4. Lost and Found in California

San-Franciscan trolley car, so reminding of old Leningrad trolleybuses.

The diagonal Star family members function exceptionally well,

but they are not spawned by a true platonic solid.

Alcatraz on the right…

 

My dear Star of Red Pyramids inspired by Sir Penrose’s famous Coordinate Puzzle is a dodecahedron descendant. Its current reincarnation – Dodecon – works like a charm…

But the dissections are artificial – they are not the extensions of its faces. 

And here it is – the Golden bridge – magnificent and rusty (I heard this phrase before). It’s got to be a sign!
The green-orange model inspired by the Rusty One – has it all, its parts are perfect, they use only extrapolated faces of a true platonic solid… 

Well, almost perfect, except it doesn’t work.

So this is it? Did I loose my way? Where am I?

Well,  I got lost. 

Really lost – I literally missed my exit.
Here is a U-turn. I am expecting something usual – a double jug handle of sort.

But no, this U-turn is something completely different. I am being redirected to a long bumpy ride through a unpaved road. Can all this be random?

Rusty tractor,
Rusty plough,

So much rust must be there for a reason…

And suddenly – Sonya gives me a great book! The  wonderful book of Quadrivium. 

Here I found them all –
The platonic Dodecahedron itself on the cover.

The Great Dodecahedron, the second stellated form, AKA the Rusty One from Woodshole,

And finally – how could I forget – The Great Stellated Dodecahedron, the third stellated form, which I never tried, never considered was also there! 

Johannes Kepler did a great work back in 1619, and Louis Poinsot made an excellent progress almost two centuries later, in 1809. 

Maybe they just didn’t finish something important, and it has been waiting another 200 years? Maybe it has to be completed by 2012?

A Rotational symmetry assembly of the green Great Dodecahedron.

Suddenly I see how the green parts can fit together in an unexpected way, they roll around an inner axis, five of them, not six. The sixth one is left out.

The construction is not stable to say the least, but it’s not supposed to be!

It’s supposed to be held together by an outer shell, and the outer shell will be the Great Stellated Dodecahedron! 

Perfecto! Then the whole mechanism should work as 

a

FIVE PIECE COORDINATE MOTION MACHINEImmediately I started the model. This time I bought perfect paper. A special set of colored textured paper.

Like a Japanese calligrapher I carefully prepared my arsenal. I knew this model is going to be very complex, each part will have four beams intricately connected using intermediate layer consisting of the parts of the green model.

Nothing is lost in vain! All prior steps are still meaningful. 

Well this time the model turned to be complex. I mean VERY COMPLEX. It took me a month to assemble just one part out of five.

To be continued as a birth of the third stellation…