Read on Twitter
I wrote a 328 tweet maths thread, so I thought I’ll give it a bit of an index. https://twitter.com/yet_so_far/status/1270355064218157063
We start with a discussion of the symmetries of the equilateral triangle. https://twitter.com/yet_so_far/status/1270369778578993152?s=21
And we construct the group of its symmetries. https://twitter.com/yet_so_far/status/1270433418531217408?s=21 https://twitter.com/yet_so_far/status/1270433418531217408
We talk a little bit about what groups are, even though we mostly care about what groups do. https://twitter.com/yet_so_far/status/1270439258667528193?s=21 https://twitter.com/yet_so_far/status/1270439258667528193
Then we do the same thing (ie construct the group of symmetries of) the square. https://twitter.com/yet_so_far/status/1271112842566160385?s=21 https://twitter.com/yet_so_far/status/1271112842566160385
Then we go up a dimension and talk about the Platonic solids. https://twitter.com/yet_so_far/status/1271127375246438405?s=21 https://twitter.com/yet_so_far/status/1271127375246438405
Compute the symmetries of the tetrahedron. https://twitter.com/yet_so_far/status/1271166381229309954?s=21 https://twitter.com/yet_so_far/status/1271166381229309954
During which we introduce the idea of a permutation. https://twitter.com/yet_so_far/status/1271429424433582080?s=21 https://twitter.com/yet_so_far/status/1271429424433582080
And after that we moved on to the cube. https://twitter.com/yet_so_far/status/1271871173396234240?s=21 https://twitter.com/yet_so_far/status/1271871173396234240
I said I’d get back to the icosahedron and dodecahedron, which I did, but not quite as a jumping-off point. https://twitter.com/yet_so_far/status/1273005863872147456?s=21 https://twitter.com/yet_so_far/status/1273005863872147456
We moved on to graphs and their automorphisms and talked about what I like to do with them. https://twitter.com/yet_so_far/status/1273211167385825281?s=21 https://twitter.com/yet_so_far/status/1273211167385825281
And for an example of that, we talked about the real projective plane, and specifically a triangulation of it. https://twitter.com/yet_so_far/status/1273385967588724738?s=21 https://twitter.com/yet_so_far/status/1273385967588724738
And drew a graph. https://twitter.com/yet_so_far/status/1273607475028254720?s=21 https://twitter.com/yet_so_far/status/1273607475028254720
Coloured it in a very nice (symmetric!) way, and calculated its symmetries. https://twitter.com/yet_so_far/status/1273960353936875521?s=21 https://twitter.com/yet_so_far/status/1273960353936875521
After which we finally talked about the exceptional symmetry of sets of size six. https://twitter.com/yet_so_far/status/1274778194915348481?s=21 https://twitter.com/yet_so_far/status/1274778194915348481
We gave Sylvester’s construction, then went on to talk about how the partitions of a set of size six into disjoint triad are the perfect vantage point to see the dual sixes we constructed. https://twitter.com/yet_so_far/status/1275018248849952772?s=21 https://twitter.com/yet_so_far/status/1275018248849952772
And wrapped up by linking back to our earlier discussion of the icosahedron and the Petersen graph. https://twitter.com/yet_so_far/status/1275211751966064641?s=21 https://twitter.com/yet_so_far/status/1275211751966064641
Hope that overview makes it easier to navigate! I’m always happy to chat about any of this. Thanks for reading!
Threadreader version of the original thread: https://twitter.com/threadreaderapp/status/1275253729932070913?s=21 https://twitter.com/threadreaderapp/status/1275253729932070913
