Twisted geometries are understood to be the discrete classical limit of Loop Quantum Gravity. In this paper, SU(2) flat connections on (decorated) 2D Riemann surface are shown to be equivalent to the generalized twisted geometries in 3D space with cosmological constant. Various flat connection quantities on Riemann surface are mapped to the geometrical quantities in discrete 3D space. We propose that the moduli space of SU(2) flat connections on Riemann surface generalizes the phase space of twisted geometry or Loop Quantum Gravity to include the cosmological constant.