• ABSTRACT ALGEBRA Edges e, e of a tetrahedron T are said to be opposite if they are disjoint (that is, they do not share a vertex). The 6 edges can be partitioned into a set X of three pairs of opposite edges. Prove that G3, the group of symmetries of T , acts on X and the kernel K

Exercise 4.2.3 Edges e' e' of a tetrahedron T are said to be opposite if they are disjoint (that is, they do not share a vertex). The 6 edges can be partitioned into a set X of three pairs of opposite edges. Prove that 03, the group of symmetries of T, acts on X and the kernel K