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This 3D lattice of icosahedra and octahedra was inspired by the paper that Dirk Huylebrouck submitted to the 2017 Bridges conference entitled “On Infinite Kepler-Poinsot Polyhedra” and available at http://archive.bridgesmathart.org/2017/bridges2017-313.pdf.
All shared icosahedra and octahedra faces are removed leaving a single infinitely repeating polyhedron with 7 equalateral triangles joining at each vertex. Three faces coming from an octahedron and four from an icosahedron.
The finite portion shown here contains 2600 faces. The openings on each octahedral tunnel between Icosahedron reveal what could be considered the “inside”, though in reality, there are two sides to this infinite surface, but no real inside or outside except to the individual polyhedra from which it is generated. Hexagonal and triangular tunnels are visible as well.
Try traveling around through them from either the inside or the outside without crossing through any faces.
The model was generated with vZome.
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