LATTICE STRUCTURES

1 . A lattice structure, comprising:

nodes disposed at respective vertices of a quasi-prism model, at respective polygonal face centers of the quasi-prism model, and between the respective vertices and a central axis of the quasi-prism model; and

beams connecting the nodes, wherein each node disposed between a vertex and the central axis is connected to a node at the vertex and to nodes at three neighboring polygonal face centers with respective beams.

2 . The lattice structure of claim 1 , further comprising, for each non-base face of the quasi-prism model, a first quadrilateral structure and a second quadrilateral structure, the first quadrilateral structure being disposed between a first base face and a non-base face of the quasi-prism model, and the second quadrilateral structure being disposed between the non-base face and a second base face of the quasi-prism model.

3 . The lattice structure of claim 1 , further comprising, for each edge between bases of the quasi-prism model, a quadrilateral structure disposed between neighboring non-base faces of the quasi-prism model.

4 . The lattice structure of claim 1 , wherein a first cell that includes the nodes and the beams is connected to a second cell including second nodes and second beams that conform to a second quasi-prism model, wherein a first face of the quasi-prism model overlaps with a second face of the second quasi-prism model.

5 . The lattice structure of claim 4 , wherein the first cell is disposed internally in the lattice structure and the second cell is disposed at a boundary of the lattice structure relative to a dimension of the lattice structure.

6 . The lattice structure of claim 4 , wherein one node at a center of the first face and four nodes at vertices of the first face are connected to the second cell at the second face.

7 . The lattice structure of claim 4 , wherein the second quasi-prism model has a different quantity of faces than the quasi-prism model.

8 . The lattice structure of claim 1 , wherein the lattice structure is included in a cushioning element.

9 . The lattice structure of claim 8 , wherein the cushioning element is included in an insole or a midsole.

10 . A lattice structure, comprising:

a plurality of cells being structured according to a plurality of quasi-prism models, wherein boundary quasi-prism models are fitted to a superstructure boundary, and wherein a first cell of the plurality of cells comprises a peripheral node at each vertex of a first quasi-prism model and at each face center of the first quasi-prism model.

11 . The lattice structure of claim 10 , wherein peripheral beams that are connected to the peripheral nodes at the vertices of the first quasi-prism model are angled to a centroid of the first quasi-prism model without a node at the centroid of the first quasi-prism model.

12 . The lattice structure of claim 10 , wherein the first quasi-prism model comprises a regular triangle base.

13 . A method, comprising:

fitting, by a processor, a plurality of quasi-prism models to a superstructure model having a curved boundary, wherein a set of faces of the quasi-prism models conform to the curved boundary;

determining, by the processor, a lattice structure comprising a plurality of cells corresponding to the plurality of quasi-prism models; and

writing, by the processor, the lattice structure to a file in a memory.

14 . The method of claim 13 , wherein each of the plurality of cells comprises:

nodes disposed at respective vertices of a quasi-prism model, at respective polygonal face centers of the quasi-prism model, and between the respective vertices and a central axis of the quasi-prism model; and

beams connecting the nodes, wherein each node disposed between a vertex and the central axis is connected to a node at the vertex and to nodes at three neighboring polygonal face centers with respective beams.

15 . The method of claim 13 , wherein the superstructure model represents a cushioning element.