Age 14 to 16 Challenge Level:
The second segment will stretch from (1,1,1) to (2,2,2), the third from(2,2,2) to (3,3,3) and so on. So the tenth segment will have its ends at (9,9,9) and (10,10,10).
Establishing a rule for what is happening to each of the coordinates in turn is best achieved by thinking of the effect at seeing just a 2-D image.
In the last section there are a number of options to consider.