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A micro-truss sheet having material properties varying across the sheet. The sheet may include a plurality of truss members intersecting at nodes. The diameter of the truss members at one point in the sheet may differ from the diameter of the truss members at another point in the sheet. In one embod

A micro-truss sheet having material properties varying across the sheet. The sheet may include a plurality of truss members intersecting at nodes. The diameter of the truss members at one point in the sheet may differ from the diameter of the truss members at another point in the sheet. In one embodiment the spacing between adjacent truss members may be different in one part of the sheet from the spacing between adjacent truss members in another part of the sheet.

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1. A micro-truss sheet, including: a plurality of first truss members defined by a plurality of first self-propagating polymer waveguides and extending along a first direction;a plurality of second truss members defined by a plurality of second self-propagating polymer waveguides and extending along

1. A micro-truss sheet, including: a plurality of first truss members defined by a plurality of first self-propagating polymer waveguides and extending along a first direction;a plurality of second truss members defined by a plurality of second self-propagating polymer waveguides and extending along a second direction; anda plurality of third truss members defined by a plurality of third self-propagating polymer waveguides and extending along a third direction;wherein each truss member has a diameter;the sheet having a length substantially greater than its thickness, andthe sheet having a first region comprising a plurality of first unit cells and a second region comprising a plurality of second unit cells, the first region and the second region being separated along the length of the sheet,wherein all the truss members within the first unit cells have the same diameter,wherein all the truss members within the second unit cells have the same diameter,wherein the diameter of each of the plurality of first truss members, the plurality of second truss members, and the plurality of third truss members within the first unit cellsin the first regionis at least 10% greater thanthe diameter of each of the plurality of first truss members, the plurality of second truss members, and the plurality of third truss members within the second unit cellsin the second region, andwherein the micro-truss sheet forms one continuous body, having a gradient in the diameter of the truss members of the plurality of first truss members, the plurality of second truss members, and the plurality of third truss members, along the length of the sheet. 2. The micro-truss sheet of claim 1, wherein the diameter of each of the plurality of first truss members, the plurality of second truss members, and the plurality of third truss members within the first unit cells in the first region along the length of the sheetis at least a factor of two greater thanthe diameter of each of the plurality of first truss members, the plurality of second truss members, and the plurality of third truss members within the second unit cellsin the second region along the length of the sheet. 3. The micro-truss sheet of claim 1, wherein the first truss members, the second truss members, and the third truss members form a periodic structure, wherein a unit cell size of the periodic structure is substantially constant along the length of the sheet. 4. The micro-truss sheet of claim 1, wherein the diameter of each of the plurality of first truss members, the plurality of second truss members, and the plurality of third truss members is less than 10 mm. 5. The micro-truss sheet of claim 1, wherein the diameter of each of the plurality of first truss members, the plurality of second truss members, and the plurality of third truss members is greater than 10 microns. 6. The micro-truss sheet of claim 1, wherein the plurality of first truss members, the plurality of second truss members, and the plurality of third truss members intersect at nodes, wherein the diameter of each of the plurality of first truss members, the plurality of second truss members, and the plurality of third truss members is less than ⅓ of a minimum distance between nodes. 7. The micro-truss sheet of claim 1, wherein the plurality of first truss members, the plurality of second truss members, and the plurality of third truss members intersect at nodes, wherein, in the first region, the diameter of each of the plurality of first truss members, the plurality of second truss members, and the plurality of third truss members is greater than 1/20 of a minimum distance between nodes. 8. The micro-truss sheet of claim 1, wherein the sheet has a width, in a direction orthogonal to the length, substantially greater than its thickness, the sheet having a third region comprising a plurality of third unit cells and a fourth region comprising a plurality of fourth unit cells, the third region and the fourth region being separated along the width of the sheet,wherein all the truss members within the third unit cells have the same diameter,wherein all the truss members within the fourth unit cells have the same diameter, andwherein the diameter of each of the plurality of first truss members, the plurality of second truss members, and the plurality of third truss members within the third unit cellsin the third regionis at least 10% greater thanthe diameter of each of the plurality of first truss members, the plurality of second truss members, and the plurality of third truss members within the fourth unit cellsin the fourth region. 9. The micro-truss sheet of claim 8, wherein the diameter of each of the plurality of first truss members, the plurality of second truss members, and the plurality of third truss members within the third unit cellsin the third regionis at least a factor of 2 greater thanthe diameter of each of the plurality of first truss members, the plurality of second truss members, and the plurality of third truss members within the fourth unit cellsin the fourth region. 10. The micro-truss sheet of claim 1, wherein the first truss members, the second truss members, and the third truss members form a periodic structure, wherein a unit cell size of the periodic structure in the first region along the length of the sheet differs from a unit cell size in the second region along the length of the sheet. 11. The micro-truss sheet of claim 10, wherein: the unit cell shape of the periodic structure in the first region along the length of the sheet is the same as the unit cell shape in the second region along the length of the sheet, andthe unit cell size of the periodic structure in the first region along the length of the sheet is a positive integer times the unit cell size in the second region along the length of the sheet. 12. The micro-truss sheet of claim 1, wherein the ratio of the diameter of a truss member of the plurality of first truss members, the plurality of second truss members, and the plurality of third truss members in the first region, toa minimum distance between nodesin the first regionis substantially the same as the ratio ofthe diameter of a truss member of the plurality of first truss members, the plurality of second truss members, and the plurality of third truss members in the second region, toa minimum distance between nodesin the second region. 