A geometric regular pyramid is a type of pyramid that has the following characteristics:

1. Base: The base of a regular pyramid is a regular polygon, meaning all sides of the polygon are equal in length, and all interior angles are equal. Examples of regular polygons include equilateral triangles, squares, and regular pentagons.
2. Apex: The apex is the point directly above the center of the base. In a regular pyramid, the apex is aligned such that the line segment (height) from the apex to the center of the base is perpendicular to the base.
3. Lateral Faces: The lateral faces of the pyramid are congruent isosceles triangles. Each triangle shares a side with the base of the pyramid and meets at the apex.
4. Height: The height of the pyramid is the perpendicular distance from the apex to the center of the base.

Because of these properties, a regular pyramid is symmetric around its vertical axis (the line connecting the apex to the center of the base).