  We characterize a set of positive maps in matrix algebra of 4x4 complex
matrices. Equivalently, we provide a subset of entanglement witnesses
parameterized by the rotation group SO(3). Interestingly, these maps/witnesses
define two intersecting convex cones in the 3-dimensional parameter space. The
existence of two cones is related to the topological structure of the
underlying orthogonal group. We perform detailed analysis of the corresponding
geometric structure.
