In the background/introduction to my Space SE question Have Kagome lattice patterns been used as structural reinforcement in spacecraft in non-Iranian spacecraft? Can we help Scott Manley "unsee" this one? I wanted to highlight that the Kagome-like cross-hatched pattern seen there can be uniform and repeating on the cylindrical surface of a rocket body.
So to illustrate that I said:
On a flat or cylindrical surface the pattern has three sets of parallel lines, call them A, B, and C, but instead of all three intersecting at the same points, they are offset so that AB, BC, and CA intersections are at different points, dividing the surface into twice as many triangles as hexagons.
Question(s):
- Can a Kagome lattice or trihexagonal tiling be made from three sets of parallel lines on a flat and/or cylindrical surface?
- Are there other 2D surfaces in 3D space on which it can be made from three sets of parallel lines?
notes:
- "can be made" doesn't mean will always be, just that it is possible.
- corrections of vocabulary are just as welcome as those of mathematics. For example I may be conflating lattice with tiling