4D Euclidean space

Polytope of the Month

This month, we present a Catalan polychoron from the 24-cell family:

The Joined 24-cell

This is the joined 24-cell, the dual of the rectified 24-cell. Its surface consists of 96 triangular bipyramids, 288 isosceles triangles, 240 edges, and 48 vertices. Check out the joined 24-cell page for more details!

Full algebraic coordinates are provided, as usual.


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 01 May 2024.

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