For the sake of clarity and brevity in this article, Captive Orbital Hex Cage will be referred to as 'COHC'.
COHC is a weave I discovered while experimenting with Japanese maille weaves. It is a structurally rigid weave which is outstanding for 2-d sculpture, wall-hangings, etc. It is broadly a variant of Japanese 3-1, with cages replacing connector rings, and orbital rings around every point of connection.
COHC requires a minimum aspect ratio of approximately 6. It can be woven into any pattern J3-1 can achieve. This tutorial in its construction is also my first attempt at a 3-d rendered tutorial.
Step 1:
Start by "nesting" two parallel rings into a third.
Step 2:
Attach two more parallel rings to the first two, through their point of intersection with the "nest" ring. This creates a single unit of 2-2 chain with an orbital ring.
Step 3:
Separate two of the parallel rings, and insert a ring in between them at right angles. Make sure this ring slides between the two parallel rings to which the separated rings are linked. This will be the captive ring in the cage about to be created.
Step 4:
Nest the cage ring just added into another ring. Link a temporary ring through the cage ring's point of intersection with the nest ring to hold it in place. This creates a cage, with 3 rings trapping a fourth.
Step 5:
Nest one of the free corners of the cage into a ring, and attach two more parallel rings to the cage rings through their point of intersection with the nest ring. Make sure the parallel rings are on either side of the captive ring, thereby locking it in place.
Step 6:
Repeat step 5 for the last remaining free corner of the cage.
Step 7:
Remove the temporary ring. This completes a single cage unit of OCHC.
Step 8:
Add another cage unit to two of the parallel link rings from the existing unit. Leave one corner of this new cage unlinked.
Step 9:
Add a third cage unit to two more of the parallel link rings from the first unit. Note that the link rings necessary to finish the inside corner of this cage should also be used to close the previously added cage. This completes a single unit of OCHC.
Continuation:
This weave can expand in any or all of three directions, in the same way as Japanese 3-1. Just keep adding cages in linked pairs at the periphery of an existing piece to expand in that direction.