User:Cullinane

Full name: Steven H. Cullinane

Reflection groups: The missing link

Note of Nov. 11, 2007:

Thanks to Wikipedia administrator Charles Matthews and an anonymous user from New Delhi, India, a number of Wikipedia articles no longer contain references (admittedly self-promotional) to my own unpublished work. (See user talk.) Whether this improves the altered articles is not clear.

My one enduring contribution to Wikipedia is the creation of the article Reflection group in August, 2005. On Yom Kippur last year (Oct. 2), Charles Matthews removed a link to my own work from that article; later that October, on Halloween, user Melchoir replaced the missing link with a reference to a new arXiv paper, "Reflection groups in algebraic geometry," by Igor Dolgachev, timestamped less than 14 hours earlier. The Dolgachev paper has now been published; it appears in the "Recently posted articles" section of the Bulletin of the American Mathematical Society. Since the Dolgachev paper's publication indicates that reflection groups are of current mathematical interest, and since the Wikipedia article Reflection group was created specifically to supply background for the link Matthews deleted, it now seems appropriate to recall the missing link. It was to a JavaScript page that illustrates how an affine reflection group of order 322,560, acting on a finite space, may be used to create a number of symmetric patterns resembling those found in traditional American quilts.

The link is to a page titled Kaleidoscope Puzzle.

Update of December 7, 2007: For some further background, see Reflection Groups in Finite Geometry.

The Fano Plane

Note of Dec. 22, 2015:

See the Fano-plane page before and after the Eppstein edit of 03:52 Dec. 22, 2015. Eppstein deleted my Dec. 6th 3-space image as well as today's Fano-plane image. He apparently failed to read the explanatory notes for both Wikimedia Commons images he deleted, those of the square Fano 3-space model and of the rectangular Fano 2-space model. The research he refers to was original (in 1979) but has been published for some time now in the online Encyclopedia of Mathematics, as he could have discovered by following a link in the notes for image of the 3-space model.

User subpages

User subpage: a trial article stub-- /Reflection group

User subpage: Letter from Anne V. Shepler-- /Shepler letter

User subpage: stub article, /Translation plane