Fun Topology

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Fun Topology
Field: Topology
Image Created By: Paul Nylander
Website: Paul Nylander's Website

Fun Topology

The topology is equivilent to a sphere with 30 holes. The boundary of each hole loops over itself twice with two Reidemeister-I twists and links with 6 others.


A More Mathematical Explanation

Author's Comments: "Here is my attempt to recreate a similar-looking structure to Bathsheba Grossman’s beautiful Quin Pendant Lamp. The topology is equivilent to a sphere with 30 holes. The boundary of each hole loops over itself twice with two Reidemeister-I twists and links with 6 others. I’m still not sure what the linking number of this 30-component knot is (let me know if you find out). In terms of symmetry, it can by described as: # a dodecahedron with a hole over each edge # an icosahedron with a hole over each edge # an icosahedron with a hole over each vertex # a rhombic triacontahedron with a hole over each face (the arms trace a graph isomorphic to the edge graph) Special thanks to Jonathan Schneider for pointing out these interesting observations to me."









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