Question

Which one of the following defines a hexagonal dipyramid?

• A. A vertical six fold axis of symmetry
• B. A horizontal mirror plane
• C. Six vertical mirror planes at an angle of 30° with each other
• D. A mirror plane that is perpendicular to the vertical six fold axis of symmetry

Hint:

A hexagonal dipyramid has six faces and a vertical six-fold axis of symmetry.

Answer 1

The Correct Option is D

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