Jeff Weeks’

Topology and Geometry Software

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
Create colorful symmetrical paintings based on the 17 tiling patterns.
العربية Deutsch English español français italiano 日本語 Nederlands português русский 简体中文 繁體中文
KaleidoTile icon
Explore polyhedra and tessellations while creating colorful works of art.
iOS, macOS, Windows
Cymraeg 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 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
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.
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.
Hyperbolic Games
Non-Euclidean billiards in VR
Body coherence in curved-space virtual reality games

Recent Updates

2022-05-25 4D Maze
Added Turkish translation, thanks to Süleyman Saltuk Güngör
Minor aesthetic changes for iOS 15
2022-05-25 Curved Spaces
Added Turkish translation, thanks to Süleyman Saltuk Güngör
Minor aesthetic changes for iOS 15
2022-05-17 KaleidoTile
Replaced legacy version (which used deprecated OpenGL graphics) with MacCatalyst version (which uses Metal graphics)
2022-04-05 4D Draw
Entire app re-written in Swift for simplicity and easier maintainability
2022-02-27 Crystal Flight
Rewrote frustum culling on GPU for better efficiency on devices with A9 or newer processors

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Contact Jeff Weeks

This material is based upon work supported by the National Science Foundation under Grant No. 1503701. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author and do not necessarily reflect the views of the National Science Foundation.