Math Embroidery: Platonic Solids

Six strand linen and cotton
floss on 20 ct linen.
Same for all other photos.

Anyone who has played with dice or looked at pictures of the Egyption pyramids has seen the five Platonic solids.  They are found in art and decoration from every known culture.

They are called 'Platonic' because Plato wrote about them and identified each solid with one of the elements.  The element, earth, was associated with the hexahedron (cube) because Plato considered earth stable, for example.

My embroidery is based on an old textbook illustration.  I choose it because I liked the unfolded, 2D shapes below each 3D representation.

Doing this piece got me thinking about how most of our representations are 2D; artists and drafters have developed techniques for showing 3D on a 2D surface.  In elementary school, most of us are taught to drawn a path or river by diminishing the lines towards the horizon.  Those that wear glasses probably have noticed that their 3D vision is weaker as they look to the far edges of their lenses.  We call video games 3D even though they are depicted on a 2D screen on a TV or computer monitor.
We move between the 2D and 3D world pretty seamlessly in our every day lives. We experience what Relativity teaches is the 4D, time, in only one direction.

 If you think of time as an axis on a Cartesian graph, we only move in the positive direction.  Our memories and our language give us ways to express the negative axis of time, but we don't physically move along the negative axis on our Newtonian earth.

If String Theory can explain Quantum and Relativity Theory in one unified theory, then perhaps there are other dimensions that we aren't aware of.  Will artists of the future learn to depict more dimensions by using techniques like horizon -- techniques we can't begin to image?  Or will math formula and computer generated geometric abstractions be the only way we have to express these other dimensions around us?