4. Lost and Found in California
I was riding a falling apart car along a picturesque Californian highway.
Incredible views were passing by car windows…Time do put thoughts together… So where am I?
I was lost inside my mind and in an outer space…
San-Franciscan trolley car, so reminding of old Leningrad trolleybuses.
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.
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.
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?
Even cows here look rusty…
So much rust must be there for a reason…
And suddenly – Sonya gives me a great book! The wonderful book of Quadrivium.
The Great Dodecahedron, the second stellated form, AKA the Rusty One from Woodshole,
The Small Stellated Dodecahedron, the first stellated form, AKA my Dodecon,
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
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.