We examine a multistate logic computation scheme based on nanomagnets with configurational anisotropy (CA). We present a case study of a structure comprising a thin equilateral triangle - exhibiting sixfold CA - and three surrounding bistable inputs/outputs, where all nanomagnets generally can be interconnected by nanomagnetic chains and adiabatically clocked by external magnetic fields. We analyze the design and operation of the triangle with three-dimensional micromagnetic simulations of the magnetization configurations and dynamics, the effect of thermal fluctuations, and the propagation of information to an output nanomagnet. As a proof of concept, we demonstrate reconfigurable nand/nor and or/and gates as potential logic applications. We highlight further applications and suggest directions for future research.