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 diagonalsAny 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?

Symmetry of cube means it is something which preserves the structure of cube.

Answered: Consider the four long diagonals of the…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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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?

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