Wednesday, July 10, 2013

Study of Escher's Print "Gravity"

In his print Gravity, Escher placed 12 monsters on the star faces of the small stellated dodecahedron. He had thought of using turtles. I wish he had. With all their polygons, turtles are walking polyhedra.

So I did this polyhedra study using polyhedral turtles:

I've tried to follow Escher's patterns. Each turtle is looking at his neighbor's right leg, which forms rings of three. For example the yellow turtle is looking at the green turtle which is looking at the purple which is looking at the yellow. There are 4 sets of triple turtles and these four sets suggest a tetrahedron. There are other polyhedra suggested by other turtle groupings.

Here is a picture of a turtle along with the net used to make his shell:

To make this net I used rotation matrices, vector norms, vector cross products as well as dot products and an equation for finding the intersection of two coplanar lines. It was hard but fun.


Mark Dow said...

Very cool, beautiful!

It looks like with a small modification to the angle of the foot contact, and a slight global contraction, that the turtles could be standing on each other's shell. I'd like to see this without the dodecahedral framework.

Maybe it's not turtles all the way down, but self-supporting turtles.

Hop David said...

Mark, that's a really neat idea! I already have something visualized. Hope I will have time and energy to construct this soon.

Robert Clark said...

Thanks for that. Ultra cool.

Bob Clark