Introduction
Basemath is a wife of Esau, mother of his son Reuel, described in Genesis 36:3 as "daughter of Ishmael", making her marriage to Esau a union between the two branches of Abraham's grandsons through Isaac and Ishmael respectively.
Note: Genesis 26:34 gives a different name, Basemath daughter of Elon the Hittite, for one of Esau's wives, a discrepancy with the Genesis 36 list that scholars generally attribute to differing underlying source traditions.
Family
Marriage and son
Genesis 36:3-4 lists Basemath among Esau's wives, identifying her as Ishmael's daughter, and names their son as Reuel, who becomes, in the same chapter, the father of several further Edomite chiefs.
A marriage across Abraham's two lines
Basemath's identification as a daughter of Ishmael means that, through this marriage, Esau's own Edomite descendants trace ancestry back to both of Isaac's brothers (Ishmael being his half-brother) as well as to Isaac himself, an intertwining the text does not comment on directly but which reflects the close-knit, intermarried character of Abraham's extended family across Genesis.