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...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.