4D Euclidean space
This month, we're back to our regularly-scheduled uniform polytopes. But we've added a new twist: this time, we're presenting our polytope of the month, the cantitruncated 24-cell, with 3D stereoscopic projections!
These pair of images are cross-eyed stereograms; you can view them cross-eyed to see the 3D effect. Seeing the 3D depth in these images is very helpful for understanding the structure of the 4D to 3D projection, and consequently in visualizing the 4D geometry of the polytope.
We chose cross-eyed stereograms over other 3D viewing techniques because it does not require any special glasses or equipment, and the images themselves can be viewed as normal, flat images just like before, should you prefer not to do cross-eyed viewing. There is also no limit on the width of each image, unlike the wall-eyed technique.
As usual, this pretty polychoron comes with full Cartesian coordinates.
31 Aug 2012:
The polytope of the month for September is up!
The polytope of the month for August is the runcitruncated 16-cell:
22 Aug 2012:
1 Aug 2012:
This month, we decided to take a break from the usual fare of uniform polytopes and throw in something a little more unusual to keep things interesting:
This unusual polytope is a member of the class of CRF polychora, convex 4D polytopes whose ridges are all regular polygons. Its cells are tridiminished icosahedra, which are Johnson solids, and it is therefore not a uniform polytope. However, it does more symmetry than might seem at first glance, and a very interesting kind of symmetry at that.
So check out the bi-tetraicosidiminished 600-cell page to find out more!
24 Jul 2012:
The 4D visualization document has undergone a major revision, with the addition of a new chapter between the original chapters 2 and 3 and the revision of the subsequent chapters to clarify some important points that were not made clear previously. As a result, the chapters have been renumbered; you will want to update your bookmarks if you have bookmarked any of the individual chapters previously. Thanks to Pascal R. (aka Ovo on the Tetraspace Forum) for the valuable feedback that led to this update.
23 Jul 2012:
Added Johnson solid J2: the pentagonal pyramid.
9 Jul 2012:
7 Jul 2012:
3 Jul 2012:
2 Jul 2012:
We're a day late, but this month's Polytope of the Month is finally up! And it's an unusual one, too, with a very interesting kind of symmetry. We hope you'll enjoy finding out about it!
Along with our special Polytope of the Month, we have added a page to describe the tridiminished icosahedron, a Johnson solid which is the shape of its cells.
And along with that, we've added a brief description page on the Johnson solids, as well as an introductory page to the CRF polychora, a generalization of the Johnson solids to 4D, of which our Polytope of the Month is an example.