Polyhedral annular structures, and blanks therefor

Claim 2

A polyhedral structure which is radially substantially symmetrical about a central axis, said structure comprising a number of planar trapezoids hinged together at their sides so as to form a continuous multiplanar toroidal web having two edges, which structure can be rotated, about its core, into a plurality of different stable configurations each of which is radially substantially symmetrical about said central axis, said structure comprising congruent plane trapezoids arranged in at least three rows of adjacent trapezoids, each of said rows being a ring of single trapezoids arranged in alternation so that each trapezoid has a hinged longer side in common with one of its two neighbors of its row and has a hinged shorter side in common with the other of its neighbors of its row, said rows interfitting so that each trapezoid of each row has a side in common with a trapezoid of the adjacent row, the longer and shorter common sides within a row being respectively, infold and outfold hinges arranged within planes which radiate from and include said axis and the sides which adjacent rows have in common being outfold hinges.

Claim 3

A structure as in claim 1 in which two of said rows are adjacent to said edges of said structure and the others of said rows are arranged between said edge-adjacent rows, the trapezoids of said edge-adjacent rows each have a side which is not common to another trapezoid of said rows, and said non-common sides of adjacent trapezoids of said rows are connected by a folded web having an infold hinge in one of said radial planes, with outfold hinges at said non-common sides.

Claim 4

A structure as in claim 1 in which there are four of said rows, said structure being rotatable to 10 different stable positions.

Claim 5

A structure as in claim 1 in which there are three of said rows, said structure being rotatable to eight different stable positions.

Claim 6

A structure as in claim 1 in which said congruent trapezoids are symmetrical.

Claim 7

A structure as in claim 1 in which said congruent trapezoids are asymmetrical.

Claim 8

A flat blank of sheet material, said blank having means, including score lines at which said blank can be folded and edges adapted to be secured together to form a continuous web after said blank is folded at said score lines, for converting said blank to a polyhedral structure which is radially substantially symmetrical about a central axis, said structure comprising a number of planar trapezoids hinged together at their sides so as to form a continuous multiplanar toroidal web having two edges, which structure can be rotated, about its core, into a plurality of different stable configurations each of which is radially substantially symmetrical about said central axis, said structure comprising congruent plane trapezoids arranged in at least three rows of adjacent trapezoids, each of said rows being a ring of single trapezoids arranged in alternation so that each trapezoid has a hinged longer side in common with one of its two neighbors of its row and has a hinged shorter side in common with the other of its neighbors of its row, said rows interfitting so that each trapezoid of each row has a side in common with a trapezoid of the adjacent row, the longer and shorter common sides within a row being, respectively, infold and outfold hinges arranged within planes which radiate from and include said axis and the sides which adjacent rows have in common being outfold hinges, said score lines being situated so that, on folding, they form the boundaries of said trapezoids.

Claim 9

A flat blank of sheet material, said blank having means, including score lines at which said blank can be folded and edges adapted to be secured together to form a continuous web after said blank is folded at said score lines, for converting said blank to a polyhedral structure which is radially substantially symmetrical about a central axis, said structure comprising a number of planar trapezoids hinged together at their sides so as to form a continuous multiplanar toroidal web having two edges, which structure can be rotated, about its core, into a plurality of different stable configurations each of which is radially substantially symmetrical about said central axis, said structure comprising congruent plane trapezoids arranged in at least three rows of adjacent trapezoids, each of said rows being a ring of single trapezoids arranged in alternation so that each trapezoid has a hinged longer side in common with one of its two neighbors of its row and has a hinged shorter side in common with the other of its neighbors of its row, said rows interfitting so that each trapezoid of each row has a side in common with a trapezoid of the adjacent row, the longer and shorter common sides within a row being, respectively, infold and outfold hinges arranged within planes which radiate from and include said axis and the sides which adjacent rows have in common being outfold hinges, said score lines being situated so that, on folding, they form the boundaries of said trapezoids.

Claim 10

A blank as in claim 7 in which two of said rows are adjacent to said edges of said structure and the others of said rows are arranged between said edge-adjacent rows, the trapezoids of said edge-adjacent rows each have a side which is not common to another trapezoid of said rows, and said non-common sides of adjacent trapezoids of said rows are connected in said structure by a folded web having an infold hinge in one of said radial planes, with outfold hinges at said non-common sides.

Claim 11

A blank as in claim 7 in which there are four of said rows, said structure being rotatable to 10 different stable positions.

Claim 12

A blank as in claim 7 in which there are three of said rows, said structure being rotatable to eight different stable positions.

Claim 13

A blank as in claim 7 in which said congruent trapezoids are symmetrical.

Claim 14

A blank as in claim 7 in which said congruent trapezoids are asymmetrical.