Monday, October 15, 2012

Link with 4 Rings in Felt

This piece is made from felt, and making this piece gave me many surprises.  The image above shows that it has the chiral symmetry of a tetrahedron, but this isn't how I thought it would look before I made it.   I made this object because a friend of friend asked if I could bead a version of the logo for Alximia winery, shown below.   I decided to make one in felt instead because felt is so flexible, and I imagined that this particular link would be especially fun to play with if it were made from felt.  And so it is.
Each component  in the Alximia logo is supposed to represent one of the four alchemic elements: earth, air, water and fire, and they suggested using some colors related to these.  So I made earth brown, air blue, water green, and fire red.  Green water?  Anyway, moving on...
To my great surprise, I found many different ways to arrange the four felt rings, shown in the Doceri drawing below.  You can see the logo represented in the two photos on the top right (just below my signature).  It has 3-fold symmetry.
We can see from the logo that it is an alternating link with 4 rings (components).   (By alternating, I mean that if you follow the path of a ring, it weaves over, under, over, under, and so on around the other rings.  You never get two overs in a row, or two unders.)   But if you look at the photo on the far left of the picture above, below the words "chiral tetrahedral" you can see it's an alternating link in this arrangement too.  This arrangement has 4-fold symmetry.  These two different arrangements both show that the link is alternating.   I wasn't expecting that.  Cool. 

This link has 12 crossings.  Twelve crossings is a lot.  Some link tables only go to 11.  So I was having a hard time figuring out which link I had.  But when I built the logo in felt,  it turned into my old favorite, the four intersecting triangles.   You might remember this beaded bead:
You can see it's the same mathematical object in the same orientation as in the largest (first) photo of the felt above.  Well, almost, one is a reflection of the other.  They are opposites.  In other words, the felt piece and the beaded piece have opposite chiral symmetry, but otherwise, they are identical. 

And the last surprise for this felted logo... If I pull hard, I can fit it over my hand and wear it on my wrist.  I had no idea it was going to be a bracelet.  Sometimes, you just get lucky.  The felt bracelet is for sale.  Click the photos.


  1. Wow.

    Thank you for the link to the knot table that ought to keep me occupied for a good long while.

    1. Indeed. Knot tables are endless sources of wonder. Have fun.

  2. Thank you soooo much Gwen! Indeed many unexpected things have come out of the original Logo design! I´m so happy! Please, if you ever come down to Ensenada, Baja California don´t even think twice and come visit our winery: there´s a bottle of our best waiting for you!

  3. Gracias por esos detalles ,besos


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