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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