4D Euclidean space
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:
11 Sep 2011:
Added the hexagonal prism.
9 Sep 2011:
7 Sep 2011:
Added a new rendering of the 600-cell showing some of icosahedral polyhedra embedded in its edges:
6 Sep 2011:
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!
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:
3 Aug 2011: For the month of August, the polytope of the month is the cantellated 24-cell:
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.
This viewpoint gives a slightly more interesting, less ‘squarish’ view of the cantellated tesseract.
12 Jul 2011: