Interpenetration of 1D Nets

1D nets can display one of two categories of interpenetration - parallel or inclined.

Parallel 1D interpenetration

Parallel interpenetration of 1D nets occurs when the mean directions of propogation of the nets are parallel. When the mean propogation directions are also colinear, then the overall entaglement is 1D. When they are not colinear, then the overall entanglement can be 1D, 2D or 3D. Examples are illustrated below for overall 1D and 2D entanglements; no example exists to date of an overall 3D entanglement.

1D → 1D parallel interpenetration
1D → 2D parallel interpenetration

Inclined 1D interpenetration

Inclined interpenetration of 1D nets occurs when the mean directions of propogation of the nets are inclined to each other. This generates an overall entanglement can be either 2D or 3D. An example of each are illustrated below.

1D → 2D inclined interpenetration

1D → 3D inclined interpenetration