Step 1: Identify atomic configuration of Pt.
Platinum (Pt, Z = 78):
\[
[Xe]\,4f^{14}5d^9 6s^1
\]
Step 2: Determine period number.
Highest principal quantum number is 6:
\[
\text{Period} = 6
\]
Step 3: Determine group number.
d-block element, group = (d + s electrons):
\[
9 + 1 = 10
\]
Step 4: Periodic table rule.
Transition metals group number depends on total valence electrons in d and s orbitals.
Step 5: Verify classification.
Pt belongs to group 10 transition metals.
Step 6: Final conclusion.
Thus, period 6 and group 10.
Final Answer:
\[
\boxed{6, 10}
\]