Jeff Weeks’

Topology and Geometry Software

Curved-Space Pool Hall icon
Curved-Space Pool Hall
Shoot some pool in curved space.
visionOS
Crystal Explorer icon
Crystal Explorer
Immerse yourself in crystals to understand and enjoy their structure.
visionOS
Torus Chess icon
Torus Chess
Play chess on a wraparound board.
visionOS
3-Torus Maze icon
3-Torus Maze
Solve 3D mazes in a wraparound space.
visionOS
Torus Games icon
Torus Games
Eight familiar games introduce children age 10 and up to the concept of a finite yet unbounded universe.
iOS, macOS, Windows
Deutsch ελληνικά English español suomi français italiano 日本語 한국어 Nederlands português русский tiếng Việt 简体中文 繁體中文
KaleidoPaint icon
KaleidoPaint
Create colorful symmetrical paintings based on the 17 tiling patterns.
iOS
العربية Deutsch English español français italiano 日本語 Nederlands português русский 简体中文 繁體中文
KaleidoTile icon
KaleidoTile
Explore polyhedra and tessellations while creating colorful works of art.
iOS, macOS, Windows
Cymraeg Deutsch English français italiano 日本語 한국어 português 简体中文 繁體中文
Curved Spaces icon
Curved Spaces
Fly in a multiconnected universe (for math and physics students).
iOS, macOS, Windows
English español français italiano 日本語 português Türkçe 简体中文 繁體中文
4D Maze icon
4D Maze
Have fun solving 4D mazes (for everyone).
iOS, macOS, Windows
Deutsch English italiano 日本語 polski português русский Türkçe
4D Draw icon
4D Draw
Draw simple 4D figures (for geometry students).
iOS, macOS
English italiano português
Crystal Flight icon
Crystal Flight
Fly freely in crystals (for everyone).
iOS, macOS
Deutsch English italiano português

Other Resources

Shape of Space icon
The Shape of Space 3rd edition English
A gentle introduction to topology and geometry, with full-color figures throughout.
Arabic translation: شكل الفضاء العربية
Hyperbolic Blanket icon
How to Sew a Hyperbolic Blanket العربية English 日本語
Step-by-step instructions for sewing a hyperbolic surface from fleece.
Source code for visionOS apps
Hyperbolic Games
Kali
SnapPea
Non-Euclidean billiards in VR
Body coherence in curved-space virtual reality games

Recent Updates

2024-10-2 Torus Chess
Minor tweaks for visionOS 2 compatibility
2024-9-18 Curved-Space Pool Hall
Smoother cue stick animation in visionOS 2
Optional beginner's mode
Avoids walleyed vision for distant objects in spherical space
2024-8-21 3-Torus Maze
New application
2024-8-7 Curved-Space Pool Hall
Immersive space appears only when you tap Play button
2024-7-28 Curved-Space Pool Hall
Shows where your hands are in the curved space
Uses half-length cue stick to keep hands visible
Allows higher table for greater comfort
No longer shows empty table when control panel is up
2024-7-27 Crystal Explorer
Double tap (instead of single tap) to close a crystal, to avoid closing accidentally

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