Biaxially twisted structure

Abstract

The present invention provides a biaxially twisted structure having curved developable surfaces which can be represented by a simple net. The net is in a two-dimensional shape of two congruent rotationally symmetric convex polygons misalignedly connected along a shared edge. A three-dimensional shape of the structure can be reconstructed from the net by sequentially connecting its edges. The structure has a unique design and mechanical feature, which can be utilized as a box, container, part, toy, building and so on.

1 . A structure, having a three-dimensional shape that can be represented by a net in a two-dimensional shape, the two-dimensional shape of the net comprising:
 2 congruent rotationally symmetric convex polygons,
 wherein the polygon is a n-gon and n is an integer more than 3; 
   2n three-valent main-vertices,
 wherein each of the main-vertices is placed at each corner of the polygons without overlapping; 
   2n three-valent sub-vertices,
 wherein n of the sub-vertices are placed at rotationally symmetric positions within each of the polygons without overlapping; 
   2n main-edges,
 wherein each of the main-edges is straight, and 
 each of the main-edges connects 2 of the main-vertices without crossing; and 
   4n sub-edges,
 wherein each of the sub-edges is either straight or curved, 
 each of the sub-edges connects two of the sub-vertices or 
 connects one of the main-vertices and one of the sub-vertices, and 
 2n of the sub-edges are placed at rotationally symmetric positions within each of the polygons without crossing, 
   wherein:   each of the main-vertices contacts 2 of the main-edges and one of the sub-edges, and   each of the sub-vertices contacts 1 main-edge and the 2 sub-edges, and   wherein the structure has curved developable surfaces with a biaxially twisted appearance.   
     
     
         2 . The structure of  claim 1 , wherein the polygon is a regular polygon. 
     
     
         3 . The structure of  claim 1 , wherein the structure is a box and the net further comprises a plurality of flaps and/or crease lines. 
     
     
         4 . The structure of  claim 1 , wherein the structure is a container formed in the three-dimensional shape that can be represented by the net. 
     
     
         5 . The structure of  claim 1 , wherein the structure rotates in a flow about its rotational axis when a direction of the rotational axis is in parallel to a direction of the flow.