# Greek keys - corners

Index --- style --- turns --- designs --- compare keys --- corners --- 2 dimensional --- modern --- triangular --- circular --- fractal --- copying --- origins

Greek keys are borders, so it would be a good thing if we could get them to turn corners. Unfortunately, this isn't trivial. Here are some possible solutions to the problem. I am not going to do corners for all the Greek key patterns of this site - there are hundreds of them! But I have done some typical patterns. I have enjoyed myself colouring them in various ways to get different effects. I hope you can make out the underlying Greek knot in each case. To save room, I have nested the different sized keys within each other. Make a border by extracting the one you want, although some of them make quite attractive patterns as they are. By the way, you don't need to make the border a square. Make a rectangle by having different numbers of keys along than down.

### Running one side into the corner

The first technique is to run the border pattern along one side until it hits the corner. Then carry the line on to the next side. Unfortunately, Greek keys are not square patterns. This means that you can match the pattern either on the outside of the corner, or the inside. This gives different effects. The first pair of patterns is a standard simple Greek key (which has a double spiral in the middle). The first pattern matches on the inside, which gives a jagged outside. This looks vaguely Aztec to me, so I coloured it accordingly. The second pattern is smooth on the outside, so I coloured it in a more conventional way.

The next pattern is single spirals, rotated alternately. Here I have added straight line borders to make the key stand out. The next is edge to edge. I thought the middle looked like rays of the sun, so it's ended up a very hot pattern. See designs for more information on the patterns.

### Square in the corner

Another technique is fill in the corner with a different pattern - a square, or possibly several squares inside each other. This looks OK for this first pattern below, but a conventional Greek key has a definite direction, and so the pattern has a rotational symmetry rather than a reflective symmetry. (In fact, the first pattern has a rotational symmetry as well, but it just seems less obvious).

If you want a reflective symmetry at the corners, then you can reverse the pattern every time you go round a corner. This unfortunately means that alternate corners are different.

So you can put another square in the centre of the line and reverse the direction again. You must reverse direction half way along the line, so you will need an even number of keys on a side (so half can go either side of the centre). Since the conventional Greek key is goes in a particular direction, there are two ways to get it symmetrical. The first pattern had the dark red spirals travelling away from the corners and towards the centre of the lines. The second pattern reverses this. One colouring emphasises the squares, and the other, the meander.

The next pattern leaves the centre square out and just reverses the direction of the key half way along the line. The corners are mini Greek keys rather than simple squares, so they aren't square. In fact, the whole pattern isn't a square, but it is symmetrical (reflective).

### Reversing key in corner

Here is a different technique. The key at the corner is reversed. This does make it look a little strange, but does mean that the inner and outer edges match, unlike the first method.

This uses the same sort of corner, but gets some symmetry by reversing the direction of the key in the middle of each edge. The pattern runs right along the top and bottom as well, with the sides not going right into the corner. This gives more symmetry. There are two different colourings on the same pattern.

### Reversing meander in corner

Rather than changing the direction of the key in the corner, here the meander itself changes colour. This only works in alternate sized keys (the green ones on the right). The others need an extra line to fill the pattern (this is in yellow on the left. There are two forms below, very similar although the colouring makes them look very different. The only difference is how long the lines are in the corners.

### Corners for symmetrical keys

Many of these problems arise because we are starting with the conventional Greek key, which has no symmetry apart from rotational. If we have a symmetrical key, such as below, it becomes a lot simpler.

That pattern above still has asymmetrical corners. We can fill in the corner with a regular pattern. A square would work, of course, but here is another idea. There are two versions depending facing outwards or inwards.