi Diagram & Delaunay Triangulation

Generate Voronoi diagrams and their dual Delaunay triangulations from seed points — explore spatial partitioning, nearest-neighbor regions, and computational geometry