Date: Mon, 2 Jan 1995 18:00:33 -1000 From: Drake@cup.portal.com (Drake Drake Smith) Message-Id: <130303@cup.portal.com> Organization: The Portal System (TM) Subject: Rhombicosi-Dodecahedron In a fit of creativity this past week, I decided to make something, and dragged out the files I had saved from here on the subject of line-toys. There was a lot on soccerball construction, and I kind of yearned for something different, which I found in a kid's paper construction book. If you followed the soccerball thread, it's basically pentagons surrounded by hexagons. A design rule would be that every edge of the pentagon must ajoin a hexagon, and alternate faces of the hexagons touch either pentagons or other hexagons. Keep going until you are one 'gon short of a full ball, and you have a line-toy. Simple. The actual shape is a truncated icosihedron, or "Buckyball" after Buckminster Fuller, chief Dome-Dude. You can also make a ball using triangles (20) and pentagons (12) called an icosi-dodecahedron. So, eventually I decided to make not a Buckyball, and not an icosi-dodecahedron, but a *Rhombicosi Dodecahedron* just for the thrill of being the first to have one, and the pleasure of watching what happens to peoples' faces when I tell them the name of it, heheh. Then I will say that I have applied for a patent on the Platonic Solids, and anyone caught making illegal shapes will have hell to pay, heheheh. But I digress, so here's how to make one (with no ascii grafix). Sooo, to start, cut out a triangle, square, pentagon, and a hexagon - all with four inch sides - from cardboard. Now put the hexagon away. Cut out eleven pentagons (12 would make a solid, but we need a hole here), also 30 squares, and 20 triangles. I chose orange pentagons, yellow squares, and white triangles. Seam allowances won't matter, just be sure to align each face carefully, point to point. The design rules are thus: Each face of a pentagon joins to a face of a square. Each point of a pentagon touches a point of a triangle. Each face of a triangle joins a face of a square. Each face of a square alternately joins a triangle or a pentagon. I started sewing each edge one at a time, then began making rings of shapes in hopes of speeding things up, but you basically have to sew one seam at a time. When you get to the last ring, you should have five squares and five triangles surrounding the invisible, missing twelfth pentagon. It will be easier to sew some ribbon around the five-sided hole at this point, BEFORE finishing the ball, because your elbow is too big to go inside the ball at the end. Finished diameter is roughly 15 inches. The basic sewing problem with making these things, is how do you stitch right up to the apex where the four seams meet? When I looked at Jeff Burka's soccerball one time (which has three seams meeting at the same point), he showed me how he avoided the problem by simply stopping *before* reaching the trouble spot. This leaves a hole. The alternative, sewing across the apex, usually leaves a puckered spot. Any suggestions?? Drake@cup.portal.com + Work Motto: Everything Counts. Recommending Amigas since 1985 + Life Motto: More Good Times. MKS, LVKS too. + (Jack Nicholson) = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = Date: Tue, 3 Jan 1995 03:07:11 -1000 From: crowell@teleport.com (Carl Crowell) Message-Id: Organization: Kites By Carl Crowell Subject: Re: Rhombicosi-Dodecahedron >The basic sewing problem with making these things, is how do >you stitch right up to the apex where the four seams meet? >When I looked at Jeff Burka's soccerball one time (which has >three seams meeting at the same point), he showed me how he >avoided the problem by simply stopping *before* reaching the >trouble spot. This leaves a hole. The alternative, sewing >across the apex, usually leaves a puckered spot. Any >suggestions?? instead of stopping before, or after the point, stop AT the point. If you are using a 2.5-3mm stitch, any distance under 2mm is not a 'hole' any more than the rest of your stitching. Therefore, an accuracy of 1mm (not hard to eyeball) is fine. Now, play with the big boys. Instead of using flat panels of cloth, use three four and five sided pyramids. Instead of ending up with a doedecahedron, or a pentadecahedron, or a tetrabidoedecahedraon or even a heptatransvintehedraltarus, you end up with a 'cool spikey thing'. enjoy ___________________________________________________ email: crowell@teleport.com FTP: ftp.teleport.com/pub/users/crowell WWW: http://www.teleport.com/~crowell Kites By Carl Crowell - O.S.F.M. World Headquarters = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = Date: Tue, 3 Jan 1995 20:30:59 -1000 From: andrew@tug.com (Andrew Beattie) Message-Id: Organization: /usr/lib/news/organisation Subject: Re: Rhombicosi-Dodecahedron Drake@cup.portal.com (Drake Drake Smith) writes: >[About different types of footballs...] >The basic sewing problem with making these things, is how do >you stitch right up to the apex where the four seams meet? 1) *do* take the seam alowance into account. On patchwork, accuracy is essential. 2) Try doing things in rings. For a traditional football, make a bunch of: - half hexagons (hexagons cut from corner to corner) - Half pentagons (again from corner to corner - one "half" is triangular, the other has 4 sides. The first "ring" is simply a complete pentagon. The next is ring is 5 half-hexagons. The next ring is 5 half-hexagons and 5 triangular-half-pentagons The next ring is 5 half-hexagons and 5 4-sided-helf-pentagons I think the next ring is 10 half-hexagons and also the half-way point (ie you now have a hemisphere), but it's getting kinda hard for me to visualise... Try drawing rings round a football. The rings should make assembly easier. BTW, try changing your edge length from a few inches to a few feet. For a standard football, the diameter is about 5 times the edge length. Andrew -- Kite FAQ's: ftp.hawaii.edu:/pub/rec/kites/faq) o /\ Kite Jumping For sale: 10' Flexis with std & UF Spars. |_ \/ is for andrew@tug.com AoXoMoXoA (_\ M O R O N S = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =