On Hoffman's celebrated cycling LP example

We answer two questions that naturally arise while dealing with Hoffman's celebrated 50-year-old linear program to be solved by the primal simplex method, where an angle θ$\theta$ and a scaling factor ω$\omega$ are adjustable parameters. In particular, we determine what conditions have to be imposed on ω$\omega$ for classical cycling to occur with θ=2π/5$\theta =2\pi /5$, and what on θ$\theta$ with ω=±tan(θ)$\omega =\pm \tan (\theta )$. The first answer reveals that the sufficient condition widely spread over the literature is false, so fixing it turns this example into a correct example of classical cycling. Some progress towards necessary and sufficient conditions for cycling to occur in this example is also reported.