# Geometric Interpretation of Simultaneous Primal and Dual LP Infeasibility

There are examples of linear programming (LP) problems where both the primal and dual problems are infeasible. For example, \begin{aligned} &\min_x && x \\ &\ \ \text{s.t.} &&0\cdot x\leq -1 \end{aligned} On the other hand, there are examples of linear programming problems where the primal is infeasible and the dual is unbounded. For example, \begin{aligned} &\min_x && x \\ &\ \ \text{s.t.} && x\geq 1 \\ & && x\leq 0 \\ \end{aligned} I am wondering: is there any geometric interpretation of this phenomenon? Is there some geometric difference between those infeasible LPs with infeasible duals and those infeasible LPs with unbounded duals?