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1. (a) Find the order of the group of rigid motions of a cube. (Imagine a wooden cube place in a box just large enough to hold it. A rigid motion of the cube consists of picking up the cube and replacing it in the box, possibly in a different position.) (b) A rigid motion of a cube can be thought of either as a permutation of its eight vertices or as a permutation of its six sides. Find a rigid motion of the cube that has order 3 and express the permutation that represents it in both ways, as a permutation on eight elements and as a permutation of six elements.

1. (a) Find the order of the group of rigid motions of a cube. (Imagine a wooden cube place in a box just large enough to hold it. A rigid motion of the cube consists of picking up the cube and replacing it in the box, possibly in a different position.) (b) A rigid motion of a cube can be thought of either as a permutation of its eight vertices or as a permutation of its six sides. Find a rigid motion of the cube that has order 3 and express the permutation that represents it in both ways, as a permutation on eight elements and as a permutation of six elements.

Advanced Engineering Mathematics
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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1. (a) Find the order of the group of rigid motions of a cube. (Imagine a wooden cube placed in a box just large enough to hold it. A rigid motion of the cube consists of picking up the cube and replacing it in the box, possibly in a different position.) (b) A rigid motion of a cube can be thought of either as a permutation of its eight vertices or as a permutation of its six sides. Find a rigid motion of the cube that has order 3 and express the permutation that represents it in both ways, as a permutation on eight elements and as a permutation of six elements.
Transcribed Image Text:1. (a) Find the order of the group of rigid motions of a cube. (Imagine a wooden cube placed in a box just large enough to hold it. A rigid motion of the cube consists of picking up the cube and replacing it in the box, possibly in a different position.) (b) A rigid motion of a cube can be thought of either as a permutation of its eight vertices or as a permutation of its six sides. Find a rigid motion of the cube that has order 3 and express the permutation that represents it in both ways, as a permutation on eight elements and as a permutation of six elements.
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