The fibers that form around centrioles during animal cell reproduction are called microtubules.

Here's a breakdown:

* Centrioles: These are small, cylindrical structures found in the cytoplasm of animal cells. They are involved in the formation of the spindle fibers during cell division.

* Microtubules: These are long, hollow cylinders made of the protein tubulin. They are crucial for cell shape, movement, and the transport of materials within the cell.

* Spindle Fibers: During cell division, centrioles migrate to opposite poles of the cell. They then form a structure called the spindle, which is composed of microtubule fibers. These fibers attach to chromosomes and pull them apart, ensuring that each daughter cell receives a complete set of chromosomes.

So, to summarize, during cell division, centrioles act as organizing centers for microtubule assembly, forming the spindle fibers that are essential for chromosome separation.