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 plane elements arranged in at least two interfitting rows of adjacent elements, at least one of said rows being a trapezoid-row which is 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 of said trapezoids of said trapezoid-row has a side in common with a plane element of the adjacent row, the longer and shorter common sides within said trapezoid-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 said interfitting rows include said trapezoid-row and a row comprising trapezoids or triangles interfitting with said trapezoid row.

Claim 4

A structure as in claim 2 in which said trapezoid-row is adjacent to an edge of said structure, the trapezoids of said trapezoid-row each have a side adjacent to said edge and the edge-adjacent sides of adjacent trapezoids of said trapezoid-row are connected by a folded web having an infold hinge in one of said radial planes, with outfold hinges at said edge-adjacent sides.

Claim 5

A structure as in claim 2 in which there is a triangle-row comprising adjacent single congruent triangles arranged in alternation so that each triangle has a hinged side in common with one of its two neighbors of its row and has an apical point in common with the other of its neighbors of its row, the common sides within said triangle-row being infold hinges, arranged within planes which radiate from and include said axis, said apical points being situated on the intersections of infold and outfold hinges.

Claim 6

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 plane elements arranged in at least two interfitting rows of adjacent elements, at least one of said rows being a trapezoid-row which is 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 of said trapezoids of said trapezoid-row has a side in common with a plane element of the adjacent row, the longer and shorter common sides within said trapezoid-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 7

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 plane elements arranged in at least two interfitting rows of adjacent elements, at least one of said rows being a trapezoid-row which is 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 of said trapezoids of said trapezoid-row has a side in common with a plane element of the adjacent row, the longer and shorter common sides within said trapezoid-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 8

A blank as in claim 5 in which said interfitting rows include said trapezoid-row and a row comprising trapezoids or triangles interfitting with said trapezoid row.

Claim 9

A blank as in claim 6 in which said trapezoid-row is adjacent to an edge of said structure, the trapezoids of said trapezoid-row each have a side adjacent to said edge and the edge-adjacent sides of adjacent trapezoids of said trapezoid-row are connected by a folded web having an infold hinge in one of said radial planes, with outfold hinges at said edge-adjacent sides.

Claim 10

A blank as in claim 6 in which there is a triangle-row comprising adjacent single congruent triangles arranged in alternation so that each triangle has a hinged side in common with one of its two neighbors of its row and has an apical point in common with the other of its neighbors of its row, the common sides within said triangle-row being infold hinges, arranged within planes which radiate from and include said axis, said apical points being situated on the intersections of infold and outfold hinges.

Claim 11

A structure as in claim 1 having only two of said trapezoid-rows in mutually interfitting relationship.

Claim 12

A blank as in claim 5 having only two of said trapezoid-rows in mutually interfitting relationship.