The knot 10 124 and the dodecahedron
There is a representation of the involutive quandle of the knot 10 124 to the quandle Q
30
Joyce, D. A Classifying invariant of knots, the knot quandle. J. Pure Appl. Alg. 23 (1982) 37-65.
We use a projection of 10 124
which is not the one in the tables.
Obviously we have a non trivial representation so the knot is non
trivial (its determinant is 1). Could these two quandles be
isomorphic? I think not. The quandle of the knot is given by 3
generators and 3 relations:
Here are the 5 geodesics which contain the 30 centers of edges:
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