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Concepts of Dihedral Group- 1 Video Lecture | Mathematics for Competitive Exams
FAQs on Concepts of Dihedral Group- 1 Video Lecture - Mathematics for Competitive Exams
| 1. What is the definition of the Dihedral Group? |  |
Ans. The Dihedral Group, denoted by D(n), is the symmetry group of a regular polygon with n sides. It consists of rotations and reflections that preserve the shape of the polygon.
| 2. How many elements are there in the Dihedral Group? | |
Ans. The Dihedral Group D(n) has 2n elements. It includes n rotations and n reflections.
| 3. What is the order of the Dihedral Group? | |
Ans. The order of the Dihedral Group D(n) is 2n. It represents the total number of elements in the group.
| 4. Are rotations and reflections in the Dihedral Group commutative operations? | |
Ans. No, rotations and reflections in the Dihedral Group are not commutative operations. The order of composition matters, and the result may vary depending on the order in which the operations are applied.
| 5. Can the Dihedral Group be used to describe the symmetry of three-dimensional objects? | |
Ans. No, the Dihedral Group is specifically used to describe the symmetry of two-dimensional regular polygons. For three-dimensional objects, other symmetry groups like the Symmetric Group or the Octahedral Group are more appropriate.
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