Reversibly expandable structures having polygon links

A reversibly expandable loop assembly comprising:

• a plurality of links having a polygonal profile with three or more corners, a center pivot joint and a plurality of corner pivot joints, each of at least two of said plurality of corner pivot joints proximate to at least two of said three or more corners, respectively, said plurality of corner pivot joints comprising at least one internal corner pivot joint and at least one perimeter corner pivot joint proximately located to the outer edge of said loop assembly;
• each of said plurality of links connected to another one of said plurality of links at said center pivot joint thereby forming a link pair, said loop assembly comprising at least three link pairs;
• each of said at least three link pairs connected to at least two other link pairs, through at least one of said internal corner pivot joints;
• wherein said loop assembly has a unique polygon perimeter outline comprising a ring of line-segments, each line segment comprised of a line which intersects two perimeter corner joints of one of said link pairs, said line segments being equivalent in number to the number of link pairs in said loop assembly;
• and
• wherein the angle formed between any two line-segments corresponding to a particular two link pairs in a given position of the loop assembly, is the same as the similarly formed angle between the line segments corresponding to the same two link pairs for any other position of the loop assembly, whereby the size of the ring of line-segments increases with expansion of said loop assembly and decreases with retraction of said loop assembly.