4D Euclidean space

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September 2012

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!

The cantitruncated 24-cell

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.


August 2012

The polytope of the month for August is the runcitruncated 16-cell:

The runcitruncated 16-cell

This polytope is a member of the tesseract family of uniform polychora. As usual, we have included animations and coordinates.

July 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:

The bi-icositetradiminished

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!

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