Which of the following is NOT a trim component of a box cornice?

The header is not considered a trim component of a box cornice. In the context of architectural features, a box cornice generally consists of various decorative trim components that enhance the appearance of the upper portion of the wall and roofline.

The soffit typically refers to the underside of an architectural structure, such as the eaves or the overhangs of roofs, and is part of the box cornice. The frieze often adorns the part of the wall below a cornice and serves as a decorative band, making it essential in the assembly of a box cornice. Crown molding is another trim element that is positioned at the junction of the wall and ceiling, often included in the design of cornices to enhance their visual appeal.

In contrast, while the header may be an important architectural feature in other contexts (such as providing structural support over doors and windows), it does not directly function as a decorative trim component within a box cornice assembly. This distinction makes it the correct answer to the question regarding which option is not part of the cornice's trim components.