Consider the four long diagonals of the cube, as pictured right. Check the following two facts (“check” can mean a formal proof or a detailed argument about why it’s true): Any symmetry of the cube permutes the long diagonals Any permutation of the long diagonals gives a symmetry of the cube. E.g., what symmetry of the cube sends blue to red? The permutations of the four diagonals corresponds to a symmetric group. Which one? How do you know? Extracted text:

Consider the four long diagonals of the cube, as pictured right. Check the following two facts (“check” can mean a formal proof or a detailed argument about why it’s true): Any symmetry of the cube...

Consider the four long diagonals of the cube, as pictured right. Check the following two facts (“check” can mean a formal proof or a detailed argument about why it’s true):
1. Any symmetry of the cube permutes the long diagonals
2. Any permutation of the long diagonals gives a symmetry of the cube. E.g., what symmetry of the cube sends blue to red?

The permutations of the four diagonals corresponds to a symmetric group. Which one? How do you know?

Extracted text:

Jun 04, 2022