A radial structure is one where there is a central case and conventionalised variations on it which cannot be predicted by general rules. Categories that are generated by central cases plus general principles […] are not radial structures, as we are defining the term. We are limiting radial structures only to cases where the variations are conventionalised and have to be learned.
- Lakoff (1987), Pag. 84

The radial structuring of categories involves the following: - A conventional choice of center. - Extension principles. These characterize the possible “links” between more central and less central subcategories. They include metaphoric models, metonymic models, image-schema relations etc. - Specific conventional extensions. Though each extension is an instance of the extension principles, the extensions are not predictable from the center plus the principles. Each extension is a matter of convention and must be learned. The fact that specific extensions are instances of general principles makes them easier to learn. Every aspect of radial structuring is inexpressible in a view of objectivist cognition.
- Lakoff (1987), Pag. 204

Radial structure in categories is understood in terms of CENTER-PERIPHERY schemas.
- Lakoff (1987), Pag. 283