# 4D Euclidean space

## News Archive

### September 2011

Do you like soccer balls? This baby has 120 of
them, all nicely wrapped up into a 4D ball for your enjoyment. This is the
bitruncated 120-cell, another one of those
amazingly complex yet beautiful members of the 120-cell family of
4D uniform polytopes. And it comes with the
full set of Cartesian coordinates too!
*(Warning: there are 3600 vertices, and even after we've factored them into
permutation sets for you there are still 22 sets of coordinates left. This
isn't for the faint of heart!)*

**12 Sep 2011:**Added the octagonal prism, the decagonal prism, and the snub dodecahedron. All the Archimedean polyhedra are now covered!

**11 Sep 2011:**Added the hexagonal prism.

**9 Sep 2011:**Added the snub cube. The cubic family of uniform polyhedra is now complete!

**7 Sep 2011:**Added a new rendering of the 600-cell showing some of icosahedral polyhedra embedded in its edges:

**6 Sep 2011:**Added the pentagonal prism and the pentagonal antiprism.

Re-rendered the projections of the 600-cell to use transparent ridges instead of edges to show the projection envelope. The projections are much more pleasant to look at now.

**3 Sep 2011:**Corrected some mistakes in the posted coordinates for various polytopes.

Added coordinates for the grand antiprism, including a detailed derivation for them.

**1 Sep 2011:**You*may*have noticed that we were building up to something big towards the end of last month. And you're right! Not only have we put up the Polytope of the Month for September; we've also added many more 3D uniform polyhedra as well; in fact, all of the non-prismatic ones except the snub cube and the snub dodecahedron, plus the triangular prism. And all of them comes with explicit coordinates.But wait, there's more! We've also done a major overhaul of the uniform polychora page as well as the uniform polyhedra page. So if you haven't been here for a while, now's the time to check them out!

### August 2011

**26 Aug 2011:**Here's yet another treat before the month is up!This is the truncated icosahedron, also known as the “buckyball”. You probably already know it as the stitching pattern on a soccer ball, but the important thing is to be able to recognize it in a 4D projection. So head on over to the truncated icosahedron page and learn to spot it in 4D!

**25 Aug 2011:**Here's an end-of-the-month treat: the projections of the truncated tetrahedron, one of the Archimedean polyhedra.This simple little cutey is quite versatile, and occurs in many of the 4D uniform polychora.

**18 Aug 2011:**Here's a mid-month treat:This is a “family portrait” of the 3D uniform polyhedra, including the Archimedean polyhedra and the prisms and antiprisms. Uniform polyhedra occur as cells in the 4D uniform polychora.

**3 Aug 2011:**For the month of August, the polytope of the month is the cantellated 24-cell:This pretty polytope is a member of the 24-cell family of uniform polytopes, and is bounded by 24 rhombicuboctahedra, 24 cuboctahedra, and 96 triangular prisms.

### July 2011

**20 Jul 2011:**Fixed CSS bug that caused our pretty backgrounds not to appear in some browsers.**19 Jul 2011:**Split off older entries in the news archive into separate pages for easier navigation.**16 Jul 2011:**Added individual pages for each of the Platonic solids: the tetrahedron, cube, octahedron, dodecahedron, and icosahedron, with images of different projections of them. Being able to quickly identify projections of the Platonic solids helps in understanding projections of 4D polytopes.**13 Jul 2011:**To make up for our late update, here are bonus renders for the cantellated tesseract, this time based on a projection centered on an octahedral cell:This viewpoint gives a slightly more interesting, less ‘squarish’ view of the cantellated tesseract.

**12 Jul 2011:**We're late again for this month's polytope, but it's better late than never! Here is the cantellated tesseract:

It's another member of the tesseract family of uniform polytopes, bounded by 8 rhombicuboctahedra, 16 octahedra, and 32 triangular prisms.

- Made some minor fixes in a few pages.