Friday, May 17, 2013

Options for 2-square Puck origami units

Options for a 2 square modular origami unit for Puck weaving.

The unit at the top of the figure is its own mirror image, thus only one type of unit is needed, but the splices cannot be kept internal. The other three designs need to work as left/right enantiomorphic pairs but splices can be hidden under other weavers.

Definition: Puck is an acronym for polyphase, unit-woven, corrugated kagome.

There are two ways weavers can be spliced. They can be shingled like books fallen-over on a shelf, or laid like two courses of bricks.

To hide splices:

Shingled:  the length of the shingle must be odd since the left edge of the shingle will show on one face of the weaving and the right edge on the other; the phase shift (the spacing between successive shingles) must be even so that the corresponding edge of the next shingle on the same face can be covered as well.

Laid: the length of the shingle must be even since both left and right edge show on the same face of the weaving; the phase shift between the two courses must be odd so that correspondig edges on the reverse face are covered by the weaving.

For example, the lower three unit designs, since they have even length, must rely on a laid configuration and an odd phase shift (1 unit is the only option) in order to hide the splice edges.

In the case where the splice edges coincide with square edges (e.g., the upper design), we must settle for having the splice edges strapped-down rather than hidden. In this case, the splice must be single-edged (i.e. a shingled pattern, not a laid pattern) and—just as required above—the phase shift must be even. Here the length will also be even since half a square is gained at each end by settling for an edge that is merely strapped-down rather than hidden. The smallest such design is a four-square weaver with a two-square phase shift.

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