Recent writings in transformational theory by David Lewin and Henry Klumpenhouwer have introduced the "Klumpenhouwer network," which recognizes both transpositional and inversional relationships within a single pitch-class collection. In constructing their networks, Klumpenhouwer and Lewin have insisted that an interval within each network remains invariant while inversional relationships change. They describe transformations of this kind as either "positive" or "negative" isography. There are, however, some relationships that cannot be accounted for by conventional network isography. Graphs may be musically and orthographically connected and yet not fit one of Klumpenhouwer's or Lewin's definitions. This paper demonstrates another kind of isography, deemed "axial" isography, in which an inversional relationship is preserved. The paper draws from the music of Schoenberg and Berg to illustrate operations that map axially isographic networks onto each other. I then demonstrate how positive, negative, and axial isography can work together for a single analysis. The results thus extend the applicability of network isography into a broader range of musical contexts.