Polyscheme

Polyscheme is the name given to geometric objects of any number of dimensions (polytopes) by Ludwig Schläfli, the Swiss mathematician who discovered all the regular polytopes which exist in the higher dimensions of Euclidean space before 1853, at "a time when Cayley, Grassmann and Möbius were the only other people who had ever conceived the possibility of geometry in more than three dimensions." The Wikiversity was hosted on very slow servers in those days, and other researchers also discovered the 4-polytopes before Schläfli's article was published posthumously in 1901, but Schläfli is the founding author of the Polyscheme learning project. H.S.M. Coxeter is its founding editor, whose 1948 book Regular Polytopes tells the whole story of the project.

Polyscheme learning project
The Polyscheme project is intended to be a series of wiki-format articles on the regular polytopes, the fourth spatial dimension, and the general dimensional analogy of Euclidean and spherical spaces of any number of dimensions. This series of articles expands the corresponding Wikipedia encyclopedia articles to book length, to provide textbook-like treatment of the subject in depth, additional learning resources, and a subject-wide web of cross-linked explanatory footnotes which pop-up in context.

Some of what is in these companion articles is opinion, not established fact, as of this date of publication, and some of it is just commentary, not essential fact. The commentary and opinion is precisely the difference between the learning project article and the corresponding encyclopedia article; you can compare them to detect it, or just read the encyclopedia instead if you don't trust it.

Most project articles are an annotated and expanded version of the Wikipedia article which they replace for learning purposes. Some project articles, however, do not reproduce the Wikipedia article, and are only a commentary on it. Participants are directed by a banner to "See also" the Wikipedia article when reading these commentaries.

Active research
Polyschemes have been a subject of active and ongoing research since their discovery by a Swiss researcher around 1850. But for the first 50 years of its history Ludwig Schläfli's paper on the subject was unpublished, entirely inaccessible to other researchers. Even after its publication, Schläfli's paper remained obscure for another 50 years, in part because the mathematics it contained was only accessible to a few mathematicans who could read that language. H.S.M Coxeter finally made the subject widely accessible in his 1948 book Regular Polytopes, which synthesized all the research that had been published since Schläfli and added Coxeter's discoveries, including his invention of the theory of reflecting symmetry groups, the group theory mathematics that underlies geometry. Since then, Coxeter's book has been the encyclopedia of Euclidean geometry, and every polyscheme researcher has been able to begin with it instead of reinventing the wheel, and contribute new chapters to it.