**Question 22: Determine the Symmetry Type**The image depicts a seven-pointed star object with a black circle in the center. This object is presented for analysis to determine the type of symmetry it exhibits.**Answer Choices:**A) $ \mathbb{Z}_7 $ B) $ D_{14} $ C) $ \mathbb{Z}_{14} $ D) $ D_7 $ **Explanation of Choices:**- $ \mathbb{Z}_7 $: Refers to the cyclic group of order 7, indicating rotational symmetry around the center.- $ D_{14} $: Refers to the dihedral group of order 14, indicating both rotational and reflectional symmetry.- $ \mathbb{Z}_{14} $: Refers to the cyclic group of order 14, primarily theoretical for this context.- $ D_7 $: Refers to the dihedral group of order 7, typically not standard as dihedral groups relate to twice the vertex count.**Analysis:**The seven-pointed star suggests the potential for rotational symmetry divisible by 7. Reflectional symmetry (i.e., symmetry across axes) would be analyzed for dihedral group applicability assuming 14 symmetries (7 rotations and 7 reflections), which would match the $ D_{14} $ choice given a seven-point array.The correct answer indicates a more nuanced symmetry considering potential for both rotation and reflection.

Dn is group of symmetries of a regular polygon with n-sides.where Dn=2nHere,D7=2 × 7D7=14The figure…

Answered: Determine the symmetry type of the…

Math

Advanced Math

Determine the symmetry type of the object shown below. A) Z7 B) D14 C) Z14 D) D7

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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