Wednesday, April 16, 2014

Infinite Skew Polyhedron Faujasite (

I beaded another infinite tiling. This one represents the crystalline structure of faujasite

This piece of beadwork has nearly perfect tetrahedral symmetry, but I left out a few of the beads for aesthetic reasons.  If you look closely at the photo below, you will see the bottom edge is different from the other five.  For one thing, leaving out the extra beads makes it much easier to balance the piece on edge.
This piece contains over 19 grams of size 11° seed beads.  That's almost a whole box of beads, and as far as I know, it's flawless.  No mistakes.
You can think of this piece as a tiling of squares and hexagons in 3D.  Thought of as a tiling, every vertex is the same type, That means there three squares and a hexagon around ever corner.   Consequently, this piece contains loops of 4 beads and loops of 6 beads. 

When I made it, I thought of it as a bunch of polygons glued together.  We have truncated octahedra and hexagonal prisms glued together on the hexagonal faces.  All of the hexagons on the prisms are glued, but only half of the hexagons on the truncated octahedra are glued.
My inspiration for this piece came from Figure 7.41 in the book, Crystal Structures I: Patterns and Symmetry by M. O'Keeffe and B. G. Hyde.  The illustration above (Figure 7.41) is what I used from that book.

Here you can me holding it showing off a triangular face of the tetrahedron.  This qualifies as one of my larger non-wearable pieces of beadwork.
A tetrahedron has six edges.  On this tetrahedron, I made one of the edges is different from the other four. It's the bottom edge in this photo.
And it's the front edge in this photo.  I like the way it looked without the extra beads.  It's adds variety, and the piece doesn't need them to hold itself in position. 
For comparison, the other five edges look like the front of this.
Next I show you a few process shots so you can see how the piece started.  First, I made a ring of six truncated octahedra and six hexagonal prisms.
After adding more beads, I had two of these rings joined together.
With more beads came three joined rings. If this were actual faujasite, the inner cavity would have a diameter of 12 Å.   It has tetrahedral symmetry at this point.  This would be a nice place to stop if you wanted a little beaded bead to wear as a pendant.  
But since I knew I was beading a repeating pattern, I couldn't help but make more repeats. This is like two tetrahedrons glued face to face, but with a half turn rotation first.  The symmetry of this is an antiprism with a 3-fold rotation.  It's a very weird symmetry. 
 And then this...

And one last photo of the finished piece.  This piece is SOLD!
If you liked this post, you might enjoy these posts on beaded infinite polyhedra:
Thanks for looking!

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