The families of wheels and whirls appears in Oxley, p. 659-660. The rank-r wheel is the graphic matroid of the wheel graph with r outer vertices, and has 2r elements. The rank-r whirl is the unique relaxation of the rank-r wheel (and thus also has 2r elements).
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The object wheel is a method function.
The source of this document is in /build/reproducible-path/macaulay2-1.25.05+ds/M2/Macaulay2/packages/Matroids/doc-Matroids.m2:3319:0.