Step 1: Recall what a centriole is.
A centriole is a tiny cylinder-shaped structure in the cell that helps organize the spindle during cell division. Its wall is built from fine fibres called fibrils.
Step 2: Look at the fibrils.
Each centriole wall has nine sets of peripheral fibrils, and these fibrils are actually microtubules arranged in groups.
Step 3: Find what microtubules are made of.
Microtubules are hollow protein tubes built mainly from a protein called $tubulin$. So the peripheral fibrils are made of tubulin.
Step 4: Rule out flagellin.
Flagellin is the protein found in bacterial flagella, not in centrioles. So it does not fit.
Step 5: Rule out axonema and histone.
Axoneme is the inner core of a cilium or flagellum, not a building protein. Histone is the protein that wraps DNA. Neither makes up centriole fibrils.
Step 6: Conclude.
Since the peripheral fibrils are microtubules and microtubules are made of tubulin, the answer is tubulin.
\[ \boxed{\text{Tubulin}} \]