Polytypes are a special case of polymorphs, where multiple close-packed crystal structures differ in one dimension only.  Polytypes have identical close-packed planes, but differ in the stacking sequence in the third dimension perpendicular to these planes. Silicon carbide (SiC) has more than 170 known polytypes, although most are rare.  All the polytypes of SiC have virtually the same density and Gibbs free energy. The most common SiC polytypes are shown in Table 1.
Table 1: Some polytypes of SiC.
A second group of materials with different polytypes are the transition metal dichalcogenides, layered materials such as molybdenum disulfide (MoS). For these materials the polytypes have more distinct effects on material properties, e.g. for MoS, the 1T polytype is metallic in character, while the 2H form is more semiconducting.
Another example is tantalum disulfide, where the common 1T as well as 2H polytypes occur, but also more complex mixed coordination types such as 4Hb and 6R, where the trigonal prismatic and the octahedral geometry layers are mixed. Here, the 1T polytype exhibits a charge density wave, with distinct influence on the conductivity as a function of temperature, while the 2H polytype exhibits superconductivity.
ZnS and CdI are also polytypical. It has been suggested that this type of polymorphism is due to kinetics where screw dislocations rapidly reproduce partly disordered sequences in a periodic fashion.