An implantable apparatus, comprising: a porous three-dimensional structure shaped to be implanted in a patient's body, the porous three-dimensional structure including a plurality of interconnected organic unit cells, each organic unit cell including: a plurality of outer struts, wherein respective groups of three outer struts intersect so as to define a respective plurality of outer nodes, and wherein the plurality of outer struts combine to define a lattice structure; and a plurality of internal struts, each internal strut extending from a different respective one of the outer nodes, and the internal struts intersect so as to define an internal node, wherein the plurality of outer nodes includes a first outer node defined by the intersection of a first group of three outer struts and a second outer node defined by the intersection of a second group of three outer struts, characterized in that: the second outer node is opposite the first outer node such that the first and second outer nodes are spaced further from each other than from any other node, wherein a shortest path along the outer struts from the first outer node to the second outer node includes only three intermediate outer nodes of the plurality of outer nodes, and wherein a straight imaginary line extends through the first outer node and the second outer node, and the internal node is offset from the straight imaginary line. a porous three-dimensional structure shaped to be implanted in a patient's body, the porous three-dimensional structure including a plurality of interconnected organic unit cells, each organic unit cell including: a plurality of outer struts, wherein respective groups of three outer struts intersect so as to define a respective plurality of outer nodes, and wherein the plurality of outer struts combine to define a lattice structure; and a plurality of internal struts, each internal strut extending from a different respective one of the outer nodes, and the internal struts intersect so as to define an internal node, a plurality of outer struts, wherein respective groups of three outer struts intersect so as to define a respective plurality of outer nodes, and wherein the plurality of outer struts combine to define a lattice structure; and a plurality of internal struts, each internal strut extending from a different respective one of the outer nodes, and the internal struts intersect so as to define an internal node, wherein the plurality of outer nodes includes a first outer node defined by the intersection of a first group of three outer struts and a second outer node defined by the intersection of a second group of three outer struts, characterized in that: the second outer node is opposite the first outer node such that the first and second outer nodes are spaced further from each other than from any other node, wherein a shortest path along the outer struts from the first outer node to the second outer node includes only three intermediate outer nodes of the plurality of outer nodes, and wherein a straight imaginary line extends through the first outer node and the second outer node, and the internal node is offset from the straight imaginary line. the second outer node is opposite the first outer node such that the first and second outer nodes are spaced further from each other than from any other node, wherein a shortest path along the outer struts from the first outer node to the second outer node includes only three intermediate outer nodes of the plurality of outer nodes, and wherein a straight imaginary line extends through the first outer node and the second outer node, and the internal node is offset from the straight imaginary line.