Explore the
Fourth Dimension
Interactive visualizations and deep mathematical guides to four-dimensional polytopes. From the tesseract to the 600-cell.
The Six Regular Polychora
The Platonic solids of the fourth dimension—discovered by Ludwig Schläfli in 1852.
Learn 4D Geometry
From basic concepts to advanced classification systems.
What is the Fourth Dimension?
Understand 4D space through analogy and mathematics.
Schläfli Symbols
The notation that describes all regular polytopes.
Projection Methods
How we visualize 4D objects in 3D space.
History of 4D Geometry
From Hinton to the Discord discoveries.
The Regiment System
How 2,000+ polychora are organized.
Ready to explore?
Launch the interactive viewer to rotate, project, and explore 1,700+ four-dimensional polytopes.
Launch Interactive Viewer