13. The micro-truss sheet of claim 1, the sheet having a third region comprising a plurality of third unit cells and a fourth region comprising a plurality of fourth unit cells, the third region and the fourth region being separated along the thickness of the sheet,wherein all the truss members within the third unit cells have the same diameter,wherein all the truss members within the fourth unit cells have the same diameter, andwherein the diameter of each of the plurality of first truss members, the plurality of second truss members, and the plurality of third truss members within the third unit cellsin the third regionis at least 10% greater thanthe diameter of each of the plurality of first truss members, the plurality of second truss members, and the plurality of third truss members within the fourth unit cellsin the fourth region. 14. The micro-truss sheet of claim 1, wherein the first unit cell includes an open volume enclosed by first, second, and third truss members. 15. The micro-truss sheet of claim 14, wherein the open volume is enclosed only by the largest diameter first, second, and third truss members within the first unit cell. 16. The micro-truss sheet of claim 1, wherein the sheet has a third region, the third region comprising a plurality of third unit cells and being separated from the first region and from the second region along the length of the sheet, wherein all the truss members within the third unit cells have the same diameter, andwherein the diameter of each of the plurality of first truss members, the plurality of second truss members, and the plurality of third truss members within the third unit cellsin the third regionis at least 10% less thanthe diameter of each of the plurality of first truss members, the plurality of second truss members, and the plurality of third truss members within the second unit cellsin the second region. 17. The micro-truss sheet of claim 1, wherein the diameter of each of the plurality of first truss members, the plurality of second truss members, and the plurality of third truss members within the first unit cellsin the first regionis at least 20% greater thanthe diameter of each of the plurality of first truss members, the plurality of second truss members, and the plurality of third truss members within the second unit cellsin the second region. 18. The micro-truss sheet of claim 1, wherein the diameter of each of the plurality of first truss members, the plurality of second truss members, and the plurality of third truss members within the first unit cellsin the first regionis at least 30% greater thanthe diameter of each of the plurality of first truss members, the plurality of second truss members, and the plurality of third truss members within the second unit cellsin the second region. 19. A three-dimensional ordered open-cellular sheet, having a length substantially greater than its thickness, and including:(i) a first three-dimensional interconnected pattern of truss members defined by a plurality of first self-propagating polymer waveguides, in a first region of the sheet,the first three-dimensional interconnected pattern of truss members comprising: a plurality of first truss members defined by a plurality of first self-propagating polymer waveguides and extending along a first direction;a plurality of second truss members defined by a plurality of second self-propagating polymer waveguides and extending along a second direction; anda plurality of third truss members defined by a plurality of third self-propagating polymer waveguides and extending along a third direction;the first region of the sheet comprising a plurality of first unit cells;(ii) a second three-dimensional interconnected pattern of truss members defined by a plurality of second self-propagating polymer waveguides, in a second region of the sheet, separated from the first region along the length of the sheet,the second three-dimensional interconnected pattern of truss members comprising: a plurality of first truss members defined by a plurality of first self-propagating polymer waveguides and extending along a first direction;a plurality of second truss members defined by a plurality of second self-propagating polymer waveguides and extending along a second direction; anda plurality of third truss members defined by a plurality of third self-propagating polymer waveguides and extending along a third direction;the second region of the sheet comprising a plurality of second unit cells; the first three-dimensional interconnected pattern differing from the second three-dimensional interconnected pattern; and(iii) a transition connected with the first three-dimensional interconnected pattern of truss members and the second three-dimensional interconnected pattern of truss members as one continuous body,the transition comprising: a plurality of first truss members defined by a plurality of first self-propagating polymer waveguides and extending along a first direction;a plurality of second truss members defined by a plurality of second self-propagating polymer waveguides and extending along a second direction; anda plurality of third truss members defined by a plurality of third self-propagating polymer waveguides and extending along a third direction;wherein the transition has a gradient in the diameter of the truss members of the plurality of first truss members, the plurality of second truss members, and the plurality of third truss members, along the length of the three-dimensional ordered open-cellular sheet,wherein all the truss members within the first unit cells have the same diameter,wherein all the truss members within the second unit cells have the same diameter,wherein the diameter of each of the plurality of first truss members, the plurality of second truss members, and the plurality of third truss members within the first unit cellsin the first regionis at least 10% greater thanthe diameter of each of the plurality of first truss members, the plurality of second truss members, and the plurality of third truss members within the second unit cellsin the second region. 20. The three-dimensional ordered open-cellular sheet of claim 19, wherein the transition is a third three-dimensional interconnected pattern of truss members defined by a plurality of third self-propagating polymer waveguides, the third three-dimensional interconnected pattern differing from the first three-dimensional interconnected pattern and the second three-dimensional interconnected pattern. 21. The three-dimensional ordered open-cellular sheet of claim 20, wherein: the truss members of the third three-dimensional interconnected pattern respectively extend along different directions; andthe truss members of the third three-dimensional interconnected pattern interpenetrate each other at a plurality of nodes to form a self-supporting structure. 22. The three-dimensional ordered open-cellular sheet of claim 21, wherein at least two of the truss members of the third three-dimensional interconnected pattern intersect each other at a node of the plurality of nodes at non-perpendicular angles. 23. The three-dimensional ordered open-cellular sheet of claim 21, wherein at least three of the truss members of the third three-dimensional interconnected pattern intersect each other at a node of the plurality of nodes at non-perpendicular angles. 24. The three-dimensional ordered open-cellular sheet of claim 21, wherein at least four of the truss members of the third three-dimensional interconnected pattern intersect each other at a node of the plurality of nodes at non-perpendicular angles. 25. The three-dimensional ordered open-cellular sheet of claim 19, wherein the first and second three-dimensional interconnected patterns have order in three dimensions.