The term "parametrization," as discussed in Wikipedia,

seems useful for describing labelings that are not, at least

at first glance, of a *vector-space* nature.

Examples: The labelings of a 4×4 array by a blank space

plus the 15 two-subsets of a six-set (Hudson, 1905) or by a

blank plus the 5 elements and the 10 two-subsets of a five-set

(derived in 2014 from a 1906 page by Whitehead), or by

a blank plus the 15 line diagrams of the diamond theorem.

Thus "parametrization" is apparently more general than

the word "coodinatization" used by Hermann Weyl —

“This is the relativity problem: to fix objectively

a class of equivalent coordinatizations and to

ascertain the group of transformations S

mediating between them.”

— Hermann Weyl, *The Classical Groups* ,

Princeton University Press, 1946, p. 16

Note, however, that Weyl's definition of "coordinatization"

is not limited to *vector-space* coordinates. He describes it

as simply a mapping to a set of *reproducible symbols* .

(But Weyl does imply that these symbols should, like vector-space

coordinates, admit a group of transformations among themselves

that can be used to describe transformations of the point-space

being coordinatized.)