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Affine Oriented Matroid
An affine oriented matroid is a triple (E, F, g), where (E, F) is an oriented matroid (with ground set E and set of covectors F) and g an element of E, where g is not a loop. Then g is called the infinity element.
The equivalence classes of affine oriented matroids which are defined by isomorphisms which map infinity elements to infinity elements are called abstract dissection types.