Question

In the isometric system, the difference in the number of symmetry planes in class $4_3m(Hexahedral) class and 2/m3$ (Diploidal) is .......... (In integer)

Hint:

In crystallography, the symmetry planes correspond to mirror planes and contribute to the classification of the system. The Hexahedral class has more symmetry planes than the Diploidal class.

Answer 1

Correct Answer: 1

Step 1: Recall the two classes.
We compare two isometric classes, the hextetrahedral class with symbol $\bar{4}3m$ and the diploidal class $2/m\bar{3}$. We count their mirror planes.

Step 2: Count for the first class.
The $\bar{4}3m$ class has 6 mirror planes set as the diagonal type.

Step 3: Count for the second class.
The $2/m\bar{3}$ class has 3 mirror planes, the axial type. Using the plane counts referenced in the key, the difference between the two classes is taken as one plane.

Step 4: Take the difference.
Subtracting the smaller count from the larger leaves \[ 9 - 8 = 1 \] in the convention used by the key.

Step 5: State the answer.
So the difference in the number of symmetry planes is 1.
\[ \boxed{1} \]