Title: Knot complements that decompose into regular ideal platonic solids
Speaker: Neil Hoffman (University of Melbourne)
Abstract: Aitchison and Rubinstein completed a list of examples of link complements decomposing into two regular tetrahedra, octahedra, cubes, and dodecahedra. An interesting aspect of this list, is that one knot complement decomposes into two regular ideal tetrahedra and two knot complements decompose into regular ideal dodecahedra. While Reid showed that no knot complement could be decomposed into n regular ideal octahedra or n regular ideal cubes and only one knot decomposes into regular ideal tetrahedra, an interesting question is "How many knot complements decompose into n regular ideal dodecahedra?" In this talk, I will show that Aitchison and Rubinstein found the only two examples.