Three loops, internal rotation

Symmetry and Celtic knots

Today, I combine my two favorite topics:  symmetry and Celtic knots.

I use symmetry to design my tessellation quilts. I can also use symmetry to design Celtic knots.

Take this loop-the-loop for example.

Single loop-the-loop
Single loop-the-loop

If I rotate three copies around the center of the loop, I get this:

Three loops, internal rotation
Three loops, internal rotation

If I rotate three copies off center, I get this:

Three loops, off-center rotation
Three loops, off-center rotation

I can line loops in a row, like this:

Linear symmetry
Linear symmetry

I can cover an entire surface, like this:

Planar symmetry
Planar symmetry

What next??

Medallion 7

How to fit a square peg in a round hole

I would like to fill in the center of this medallion.

Medallion 3
Medallion 3

I could position a smaller version of the medallion in the center.

Medallion 5
Medallion 5

Instead, I merged the larger and smaller versions together.

Medallion 6
Medallion 6

How many loops are in Medallion 3? How many loops are in Medallion 6?

Again, I merged a smaller version of Medallion 3 with Medallion 6.

Medallion 7
Medallion 7

Now, how many loops?

Finally, I merged an open-sided knot section with Medallion 6.

Medallion 8
Medallion 8

How can I get more knotting in the center?