This paper describes the construction, properties and potential applications of a cartographic projection recently developed by the author, called the Zenithial Orthotriangular (ZOT) projection of an Octahedron. ZOT maps a planet to a plane by modelling it as an octahedron (a regular solid having 8 equilateral triangular facets), which is then unfolded and stretched to fit within a square. As described below, ZOT is developed from a regular octahedron mapped in North polar aspect, by cutting octant edges of the southern hemisphere from pole to equator, and stretching all octahedral facets to occupy eight identical right triangles (extensions to the ellipsoid are described). The North pole lies at the center of projection, while the South Pole occupies all four corners; points along map borders are mirrored across the central axes. After discussing its cartographic properties, ZOTs relation to the Quaternary Triangular Mesh (QTM ) global tessellation is explored. The use of ZOT is shown to facilitate recursive definition of QTM's geodesic graticule of nested triangles. Computationally, this structure is handled as a quadtree, even though its elements are triangular in shape. Basic procedures for mapping geographic coordinates to QTM quadtree addresses via ZOT are presented and discussed, and suggestions given for standardizing how QTM tiles are addressed in ZOT space. 1 The author gratefully acknowledges encouragement and support for this work from Prime Computer, Inc.