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The examples illustrated in the Transformation section give an indication of the range of geometric possibilities available to the network.
There is however a condition illustrated in Animation_10 that attracts the eye. It involves combinations of tetrahedral and octahedral cells resulting from specific distortions of the network. Although not immediately apparent these combinations define prolate & oblate hexahedral 'multicells' each consisting of two tetrahedra & one octahedron. The prolate multicells have six identical rhombic faces with diagonals in the ratio one:root three. The oblate multicells have four rhombic faces in the ratio one:root three and two in the ratio root two:root two. Specific combinations of these multicells define semiregular stellar polyhedra with sixty faces - 12 square and 48 rhombic.
A transition from the condition already described results in a set of multicell polyhedra with all rhombic faces identical in the ratio 1:1.618, the Golden Section or Phi. For convenience this unique rhombus is often referred to as the Phi rhomb. The phi rhomb multicells also combine to form semi regular stellar polyhedra each with 60 faces in the ratio 1:1.618.
These Phi stella are of particular interest in that they can aggregate recursively or non recursively i.e. both aggregations fill space to infinity but the recursive aggregation displays cubic symmetry (2,3,4,symmetry) with the non recursive aggregation displaying icosahedral symmetry (2,3,5,symmetry).
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