1. Internal Factors:

* Cytoskeleton: This network of protein filaments (microtubules, microfilaments, intermediate filaments) provides structural support and helps maintain cell shape. They can also be rearranged to facilitate changes in shape.

* Internal Pressure: The turgor pressure within plant cells, due to the influx of water, helps maintain their rigid shape.

* Organelles: The size and arrangement of organelles within the cell can influence the overall shape. For example, the presence of a large vacuole in plant cells contributes to their box-like shape.

* Cell Wall: In plant cells, the rigid cell wall provides structural support and defines the cell's shape.

2. External Factors:

* Extracellular Matrix (ECM): This network of proteins and polysaccharides surrounding animal cells influences their shape and behavior. It can provide structural support and signal to the cell to change its shape.

* Neighboring Cells: Cell-cell interactions through junctions and adhesion molecules can influence the arrangement and shape of cells within tissues.

* Physical Forces: Cells can respond to mechanical forces like pressure or tension, leading to changes in their shape.

* Chemical Signals: External signals, like hormones or growth factors, can trigger changes in the cytoskeleton or gene expression, ultimately influencing cell shape.

3. Genetic Factors:

* Genes: The genes within a cell determine the proteins it produces, including those involved in the cytoskeleton and cell-cell interactions. These proteins ultimately influence the cell's shape.

Note: The relative importance of these factors can vary depending on the type of cell and its function. For example, muscle cells have a very elongated shape due to their specialized function in contraction, while nerve cells have long, branching axons to transmit signals over long distances.