A system for expanding a flat-stock paper precursor material having a plurality of rows and a plurality of columns (A, B) of unfolded precursor chips into a plurality of separate expanded triangular packing elements, the system comprising: a base; an end plate rotatably engaged with the base, wherein the end plate is adapted to rotate about an axis substantially orthogonal to the base; a stage to guide the flat-stock paper precursor material onto the system; a first jaw extending from the end plate, wherein the first jaw comprises a first pivotable clamp comprising a pin configured to accept the flat-stock precursor material, a fixed base portion, and a second pivotable clamp disposed opposite the fixed base portion from the first pivotable clamp and wherein the first jaw is pivotably engaged with the end plate, wherein as the end plate rotates about the axis, the first jaw defines a first separation angle (α) when the end plate is at a first position and the first jaw defines a second separation angle (α) as the end plate rotates towards a second position, and wherein a change from the first separation angle (α) to the second separation angle (α) tears a connecting tab that separates a leading row (R 1) of the plurality of rows from an adjacent row (R 2) of the plurality of rows and folds the leading row (R 1) of the plurality of rows into a plurality of connected folded precursor chips; and a crimper comprising a plurality of teeth configured to penetrate between adjacent columns (A, B) of the plurality of connected folded precursor chips, wherein the penetration separates a first folded precursor chip from an adjacent folded precursor chip, wherein, once separated, the first folded precursor chip and the adjacent folded precursor chip comprise two of the plurality of expanded triangular packing elements and are configured to fall from the first jaw as the first jaw opens towards the first separation angle (α). a base; an end plate rotatably engaged with the base, wherein the end plate is adapted to rotate about an axis substantially orthogonal to the base; a stage to guide the flat-stock paper precursor material onto the system; a first jaw extending from the end plate, wherein the first jaw comprises a first pivotable clamp comprising a pin configured to accept the flat-stock precursor material, a fixed base portion, and a second pivotable clamp disposed opposite the fixed base portion from the first pivotable clamp and wherein the first jaw is pivotably engaged with the end plate, wherein as the end plate rotates about the axis, the first jaw defines a first separation angle (α) when the end plate is at a first position and the first jaw defines a second separation angle (α) as the end plate rotates towards a second position, and wherein a change from the first separation angle (α) to the second separation angle (α) tears a connecting tab that separates a leading row (R 1) of the plurality of rows from an adjacent row (R 2) of the plurality of rows and folds the leading row (R 1) of the plurality of rows into a plurality of connected folded precursor chips; and a crimper comprising a plurality of teeth configured to penetrate between adjacent columns (A, B) of the plurality of connected folded precursor chips, wherein the penetration separates a first folded precursor chip from an adjacent folded precursor chip, wherein, once separated, the first folded precursor chip and the adjacent folded precursor chip comprise two of the plurality of expanded triangular packing elements and are configured to fall from the first jaw as the first jaw opens towards the first separation angle (α).