You will need as many of these objects as you can make: I would
love to give detailed instructions on how to fold these "Before
the Big Bang" objects, but you can read all about it in Kasahara's
book "Extreme
Origami". As I'm going to weave these together, it pays to leave
the central hole larger than Kasahara suggests. This object, when
cut from flat paper, has an outer diameter of 10 inches, and an inner diameter
of 5 inches. You can see the object is just alternating concentric
mountain and valley creases.
Take two of these objects, and superpose them so that their two main
loops coincide.
Here they are together:
Now, the yellow unit is going to slide forward, and the black unit is
going to slide backward, so that two vertical black loops catch two horizontal
yellow loops.
Now, take another unit, and hook one of the free black loops:
... and then hook the remaining black loop:
Pull the yellow unit through so that everything is symmetric, and you
have the 3-unit construction.
Hook the fourth unit on one of the free yellow loops:
... and then through the second free yellow loop:
straighten everything out ... and you have a 4-unit construction.
You can never make such an object with closed loops (unless you want to cut and glue one of the units) but you can make a chain with branches. In fact, and graph that can be "amputated" by removing any single link can be represented with Kalmon-chains. You can make big chains ... and tie knots with them, though.