4D Euclidean space
Polytope of the Month
This month, we return to the uniform polychora. Allow us to introduce:
... the cantitruncated tesseract, a beautiful polytope bounded by 8 great rhombicuboctahedra, 32 triangular prisms, and 16 truncated tetrahedra.
This polytope is the last in the tesseract family of uniform polytopes to be added to this site. With this, we now have complete coverage of all the 4D uniform polytopes in the 5-cell, tesseract, and 24-cell families. In a few more months, we will wrap up the 120-cell family, and the coverage of the convex uniform polychora will finally be complete! Stay tuned!
News
1 Mar 2013:
The Polytope of the Month for March 2013 is up!
POVRay-migration status
| 4D visualization document | 95% |
| Regular polychora | 100% |
| 4D geometric objects | 55% |
Uniform polychoron coverage
| Regular polychora | 100.0% |
| Non-regular uniform polychora | 90.2% |
| Overall | 91.5% |
The 4D FAQ
If you're new here, you may find it helpful to consult the 4D FAQ, which explains what this site is about.
4D Visualization
Ever wondered how to visualize 4-dimensional space? It's not as difficult as it may sound at first! Read the 4D Visualization pages to find out more.
4D Objects
These pages contain information about various 4D objects and many images of their projections into 3D.
The regular polychora: the 4D equivalents of the Platonic solids.
The uniform polychora: the 4D equivalents of the uniform polyhedra, including the Archimedean solids and the prisms and antiprisms.
The CRF polychora (Convex Regular-Faced polychora): a 4D generalization of the Johnson solids.
Other geometric objects: a collection of some simple 4D objects and their 3D projections.
