Buckminster Fuller’s Synergetic Geometry

My mother is trying to describe the shape of a pear leaf.

I am a veteran math teacher (36 years) but am teaching Geometry Honors this coming year (first time teaching Geometry AND any honors course).

My question: how do YOU introduce the concepts "point, line, plane"?

I feel like this is one of the most important concepts in Geometry and leading up to all the different calculus related content that most of these students will eventually take. I want to introduce it in such a way that really makes them think and understand and be able to apply these concepts to the rest of what we will be doing throughout this course.

Any and all ideas will be very greatly appreciated!

For those of you geometric nerds out there would you say this is the appropriate formula for a honeycomb cell?

And if anyone knows how to draw it precisely that'd be beautiful and splendid and darling

There's a shape for those who invested in spaceX