Number of crystal systems having only 2 types of bravais lattices = x, number of crystal system having at least two interfacial angles equal = y and number of crystal systems having all the three edge lengths equal = z. Then find the value of `x xx y xx z.`

Answer

To solve the problem, we need to find the values of \( x \), \( y \), and \( z \) based on the definitions provided in the question.

### Step 1: Determine the value of \( x \)

**Definition**: \( x \) is the number of crystal systems having only 2 types of Bravais lattices.

**Analysis**:
- The crystal systems that have exactly two types of Bravais lattices are:
- **Tetragonal** (Primitive and Body-centered)
- **Monoclinic** (Primitive and End-centered)

Thus, the total count of crystal systems with exactly two Bravais lattices is:
\[ x = 2 \]

### Step 2: Determine the value of \( y \)

**Definition**: \( y \) is the number of crystal systems having at least two interfacial angles equal.

**Analysis**:
- The crystal systems that have at least two equal interfacial angles include:
- **Cubic** (all angles equal)
- **Tetragonal** (two angles equal)
- **Orthorhombic** (two angles equal)
- **Monoclinic** (two angles equal)
- **Triclinic** (no angles equal)
- **Hexagonal** (two angles equal)

Thus, the total count of crystal systems with at least two equal interfacial angles is:
\[ y = 6 \]

### Step 3: Determine the value of \( z \)

**Definition**: \( z \) is the number of crystal systems having all three edge lengths equal.

**Analysis**:
- The crystal systems that have all three edge lengths equal are:
- **Cubic**
- **Trigonal** (or Rhombohedral)

Thus, the total count of crystal systems with all three edge lengths equal is:
\[ z = 2 \]

### Step 4: Calculate \( x \times y \times z \)

Now that we have determined the values of \( x \), \( y \), and \( z \):
- \( x = 2 \)
- \( y = 6 \)
- \( z = 2 \)

We can calculate:
\[ x \times y \times z = 2 \times 6 \times 2 = 24 \]

### Final Answer
The value of \( x \times y \times z \) is \( 24 \).

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