Question

Is it planar? how to prove or disprove?

Answer 1

Does ha go through e or not?
Does kc go through d or not?
Is that a node where ha and kc appear to meat just above e? It isn't labeled, so I have to assume it is not a node.
Can we reroute hea or kdc to go around the outside?

Food for thought.

Answer 2

it is planar if all the points are solutions to the equation of a plane pertaining to that of any 2 lines that can be made by joining any 3 points given

Answer 3

use color thrms .....

Answer 4

d is trapped, there is no way to get it from d to k without a removing the pencil from the plane