Rigid origami is seen as a fundamental model in many self-folding machines. A key issue in designing origami is the rigid/nonrigid foldability. The kinematic and foldability of Kresling origami, which is based on an origami pattern of the vertex with six creases, are studied in this paper. The movement of the single-vertex is first discussed. Based on the quaternion method, the loop-closure equation of the vertex with six creases is obtained. Then, the multitransformable behavior of the single vertex is investigated. Furthermore, the rigid foldability of origami patterns with multivertex is investigated with an improved dual quaternion method, which is based on studying the folding angle and the coordinates of all vertices. It can be found that the Kresling cylinder is not rigidly foldable.

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