Which of the following statement(s) is/are correct for the upper hemisphere stereographic projection of a crystal given below?
Which of the following statement(s) is/are correct for the upper hemisphere stereographic projection of a crystal given below?
Show Hint
- Angle between the axes, $\alpha = \beta = \gamma = 90^\circ$
- Crystal contains 1 tetrad
- Crystal contains 4 diads
- Crystal contains 5 mirror planes
The Correct Option is A, B, C, D
Solution and Explanation
From the upper-hemisphere stereographic projection:
A filled square at the center denotes a single tetrad (4-fold rotation axis) perpendicular to the projection → one tetrad present.
Oval symbols on the perimeter represent diads (2-fold axes). There are four diads arranged symmetrically in the horizontal plane.
The symmetry corresponds to a tetragonal crystal system, where
\[\alpha = \beta = \gamma = 90^\circ\]
The symmetry elements imply one horizontal mirror plane and four vertical mirror planes, giving 5 mirror planes total.
Answer: (A), (B), (C) and (D)
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