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This is a graph embedded in 3-dimensional space as a subset of the cubic lattice. The graph has a fractal structure, formed by a process of repeated substitution. Each vertex at each step of the construction is degree 3, and has the incident edges arranged either in a 'T' formation, or like a corner of a cube. The vertex is replaced at the next step by a subgraph of a 3 x 3 x 3 cubical grid, the choice determined by whether the edges meeting at the vertex are in the 'T' or 'corner' shape. Each edge is replaced at the next step by four parallel edges, joining to the midpoints of the sides of each 3 x 3 face of the 3 x 3 x 3 cubical grid. We begin the construction with the first step being three edges meeting in a corner formation, and this is the result at the fourth step.