4D Euclidean space
Polytope of the Month
This is it. This is the grand-daddy of them all, the largest 4D convex uniform polytope, the omnitruncated 120-cell:
Known also as the omnitruncated 600-cell, this polychoron from the 120-cell/600-cell family of uniform polychora has a whopping 14400 vertices, 28800 edges, 17040 polygons, and 2640 cells! It is the largest member of its family, and also the largest among all the 4D uniform polytopes.
So head on over to the omnitruncated 120-cell page where we explore the structure of this beautifully intricate polychoron and account for every one of its 2640 cells. Full Cartesian coordinates are provided, as is customary.
With this Polytope of the Month, we have reached a landmark: we have now covered all of the 4D convex uniform polytopes! The fun is far from over, however. You may have noticed last month that a number of Johnson solids have been added. There is a reason for this! February 2014 turned out to be a very interesting month for the CRF polychora discovery project, where an entire class of CRF polychora—4D analogues of the Johnson solids—was discovered, with the unprecedented occurrence of the bilunabirotunda and the triangular hebesphenocorona as cells, previously thought to be very difficult to build 4D polytopes out of due to their irregular shape.
So stay tuned; some of these fascinating new polychora will be featuring as Polytope of the Month in the upcoming months. Along the way, we may also throw in a few other bonuses as well, such as some of the more interesting 4D Catalans (duals of the uniform polychora).
1 Mar 2014:
The polytope of the month for March 2014 is up!
|4D visualization document||95%|
|4D geometric objects||55%|
Uniform polychoron coverage
|Non-regular uniform polychora||100.0%|
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