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# stabiliser of a vertex watch

1. Hi
"the elements which fix a given vertex are called the stabiliser of that vertex."

I am struggling to find the stabiliser of a vertex of a cube... probably because I don't fully understand the definition above. Surely the only point that has to be fixed is the vertex itself. Anyone have any explanations / links?

thanks
2. Perhaps a more general definition would make things clear - if a group G acts on a set X, the stabiliser of a point is the set (subgroup, in fact) of elements of such that . The vertices of a cube are in X, so obviously are not in the stabiliser.
3. You're looking for the symmetries of the cube (those rotations that take the cube back to itself) which won't move the vertex in question. (Clue there are three of them.)

For example, the stabilizer of a face consists of the four rotations through 0, 90, 180, 270 degrees about the axis through the midpoint of the face and the midpoint of the opposite face.

A stabilizer is always a subgroup of the symmetry group.

PS You should check that by "symmetries of the cube" the question means just rotations as indirect isometries (like reflections) might also be included in which case everything I've written above needs suitably amending.
4. ok thanks a lot you two - its making more sense now

i need to think it through but i think i've got the right idea now

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