Scattering amplitudes are key ingredients for cross sections relevant to collider physics. In the last decade, novel geometric ideas have emerged that hint at a completely different formulation of quantum field theory. For example, the Amplituhedron provides, via geometric means, the all-loop integrand of planar scattering amplitudes in maximally supersymmetric Yang-Mills theory. Unfortunately, dimensional regularization, used conventionally for integration, breaks the beautiful geometric picture. This motivates us in this talk to propose a ‘deformed’ Amplituhedron, which is well-defined in four dimensions. Leveraging four-dimensional integration techniques based on differential equations, we compute the four-particle amplitude up to two loops, as a function of the two deformation parameters. The latter can be interpreted as certain mass and energy variables. We observe simple behaviour in various physical limits of the parameters.