Octahedron fractal graph

Design by henryseg

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IRL.

Rhino render, along axis.

Rhino render.

Rhino render, along diagonal.

IRL.

IRL face.

IRL corner.

This is a graph embedded in 3-dimensional space as a subset of an "octahedral lattice", which is related to the tessellation of space using octahedra and tetrahedra. The graph has a fractal structure, formed by a process of repeated substitution. Each vertex at each step of the construction is degree 4, and is replaced at the next step by 6 vertices arranged in an octahedron, with certain choices of edges connecting them to each other. Each edge is replaced at the next step by 2 parallel edges. We begin the construction with the first step being the edges of an octahedron, and this is the result at the fourth step.

cm: 6.938 w x 6.938 d x 6.938 h

in: 2.731 w x 2.731 d x 2.731 h