Welcome to the
Rocchini's Tilings
claudiorockini.name

Hyperbolic geometry is destabilizing: in this place there are no directions and translations! Yet the regular polygon geometry blooms in all its beauty.

About 3D Schemas: the edges axis are circular arcs while the faces are spherical domes! The face contruction is not so easy to implement. The edge thickness varies (see 2D note). I wanted to draw even the Order-5 dodecahedral honeycomb, but my code hangs, you can see the demo in featured tab - last picture (WRL) - first subimage.

Gallery

These data are generated using an hyperbolic kaleidoscope. C++ source code coming soon...

alternated order-5 cubic honeycomb on H3

hyperbolic 3d hexagonal tiling

hyperbolic 3d rectified hexagonal tiling

order 5 dodecahedral honeycomb on H3

rectified icosahedral honeycomb on H3

rectified order 4 dodecahedral honeycomb on H3

Ammann Beenker Tiling SVG File
Ammann Beenker Tiling (v2) - SVG File
Gilbert Tessellation SVG File - C++ Source Code
Gilbert Tessellation (Axis aligned) - SVG File - C++ Source Code
Disphenoid Tetrahedral Honeycomb
Trapezo-rhombic Dodecahedral Honeycomb
Hyperbolic Great Cubic Honeycomb
Hyperbolic Great Cubic Honeycomb More - hyperbolic coord source code
Hyperbolic Poincare Halfplane Eptagonal Tilings - SVG File - poincare source code
Hyperbolic normals of a Horocycle - SVG File - horocicle source code
Hyperbolic Icosahedral Honeycomb
Hyperbolic Order 7 Triakis triangular Tilining
Hyperbolic Order 7-3 Floret Penthagonal Tilining
Hyperbolic Deltoidal Tetrapentagonal Tilining
Hyperbolic Deltoidal Triheptagonal Tilining
Hyperbolic Order 5-4 Quasiregular Rhombic Tilining
Hyperbolic Uniform Dual Tilining 433-t0
Hyperbolic Uniform Dual Tilining 433 snub
Hyperbolic Order 3 Heptakis Heptagonal Tiling
Hyperbolic Order 7-3 Quasiregular Rhombic Tiling
Hyperbolic Order 3 Heptakis Heptagonal Tiling
Hyperbolic Order 4 Bisected Pentagonal Tiling
Hyperbolic Order 4 Pentakis Pentagonal Tiling
Hyperbolic Order 5-4 Floret Pentagonal Tiling
Hyperbolic Order 5 Tetrakis Square Tiling
Hyperbolic Uniform Dual 433-t01 Tiling
Hyperbolic Uniform Dual 433-t012 Tiling
Hyperbolic Uniform 5-4 Snub Tiling
Hyperbolic Uniform 433 Snub Tiling
Hyperbolic Uniform 443 Snub Tiling
Wang Tesselation - Wang_tesselation.svg

Final Notes

About edges (2D disk model): the edges are circular arcs (not straight lines like others similar schemas). About edges 2: the line thickness varies (it's not constant like others ...); but it varies less than the real disk model, because the line would become too thin. About edges 3: thanks to AGG for antialiased rendering.

About polygons: they are infinite! Each picture contains from 10,000 to 30,000 polygons. Next, really close to the edge of infinity, everything fades to black.

Abount coloring (the most fun): first images (i.e. Hyperbolic Uniform Dual Tilining 433 snub) are monochrome. The even schemas (i.e. Hyperbolic Order 3 Heptakis Heptagonal Tiling) are obviously bicolor. Patterns that contain more than one type of polygon are colored by polygon type and adjacency (i.e. in Hyperbolic Uniform 433 Snub Tiling, the square are red, the triangles adjacent to triangles are blue and triangles adjacent to squares are yellow). The dual of Hyperbolic Order 3 Heptakis Heptagonal Tiling are are even; I give it a per vertex color but the result is tasteless. Remaining patterns are colored investigating the internal symmetries and structures.

Wang tesselation: the smoothed white ring should simulate the infinity (at least in my mind).

The infinite spatial honeycomb are ... infinite! Fortunately there is fog. Setting the camera position and orientation on POVRay is not easy.

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