Tilings of Hyperbolic Spaces
invariants of hyperbolic tiles. The Dehn invariant is one way
of testing whether a Euclidean polyhedron can be used to tile space.
But as Doug Zare describes, there are hyperbolic tiles
with nonzero Dehn invariant.
- Do buckyballs fill hyperbolic space?
- Gallery of interactive on-line geometry.
The Geometry Center's collection includes programs for generating
Penrose tilings, making periodic drawings a la Escher in the Euclidean
and hyperbolic planes, playing pinball in negatively curved spaces,
viewing 3d objects, exploring the space of angle geometries, and
visualizing Riemann surfaces.
Stephen Fortescue discusses some connections between basic
number-theoretic algorithms and the geometry of tilings
of 2d and 3d hyperbolic spaces.
- D. Huson's favorite hyperbolic tiling.
- Hyperbolic geometry. Visualizations and animations including
several pictures of hyperbolic tessellations.
shortbread. The Davis math department eats a Poincaré model
of a tiling of the hyperbolic plane by 0-60-90 triangles.
hyperbolic surface activity page. Tom Holroyd describes hyperbolic
surfaces occurring in nature, and explains how to make a paper model of
a hyperbolic surface based on a tiling by heptagons.
- Hyperbolic Tessellations, David Joyce, Clark U.
- Hyperbolic tiles.
John Conway answers a question of Doug Zare on the polyhedra
that can form periodic tilings of 3-dimensional hyperbolic space.
- Hyperbolic and
spherical tiling gallery, Bernie Freidin.
planar tessellations, image gallery of many regular and semiregular
tilings by Don Hatch.
- Mathematical imagery by Jos Leys.
Knots, Escher tilings, spirals, fractals, circle inversions, hyperbolic
tilings, Penrose tilings, and more.
hyperbolic tilings and software for creating them, J. Mount.
- Pavages hyperboliques dans le modèle de Poincaré.
Animated with CabriJava. Includes separate pages on hyperbolic tilings
with regular polygons including squares, pentagons, and hexagons.
on the hyperbolic plane, Misha Kapovich.
See also his Escher-like
on the Euclidean plane.
- Two-three-seven tiling of the hyperbolic plane
with lines that connect to give a fiery appearance.
From the Geometry Center archives.
From the Geometry Junkyard,
and recreational geometry pointers.
Send email if you
know of an appropriate page not listed here.
from a common source file.