[Completely OT] Footballs - Page 1
Forum section: electronics / general

author: RobK_NL
author_rank: Frequent Contributor
timestamp: November 26, 2018, 09:07:55 pm
content: ... more specifically, the shapes that go to form them.Yes, I do know that it's 12 pentagons and 20 hexagons, but please bear with me.Here in The Netherlands we have the annual feast of St. Nicholas ("Sinterklaas") and in many places, including schools, it is customary to draw lots to give others a present. These presents are not just gift-wrapped, but concealed in a creative disguise.So, my boy has drawn this other boy who happens to like football. Great, we thought, hollow styrofoam balls are readily available, put a coat of white paint on it, draw some lines for the hexagons and paint the pentagons black.Problem is: if I just cut out a paper hexagon, there is just no frigging way to get it right on the ball! I obviously need to take the curvature of the ball into account, but how? Maths was never my forte and this is advanced topology, so I'm way out of my depth here.Any thoughts and pointers would be highly appreciated.

author: LapTop006
author_rank: Unknown
timestamp: November 27, 2018, 06:51:27 am
content: Perhaps try trollingfor help.

author: Fred27
author_rank: Unknown
timestamp: November 27, 2018, 09:11:29 am
content: Try making a wire pentagon. You should be able to "flatten" this against the spherical surface. You will probably have a lot of trial and error getting the size right. Maybe make some hexagons too to help position the next pentagon. It still won't be easy.

author: beanflying
author_rank: Super Contributor
timestamp: November 27, 2018, 09:25:11 am
content: Skip the curves and straight line it from heavy paper with clear tape. I have made a few self inflatables from kite cloth using this sort of non maths pentagon/hexagon form.http://mathworld.wolfram.com/TruncatedIcosahedron.html

author: Brumby
author_rank: Unknown
timestamp: November 27, 2018, 11:29:56 am
content: Quote from: beanflying on November 27, 2018, 09:25:11 amThat will work very well for the situation where you do not have an exact final diameter to work to. With a styrofoam ball, that dimension is very much fixed.As for the geometry of a soccer ball, it is simply a truncated icosahedron. You could make a template by creating a wire frame icosahedron of the correct size (that's the tricky bit) and mark points on every edge at one third and two thirds along its length. Draw a line between these two points on the surface of the ball for all edges - making sure the end points are clearly and accurately defined. Remove the icosahedron and you will see the end points of the lines drawn will define pentagons - and the line segments will (in groups of 3) define hexagons.

author: Brumby
author_rank: Unknown
timestamp: November 27, 2018, 01:14:14 pm
content: If you look up Google, you can find all the maths behind it - but to save you the trouble, I have picked out one formula. It shows the relationship between the length of the edge of the icosahedron and the radius of a sphere that will touch at the purple points shown:Find the radius of your styrofoam balls (half the diameter) and multiply that by 1.236. This will give you the length of each edge of the icosahedron that will sit around the sphere, just touching the points (as shown above). This is the number you would need to make an icosahedron wireframe (and then follow the process mentioned in my previous post) - but there are other ways you could approach this ... and they may be more practical, but I don't know the best way to attack this.

author: Fred27
author_rank: Unknown
timestamp: November 27, 2018, 01:23:52 pm
content: Another option is to buy a cheap plastic football with the design on it, cut it open and reinforce it internally to suit your intended contents. It will probably look better.

author: bw2341
author_rank: Regular Contributor
timestamp: November 27, 2018, 04:48:27 pm
content: http://mathworld.wolfram.com/pdf/TruncatedIcosahedron.pdfPrint out the pattern from Wolfram. Make sure to manually set Custom Scale in Acrobat Reader to 100 percent.You can see a zigzag row of ten adjoining hexagons in the middle. This will be your pattern. Mark the outermost vertex on one end of the strip of hexagons. Match the ends of the strip of hexagons to find the adjoining edge on the ends. Mark the matching vertex on the other end of the strip.Measure the length of the strip with a ruler. You won’t be measuring the full length of the strip, just the length between the two marked vertices. Your ruler should be parallel to the edges of the hexagons.This value should be the circumference. Measure the ball and scale the pdf to fit it. The rescaled pattern will be a little bit small so trial and error will be need to get a good fit.Edit: typos. After thinking a bit, I’m not sure if the pattern will be a bit small, a bit big or an exact fit. Let us know if it works!

author: RobK_NL
author_rank: Frequent Contributor
timestamp: November 27, 2018, 08:56:46 pm
content: Oh wow, this is why I love this forum!Thanks a lot for all the suggestions guys. We are going to do our best and I'll show you the result in a few days.

author: BrianHG
author_rank: Super Contributor
timestamp: November 27, 2018, 09:09:36 pm
content: LOL, I think this exact topic has been covered on this forum more than 1 time within the past 3 years...

