Jesús de la Peña Hernández
CASE 2A: Tessellation by Chris K. Palmer.
Fig. 1 is a tracery among the many and very beautiful developed by the author. Figs. 2
(obverse) and 3 (reverse) are the result of folding flat Fig. 1. The three figures keep in thedrawing their natural proportions. To get the final figure in its protuberances, the octagons of
Fig. 1 have to be twisted (recall Point 11.2).
Corners of Fig. 1 are maintained in 2 and 3. One can note that flattening of Fig. 1 is
guaranteed after folding because: there is an even number of concurrent lines in each node; the
sum of their alternate angles add up to 180º, and finally, paper does not interfere at folding.
These three conditions are common to this type of tessellations, though there may exist
apparent exceptions in certain nodes. What happens in those cases is that one extra fold is pro-
vided to ease folding operation, but once this is over, that fold remains inoperative.
By merely translating the figures of the three big squares we can occupy the whole
plane. That is so because we are playing with fitting angles of 90º, i.e. multiples of 30º like in
1A.CASE 2B: Tessellation by Alex Bateman
Fig. 1 shows a quadrille as guideline to start with, and all the valley folds. Fig. 2 adds the
mountain folds. In Fig. 3 the guidelines have been erased. Fig. 4 is the result of folding, twisting and
flattening Fig 3. Fig 5 is Fig 4 seen as translucent (recall version 4 of Point 11.4).
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