# Definition Topological crystalline insulators (TCIs) are a class of [[topological insulator|topological insulators]] protected by [[Spatial Symmetry|spatial symmetries]] such as [[Mirror Symmetry]]. They cannot be deformed into a [[Trivial Insulator]] without breaking the crystal symmetries. They have [[Topological Surface State|topological surface states]] on certain high-symmetry crystal surfaces. They can be considered the counterpart of [[Time-Reversal Symmetric Topological Insulator|time-reversal symmetric topological insulators]] without [[Spin-Orbit Coupling]]. They are characterized by a different [[topological invariant]] from the $Z_2$ [[Z2 Topological Invariant|topological invariant]] used in these systems. # Examples Bismuth is a well-known TCI.