Friday, December 29, 2006

Supplementary Constraint in Using Spiral code

Is the sequence as given by the spiral code enough for the building of beaded fullerene? Well, not really, you need to have some extra conditions to get the work done. For instance, the spiral code for the dodecahedron is 1 2 3 4 5 6 7 8 9 10 11 12, which gives the spiral sequence 555555555555 of 12 pentagons. Here I will give the detailed procedure for weaving a dodecahedron based on this sequence.

The weave of our beaded molecules can be done easily with stiff thread along. I found that there is no need to use needles. So the supply we need is just beads and a wheel of lines for threading. With a simple counting, we need at least 30 (20*3/2 = 30) beads (4mm) and 50 cm of stiff thread (0.3 mm). Work clockwise or counterclockwise according to the spiral code.

Step 1: Using one end of the line. String on 5 beads into the thread, letting them fall to the center of line. Take the other end of the line and cross it back through the last bead. Pull tight to form the first group with 5 beads. If necessary, reposition it toward the middle of the line.

Step 2: Add another 4 beads into one end of line in your right hand. Pass the other end of thread (thread in your left hand) to the nearest bead in the previous group. Cross the thread in you left hand back through the last bead you just added and pull tight. A new 5-bead group should result.

Step 3: Repeat step 2 until the whole sequence of spiral code is finished, the beaded molecule will appear.

As you continue working on the beaded molecule, you will notice that it tends to curve slightly when a new pentagon is added.

When repeating the step 2, the number of beads need to be added to the thread in your right hand and also the beads in the previous group need to stitched though by the thread in you left hand can change. An experienced beader can figure out this number easily as the beading process continues. Chemists may take the advantage their chemical knowledge to decide how many beads in the neighbor group you need to stitch through with the thread in your left hand. Basic criteria is that you need to stitch through all of the beads (chemical bonds) belong to the same carbon atoms.

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