The classical kinds of design patterns, stuff like the flywheel or singleton, as I understand them, are patterns for class-based object-oriented programming. R has different semantics, so it favors a different set of design patterns.
The tidyverse is basically built around a collection of design patterns. There's the fluent function interface where the data to be manipulated is the first function argument, and nearly all functions return a similar kind of object as their input. The functions can be chained together using
%>% pipelines, which is another design pattern. (An alternative pattern to piping would require intermediate variables or nested function calls.) The concept of tidy data and tidying R objects into dataframes are also design patterns. The idea of list columns and nested dataframes would be an example of a very recent design pattern for R too.