Detailed Weaving Procedure for C60

Here I will describe the complete procedure for constructing a beaded C60 based on a tabular formulation as shown in the following table, which is quite popular in the oriental craft society. As I mentioned in the last December, the technique required for creating a beaded fullerene is the so-called "Right Angle Weave" (RAW). The whole weaving process can be viewed as a sequence of elementary steps. A loop consisted of n beades is formed in each elementary step. This is probably what the RAW meant. Then repeatly applying the RAW to generate a sequence of loops according to suitable spiral codes, a resulting network will automatically correspond to the correct fullerene structure.

We will use a column in the table to describe the details of building of a particular n-bead group. The second row of each column gives instruction on the number of beads in the neighboring groups that should be passed through from the thread in your hand, the third row the number of beads that should be added into the two ends of the thread, and, finally, the last row tell us how to form an n-bead group by crossing right thread into the last bead in your left thread.

The weave of our beaded molecules can be done easily with stiff thread alone and there is no need to use needles. So the only supply required is just beads and a wheel of lines for threading. With a simple estimate we can figure out that we need at least 90 beads and 110 cm of stiff thread (for 4mm beads). Work clockwise or counter-clockwise 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 5 beads into one end of line in your left hand. Cross the thread in your right hand back through the last bead you just added and pull tight. A 6-bead group should result.
Step 3: Pass the other end of thread (thread in your right hand) to the nearest bead in the previous group. Add another 4 beads into one end of line in your left hand. Cross the thread in you right hand back through the last bead you just added and pull tight.
Step 4: Repeat step 3 twice. Now we have the first five bead groups done. Note that one more hexagon is needed to finish up the first layer of five hexagons surrounding the central core.
Step 5: Pass the thread in your right hand to the two nearest beads in the second bead group. Add another 3 beads into one end of line in your left hand. Cross the thread in you left hand back through the last bead you just added and pull tight.
Follow each step in Table 1, 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. This is because a positive Gaussian curvature will be created whenever a pentagon is introduced. According to the Euler theorem, there will be 12 pentagons in a spheroid. When repeating the step 2, the number of beads need be added to the thread in your right hand and also the beads in the neighboring groups need to be stitched through by the thread in you left hand can change. An experienced beader can figure out this number easily as the beading process continues. You may take the advantage of your chemical knowledge to decide how many beads in the neighboring group you need to stitch through with the thread in your left hand or right hand at later stage of beading. Basic criteria is that you need to stitch through all of the existing beads belong to the same carbon atoms.

Although the spiral code is a convenient recipe for systematically constructing a beaded fullerene with the spheroidal shape, we found that this is only for monochrome beaded fullerenes. It seems that there is no easy method to generate a prescribed colored pattern on the beaded molecule based on the spiral code. The best way is probably to use the tabulated format as shown Table 1.



Table 1. The complete procedure for constructing a beaded C60 in a tabular format
Steps 1 2 3 4 5 6
RT[a] 0 0 1 1 1 2
LT[b] 5 5 4 4 4 3
Cross[c] 5 6 6 6 6 6

Steps 7 8 9 10 11 12 13 14 15 16
RT[a] 1 1 2 1 2 1 2 1 2 2
LT[b] 4 3 3 3 3 3 3 3 3 2
Cross[c] 6 5 6 5 6 5 6 5 6 5

Steps 17 18 19 20 21 22 23 24 25 26
RT[a] 1 2 2 2 2 2 2 2 2 3
LT[b] 4 3 3 3 3 3 3 3 3 2
Cross[c] 6 6 6 6 6 6 6 6 6 6

Steps 27 28 29 30 31 32
RT[a] 2 3 3 3 4 5
LT[b] 3 2 2 2 1 0
Cross[c] 6 6 6 6 6 5

[a] The number of beads passed through for the thread in your left hand. [b] The number of beads added into the thread in your right hand. [c] Form an n-bead group by crossing the thread in your right hand back through the last bead you just added and pull tight.