8. a) Show that a two-dimensional lattice may not possess a 5-fold symmetry. b) Establish the fact that the number of two-dimensional Bravais lattices is five: Oblique, square, hexagonal, simple rectangular, and body-centered rectangular.

Physical Chemistry
2nd Edition
ISBN:9781133958437
Author:Ball, David W. (david Warren), BAER, Tomas
Publisher:Ball, David W. (david Warren), BAER, Tomas
Chapter13: Introduction To Symmetry In Quantum Mechanics
Section: Chapter Questions
Problem 13.3E: Identify the symmetry elements present in the following objects. a The Eiffel Tower. You may have to...
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8. a) Show that a two-dimensional lattice may not possess a 5-fold symmetry.
b) Establish the fact that the number of two-dimensional Bravais lattices is five:
Oblique, square, hexagonal, simple rectangular, and body-centered rectangular.
(The proof is given in Kittel, 1970.)
9. Demonstrate the fact that if an object has two reflection planes intersecting at n/4,
it also possesses a 4-fold axis lying at their intersection.
Transcribed Image Text:8. a) Show that a two-dimensional lattice may not possess a 5-fold symmetry. b) Establish the fact that the number of two-dimensional Bravais lattices is five: Oblique, square, hexagonal, simple rectangular, and body-centered rectangular. (The proof is given in Kittel, 1970.) 9. Demonstrate the fact that if an object has two reflection planes intersecting at n/4, it also possesses a 4-fold axis lying at their intersection.
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ISBN:
9781133958437
Author:
Ball, David W. (david Warren), BAER, Tomas
Publisher:
Wadsworth Cengage Learning,