The Belyi maps in this puzzle are defined over the number fields \(\mathbb{Q}(\sqrt{-3})\) and \(\mathbb{Q}(\sqrt{105})\).
(6,7),(1,7,2,3,4)(5,6),(1,6)(2,4)(3,7,5).png "(1,2,3,4,5)(6,7)_(1,7,2,3,4)(5,6)_(1,6)(2,4)(3,7,5)")
(6,7),(1,4,3,2,7)(5,6),(1,6)(2,4)(3,5,7).png "(1,5,4,3,2)(6,7)_(1,4,3,2,7)(5,6)_(1,6)(2,4)(3,5,7)")
(6,7),(1,3)(2,7,4,5,6),(1,4)(2,3,6)(5,7).png "(1,2,3,4,5)(6,7)_(1,3)(2,7,4,5,6)_(1,4)(2,3,6)(5,7)")
(6,7),(1,4,5,3,6)(2,7),(1,4,5)(2,6)(3,7).png "(1,2,3,4,5)(6,7)_(1,4,5,3,6)(2,7)_(1,4,5)(2,6)(3,7)")