A regular tetrahedron exhibits a total of 24 symmetries, comprising 12 rotational symmetries and 12 reflectional symmetries.

A regular tetrahedron is a three-dimensional geometric figure characterized by four equilateral triangular faces, four vertices, and six edges. Its symmetry can be analyzed in terms of both rotational and reflectional transformations. Rotational symmetries refer to the rotations that can be performed around an axis without altering the overall appearance of the shape. For a regular tetrahedron, there are 12 distinct rotational symmetries. These include rotations of $120^\circ$ and $240^\circ$ about axes that pass through a vertex and the center of the opposite face, as well as $180^\circ$ rotations around axes that pass through the midpoints of opposite edges.

In addition to its rotational symmetries, a regular tetrahedron possesses reflectional symmetries, which involve flipping the shape across a plane of symmetry. There are 6 such planes of symmetry in a regular tetrahedron, each one passing through a vertex and the midpoint of the opposite edge. By combining these 6 reflectional symmetries with the 12 rotational symmetries, we arrive at a total of 24 symmetries.

Understanding the symmetries of a regular tetrahedron is significant in various fields, including chemistry, where the tetrahedral shape is used to describe the spatial arrangement of atoms in certain molecules. In mathematics, these symmetries contribute to a broader study of geometric transformations and group theory, which enhances our understanding of the properties and behaviors of different shapes.