Question

Which of the following statement(s) is/are correct for the upper hemisphere stereographic projection of a crystal given below? 

• A. Angle between the axes, $\alpha = \beta = \gamma = 90^\circ$
• B. Crystal contains 1 tetrad
• C. Crystal contains 4 diads
• D. Crystal contains 5 mirror planes

Hint:

In stereographic projections, tetrads represent 4-fold symmetry, and the number of symmetry elements helps in determining crystal class.

Answer 1

The Correct Option is A, B, C, D

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)