4D Euclidean space

Polytope of the Month

Yes, the Polytope of the Month is back! We apologize for the 4-year hiatus. Technical troubles and personal situations made it difficult to keep up with the updates. But we're back, and we're bringing you more CRFs (convex regular-faced polytopes) and other polytopes to look at!

This month, we'll resume updates with a modest, but nonetheless interesting addition: the tetrahedral ursachoron, a cute little 4D CRF polytope that generalizes the tridiminished icosa­hedron to 4D:

tetrahedral ursachoron

This polychoron's surface has 5 tetrahedra, 4 tridiminished icosahedra (J63), and an octahedron. Head on over to the tetrahedral ursachoron page to learn its structure and how it generalizes J63.

As usual, we give its full Cartesian coordinates.


POVRay-migration status

4D visualization document95%
Regular polychora100%
4D geometric objects55%

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.

4D Stories


Last updated 19 Feb 2018.

Powered by Apache Runs on Debian GNU/Linux Viewable on any browser Valid CSS Valid HTML 5! Proud to be Microsoft-free