4D Euclidean space

News Archive

[Later news]

December 2008

• 31 Dec 2008: Tweak the rendering settings of the 120-cell perspective projection so that the image is clearer. Also reduced the edge radius of all the projections; they should look nicer now.

• 29 Dec 2008: Added the runcinated tesseract, the 4D analogue of the rhombicuboctahedron.

• 27 Dec 2008: Added the bitruncated tesseract, a uniform polychoron bounded by 8 truncated octahedra and 8 truncated tetrahedra.

• 26 Dec 2008: Added the truncated 5-cell, a uniform polychoron bounded by 5 tetrahedra and 5 truncated tetrahedra.

• 21 Dec 2008:

  1. Added Cartesian coordinates to the bitruncated 24-cell.

  2. Fixed some XHTML and CSS compliance errors. Standards are important!

• 15 Dec 2008: added the Omnitruncated 24-cell, a beautifully intricate polychoron bounded by 48 great rhombicuboctahedra and 192 hexagonal prisms.

• 8 Dec 2008:

  1. Corrected a factual error on the cubinder page: it does not roll on its cylindrical surfaces; it rolls on the square torus!

  2. Added the bitruncated 5-cell, a cell-transitive uniform polychoron bounded 10 truncated tetrahedra.

• 6 Dec 2008: Replaced old XFig figures of the cubical pyramid with POVRay-rendered versions.

• 4 Dec 2008:

  1. The old XFig figures in chapter 7 of the 4D visualization document have now been replaced with POVRay-rendered versions. This document is now practically finished with the POVRay migration!

  2. Older news have been split off into a separate archive page.

  3. Added a table showing POVRay-migration progress.

• 3 Dec 2008: Several updates:

  1. We now have a nice oblique projection of the tesseract. This replaces the old XFig figure.

  2. The 16-cell and 24-cell pages have been updated to show the equatorial cells as well.

  3. A perspective projection of the 120-cell has been added.

• 2 Dec 2008: Replaced XFig figures of the cubical cylinder with much nicer POVRay-rendered versions. The description has also been updated, and more projections have been added.

November 2008

• 26 Nov 2008: Replaced XFig figures in chapter 6 of the 4D visualization document with POVRay-rendered images. Only one more chapter to go!

• 24 Nov 2008:

  • Added the document for computing vector rotation about any plane in n-space using only vector operations [PDF].

  • Added the omnitruncated tesseract, a uniform polychoron derived from the tesseract.

• 19 Nov 2008: Replaced the old XFig figures in chapter 4 of the 4D visualization document with POVRay-rendered versions. There are a few more chapters to go, but we will get there eventually!

• 10 Nov 2008: Added the bitruncated 24-cell, a beautiful uniform polychoron bounded by 48 truncated cubes.

• 1 Nov 2008: These pages are undergoing a major face-lift and reorganization:

  • A new navigation bar has been added for ease of navigation.

  • The old XFig diagrams are gradually being replaced with POVRay-rendered images. This is still a work in progress; currently, the regular polychora and parts of the 4D visualization document have been updated. More are on the way!

  • Nice backgrounds made with a new polytope projector that renders projections using POVRay.

  • We finally have beautiful projections of the 120-cell and the 600-cell, illustrating how their cells are put together!