Patent ID: 8072453

Claim:
A folded material formed from a sheet product, wherein: the folded material has an array of facets with neighboring facets in the array connected across fold crease edges, where the fold crease edges form a net on the folded material, and where the facet and fold crease edges in the folded material corresponds to a facet and fold crease pattern in an unfolded sheet pattern, edges in the unfolded sheet pattern forming a net of fold edges corresponding to the fold crease edges, wherein the net of fold edges comprises: a plurality of row edge chains, each row edge chain being a chain of fold edges connected along a row direction, each being of one fold convexity in the folded material; and a plurality of column edge chains, each column edge chain being a chain of fold edges connected along a column direction and of mixed fold convexity; wherein the plurality of row edge chains and the plurality of column edge chains satisfy at least one of conditions (A), (B), (C) or (D) below: A) each row edge chain comprises vertices and edge vectors that are an incremental difference between successive vertices that satisfy at least one of i) at least four edge vectors are different; ii) at least three of the lengths of the edge vectors are different; and iii) at least two unsigned included angles at the vertices of the row edge chain are different; B) each row edge chain comprises vertices and row edge vectors that are an incremental difference between successive row vertices such that at least three of the row edge vectors are different, and each column edge chain comprises vertices and column edge vectors that are an incremental difference between successive column vertices that satisfy at least one of: i) at least two unsigned included angles at the vertices of the column edge chain are different; ii) at least two of the lengths of the column edge vectors are different; and iii) at least three of the column edge vectors are different and the side of the vertex that has the angle that is less than 180 degrees varies at least once along the column edge chain; C) each column edge chain comprises vertices and edge vectors that are an incremental difference between successive vertices that satisfy at least one of: i) the column edge chain comprises at least 18 vertices and three of the edge vectors are different; ii) at least four of the edge vectors have different lengths; and iii) at least three of the unsigned included angles at the vertices are different; and D) each column edge chain comprises a quadrilateral and each row edge chain comprises vertices and row edge vectors that are an incremental difference between successive row vertices such that at least three row edge vectors are different.