We propose a new paradigm for realizing bound states in the continuum (BICs) by engineering the environment of a system to control the number of available radiation channels. Using this method, we demonstrate that a photonic crystal slab embedded in a photonic crystal environment can exhibit both isolated points and lines of BICs in different regions of its Brillouin zone. Finally, we demonstrate that the intersection between a line of BICs and line of leaky resonance can yield exceptional points connected by a bulk Fermi arc. The ability to design the environment of a system opens up a broad range of experimental possibilities for realizing BICs in three-dimensional geometries, such as in 3D-printed structures and the planar grain boundaries of self-assembled systems.Bound states in the continuum (BICs), which are radiation-less states in an open system whose frequency resides within the band of radiative channels, have recently attracted a great deal of interest for their applications in producing vector beams from surface emitting lasers [1][2][3][4][5][6][7][8] and enhancing the resolution of certain classes of sensors [9][10][11]. Originally proposed in 1929 in a quantum mechanical context [12], BICs have now been found in a broad range of physical systems, such as photonic crystal slabs [13][14][15][16][17][18][19][20][21][22][23][24][25], waveguide arrays [26-28], strongly coupled plasmonic-photonic systems [29], metasurfaces [30] acoustics [31][32][33][34][35][36], and water waves [37][38][39][40][41][42]. Additionally, lines of BICs were recently found in composite birefringent structures [43,44]. In principle, BICs can be classified into three main categories [45]: those which are engineered using an inverse construction method, those which are protected by symmetry or separability, and those which can be found 'accidentally' through tuning a system's parameters. In practice however, systems supporting BICs from the first category are difficult to experimentally realize due to the high degree of fine-tuning required. Thus, much of the current excitement surrounding BICs has focused on systems which feature symmetry-protected and accidental BICs; moreover, these BICs have been shown to possess topological protection that guarantees their existence under perturbations to the system [20,[46][47][48][49][50].Traditionally, the appearance of accidental BICs is understood in terms of modal interference [22,45,51], with two or more resonances of the device destructively interfering in the system's radiation channels and resulting in a bound mode spatially localized to the device. This interpretation emphasizes how tuning the device's parameters changes the spatial profile of its resonances to realize this modal interference, while considering the available radiation channels in the surrounding environment as fixed. This is because most previously studied * awc19@psu.edu systems with accidental BICs consider devices embedded in free space, where the outgoing propagating channels cannot be readily altered. Howev...