Peeking at the impossible (Q1276419)

In `On the cohomology of impossible figures' [Topologie Struct. 17, 11-16 (1991; Zbl 0743.52002)] \textit{R. Penrose} provides a mathematical analysis of certain geometrically impossible objects. Essentially, they are those whose parts cannot be consistently assembled, as is expressed by the failure of certain equations to have solutions. This paper demonstrates that such equations can have solutions if an inconsistent arithmetic, such as that of \textit{G. Priest} [`Inconsistent models of arithmetic. I: Finite models', J. Philos. Log. 26, 223-235 (1997; Zbl 0878.03017)] is employed, and uses this to answer the question of what it is that such an object appears to be.