All boundaries of the m=2 amplituhedron A_{n,k}^{(2)} are classified, the boundary poset is Eulerian, and the Euler characteristic equals one.
Grassmannian Geometry of Scattering Amplitudes
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On the Boundaries of the m=2 Amplituhedron
All boundaries of the m=2 amplituhedron A_{n,k}^{(2)} are classified, the boundary poset is Eulerian, and the Euler characteristic equals one.