Cube Symmetry

Animations from Cabri 3D

1. Planes of symmetry of a cube

Adrian Oldknow

November 2004

A new Cabri 3D page

Create a ray

and a point on the ray

Use point symmetry

Rotate for a 3rd point

Reflect for the 4th point

Draw a parallel

Construct a perpendicular

Find the intersection point

Point symmetry again

and some reflections

Draw a perpendicular

Draw a circle around an axis

Find the intersections

Create a parallel plane

Create another perpendicular

and find the intersection

Start tidying up!

Another perpendicular

Point symmetry for the others

Hide some constructions

Until all you see are points!

Now join up some dots

And reflect in the mid-plane

The cube is nearly there

At last – a cube!

Hide the spare dots

Colour the edges

Label the vertices

Spin it a bit

Define a polygon

Is it in a plane of symmetry?

Here’s one diagonal

Is the other diagonal equal?

How many diagonals like this?

And like this?

Did you get all these?

How many planes like this?

And like this?

Here are 2 joining green edges

And the third: the edge bisector

So how many planes of symmetry does a cube have?

Dots at the centres of each face

What shape do they make?

Looks familiar?

Well, that’s another story!