| 8/2/13 The logical proof that there can only be five regular solids is as old as Plato (with deference to Kepler, who I haven't got to yet) but when you set out to make a few of them as toys for a newborn you never know where they'll lead you next . . . . . . . having made the five "classical" forms, I decided I might as well continue with the triangles to create the "proof" that these were the only possible regular solids . . . . . . . and then kept going . . . . . . . . and suddenly the world gets very interesting and I have to start working in cardboard . . . . . . . which takes me from traditional plane and solid geometry into a world of petticoats, curtains, lettuce leaves and radiators that seems to have some pretty interesting properties of its own! Here's the numbers:
(apart from the missing ones, which are: 360, 540, 720, 1,080) And here's the full set, including pentagons: Here's 6, 7 & 8
- I woke up with a new stitching idea that would create flat rather than gathered seams that would allow much more freedom for the forms to flow in any direction - if I carried on with blanket stitch (which was great for the solid models) I would just get tighter and tighter scallops. Here's two views of the form with 8 triangles (420 degrees = 1 1/3 circles in the space of 1) showing nice flexible curves! I am quite excited by the imagination that tomorrows project, folding 720 degrees worth of triangles into 360, will allow me to create an Equator that can simultaneously touch both North and South Poles! Here's what I imagine: . . . which I consider to be quite lovely, was the first form that "fell into my hands" after constructing 1080 degrees = 10 Pentagons . . .
. . . but then I thought about things logically (in relation to previous imaginations and the three planes of space) and rearranged things ca:
. . . .which is consistent and fits with the overall scheme . . . . . . but I still think there's something quite grand about that first one! | 
