Continuing what I started in December, I finally finished making a stellated icosahedron out of 30 Sonobe units. Each Sonobe unit corresponds to an edge of the icosahedron, and interlocks with three others to give the whole thing a remarkable degree of rigidity, even though it’s made completely out of paper. 70 more words
Tags » Group Theory
My favorite question in this realm is how much of the linear ordering of the natural numbers is purely combinatorial, where we eliminate all the structure that isn’t purely combinatorial via the doubly recursive factorizations of whole numbers, ending up with two species of graph-theoretic structures that I dubbed Riffs and Rotes. 19 more words
This is fairly random, but I thought I might as well write it down. In general it seems hard to say when a tower of Galois extensions is itself Galois… 127 more words
In this post, we give an example.
Let and let
where is a character of and is an irreducible representation of its stabilizer in , . 128 more words
In this post, we discover which representations of the generalized symmetric group can be realized over a given abelian extension of .
Let be the representation defined previously, where . 136 more words