Patching a Hole

Glenn Stockton likes to auto-generate new geometry using stone age tools, found objects, and recently showed up with some pentacaps, folded from tetrahelixes passed through by Nat Bobbitt at our meeting of the minds in Eugene that time (Dr. Nick also present, plus expected later today).

:: icosacap analysis
by D. Koski w/ vZome ::

The pentacaps (Johnson Solid J13 in particular) got him musing about the role of regular tetrahedra in the world of five-fold symmetry, i.e. an "eternal war of incommensurability" as we think about it in Synergetics. I submitted a request for good data on Synergeo and Adrian Rossiter came back with some answers, as did Dave Koski in top form. In the process of checking, we discovered Wikipedia is sporting a wrong formula, not even linear, relating edges (a) to height (H). Here's the mistake:

:: oops ::

I didn't immediately apply a fix, not having the fancy math notation LaTeX or whatever, although I did figure the right answer. Instead, I posted something to the Pre-College Geometry list, suggesting some younger serious-minded person put themselves to the task, earn some street cred.

Wikipedia invites public spirited individuals to correct mistakes, one of the hallmarks of an open source literature base.

My thanks to Glenn, Nat, other cast, for getting us another step along the journey. Fighting misinformation is a full time job.

Followup: Wikipedia was fixed within a few hours of our drawing attention to this problem. Here is the corrected formula:

:: all better now ::