Turn on thread page Beta
    • Thread Starter

    "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?


    Perhaps a more general definition would make things clear - if a group G acts on a set X, the stabiliser of a point x \in X is the set (subgroup, in fact) of elements of g \in G such that g(x) = x. The vertices of a cube are in X, so obviously are not in the stabiliser.

    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.
    • Thread Starter

    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
The home of Results and Clearing


people online now


students helped last year

University open days

  1. Sheffield Hallam University
    City Campus Undergraduate
    Tue, 21 Aug '18
  2. Bournemouth University
    Clearing Open Day Undergraduate
    Wed, 22 Aug '18
  3. University of Buckingham
    Postgraduate Open Evening Postgraduate
    Thu, 23 Aug '18
How are you feeling about GCSE results day?
Useful resources

Make your revision easier


Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here


How to use LaTex

Writing equations the easy way

Student revising

Study habits of A* students

Top tips from students who have already aced their exams

Study Planner

Create your own Study Planner

Never miss a deadline again

Polling station sign

Thinking about a maths degree?

Chat with other maths applicants

Can you help? Study help unanswered threads

Groups associated with this forum:

View associated groups

The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

Write a reply...
Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.