Dihedral group
Named by 2 essays across one field — each of them below, with the objects they name alongside it.
Also named here as lagrange theorem — the same set of essays touches all of them, so they are one junction rather than several.
Eight ways to leave a square alone
A square can be picked up and put back so that nothing looks different. There are exactly eight ways to do it, and the number is not asserted here — it is what a search through all twenty-four relabellings of the corners comes back with.
Colourings nobody can tell apart
Sixteen ways to colour four corners in two colours, and only six of them are genuinely different. The count can be got by pooling the sixteen — or by never forming a single class and instead averaging how many colourings each motion leaves untouched.
Named alongside it
The objects these essays reach for when they reach for this one.
Counting argumentCyclic groupGroup actionLagrange theoremPermutationSymmetryClosureCounting two waysEquivalenceInvariantOrbitRegular polygon