Which one of the following defines a hexagonal dipyramid?
Show Hint
- A vertical six fold axis of symmetry
- A horizontal mirror plane
- Six vertical mirror planes at an angle of 30° with each other
- A mirror plane that is perpendicular to the vertical six fold axis of symmetry
The Correct Option is D
Solution and Explanation
Step 1: Understanding the hexagonal dipyramid:
A hexagonal dipyramid is a crystal form consisting of two hexagonal pyramids joined at their bases. It belongs to the hexagonal crystal system.
Step 2: Evaluating each option:
(A) A vertical six fold axis of symmetry:
- This is present in the hexagonal dipyramid
- However, this alone does NOT define the complete form
- The 6-fold axis is characteristic of all hexagonal forms, not specific to the dipyramid
(B) A horizontal mirror plane:
- This is present (perpendicular to the 6-fold axis)
- However, this alone does not define the dipyramid
- This could apply to other hexagonal forms
(C) Six vertical mirror planes at an angle of 30° with each other:
- Incorrect angle: vertical mirror planes in hexagonal system are at 60° to each other (360°/6 = 60°), not 30°
(D) A mirror plane that is perpendicular to the vertical six fold axis of symmetry:
- This is the horizontal mirror plane
- This element, combined with the 6-fold axis, specifically defines the dipyramid form
- This symmetry element creates the reflection that generates the upper and lower pyramids
- This is the defining characteristic that distinguishes the dipyramid from a single pyramid
Answer: (D) A mirror plane that is perpendicular to the vertical six fold axis of symmetry
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