Flat-twist origami patterns are of superiorly foldable properties, therefore, have been used to design metamaterials and deployable structures. However, most of the flat-twists such as hexagon-twist patterns are non-rigid foldable which limits their applications due to the complex deformations. Here, several rigid-foldable hexagon-twist patterns with lower degree-of-freedom (DOF) are proposed by adding creases and modifying the mountain-valley arrangements. Four one-DOF two-dimensional tessellations of rigid hexagon-twist patterns are created by translationally connecting facets and creases. Furthermore, one of four tessellations is chosen to construct a three-dimensional tessellation by sharing specific edges for the potential design of metamaterial. The work widens the road to construct rigid-foldable origami patterns.