What is a shape that is contained within another shape, with all its vertices on the outer shape's boundary?

A shape that is contained within another shape, with all its vertices on the outer shape's boundary, fits the definition of an inscribed polygon. An inscribed polygon is formed when the vertices of the polygon touch the circumference or boundary of another shape, typically a circle. This arrangement ensures that all corners of the polygon are perfectly aligned with the boundary of the outer shape, making it a fundamental concept in geometry.

In contrast, a circumscribed polygon refers to a polygon that surrounds another shape, often touching it at the midpoints of its sides. A central angle is formed by two radii of a circle and does not relate to the concept of containment within shapes. Point symmetry describes a shape that looks identical when rotated 180 degrees about a central point, which is unrelated to the positioning of shapes relative to one another. Thus, the inscribed polygon is the clear choice for the description provided in the question.