author: Brumby
author_rank: Unknown
timestamp: November 28, 2018, 12:44:40 am
content: Quote from: bw2341 on November 27, 2018, 04:48:27 pmThis is one approach that I had considered also - but I fear the flat nature of the cutout may not wrap around the curved surface too well. This is why my thinking went to a wireframe that was just touching the surface.However ... having slept on it and being prompted by this suggestion frombw2341, I have an idea.Give me a few minutes.....

author: Brumby
author_rank: Unknown
timestamp: November 28, 2018, 02:00:17 am
content: Find the radius of your styrofoam balls (half the diameter) and multiply that by 1.323. This will give you the length of each edge of the icosahedron that will sit around the sphere, just touching the centre of each face.This means the length of the edges of the hexagons and pentagons of a truncated icosahedron will be one third of that - or 0.441 times the radius.Starting with the net provided by that PDF, I have cut it in half, removed the pentagons and added a couple of tabs:Print it out - having found the right scale - cut it out, score along all the fold lines, crease each of these fold lines and stick it together with the tabs to help secure it. I put the tabs on the outside because it was easier and the look of the half shell isn't important - just the location of the vertices. It should look like this:This was made using regular80gsm A4 paper and I waspleasantly surprised to seehow well it held its shapewithout any reinforcement.You then take this half shell and place it around your styrofoam ball. If you've got the dimensions right, the ball should sit neatly inside the shell, just touching the centre of each hexagonal face.You then take a felt tip pen and mark EVERY vertex on the ball using the half shell as a guide. Once done, rotate the ball 180 degrees and align the vertices marked on the ball with those at the edge of the half shell. There will be 12 of these. The quality of your result will be determined by how well these 12 points line up - and that is determined by how accurately the dimensions are of the printed out sheet.Once you have all the dots, join them and colour in the shapes as you like.

author: Brumby
author_rank: Unknown
timestamp: November 28, 2018, 02:17:37 am
content: If you were to do two half shells, you could put them together around a ball and spray paint through the pentagonal holes. You wouldn't get crisp edges doing this, but it would be way faster.If you want to give this a try, use the template here - I've added 3 more tabs. Just print two of them and join them around the sytrofoam ball.

author: Cyberdragon
author_rank: Super Contributor
timestamp: November 28, 2018, 02:28:53 am
content: *Finds this thread*ICBM launch control systems?*disappointment...**activate football memes...*

author: Brumby
author_rank: Unknown
timestamp: November 28, 2018, 06:58:05 am
content: How can you call gridiron football? The only time the ball makes contact with a foot is at kick off and when going for the extra point. Any other times are incidental.Rugby league makes a better effort with the foot. Rugby union is a step up from that. Jump up to Aussie Rules and then Gaelic football until you reach the original: Soccer.

author: RobK_NL
author_rank: Frequent Contributor
timestamp: November 28, 2018, 03:04:15 pm
content: Brumby, you are amazingLet me know if there is any way of getting a liberal amount of your favourite poison your way.

author: Brumby
author_rank: Unknown
timestamp: November 29, 2018, 12:56:26 am
content: Let me know if it works, first.

author: bw2341
author_rank: Regular Contributor
timestamp: November 29, 2018, 05:50:27 am
content: I came up with 0.419 of the radius for the edge length. I calculated this value by taking 1/15 of the sphere's circumference.One pair of the zigzag hexagons covers the length of 3 edges. This consists of one edge of the hexagon plus the distance between opposite vertices of the next hexagon (2x the edge length). A strip of five pairs of hexagons will cover the circumference of the sphere.

author: Brumby
author_rank: Unknown
timestamp: November 29, 2018, 06:45:12 am
content: That is an approximation that doesn't take into account the fact that the line segments you refer to do not follow the curved surface - they are straight lines. Add to that the fact that the actual point of contact for the model I have used is in the centre of each hexagonal and pentagonal face and you can see the line segments are actually above the surface of the sphere. Thus, the actual line segments will be longer.FYI - the numbers I have used were taken from the Wikipedia entry on the regular icosahedron:https://en.wikipedia.org/wiki/Regular_icosahedron#DimensionsThese numbers have been created from the fundamental mathematics which describe the geometry. There is no approximation until we turn the answers into a simple number - but there are enough decimal places for this exercise.

author: beanflying
author_rank: Super Contributor
timestamp: November 29, 2018, 07:02:15 am
content: Quote from: RobK_NL on November 26, 2018, 09:07:55 pmMuch as it the thread is interesting rereading the original post and what they were looking for needs to be kept in mind. This is primary or maybe secondary school children wrapping a present in a creative manner. If the intent was for the child to make the parcel then simple would be what is needed which is why straight lines and a simple pattern like from the link I posted are appropriate. Breaking up the shape like Brumby has done should make construction and printing it out initially easier too.Approximating 3D curves from square panels of paper or fabric I have done some by guesswork and or flexed timber in the case of kite repairs where there is no pattern or in some cases no usable cloth panel to work from (barb wire or rock shredded panels) this never yields a perfect result without unpicking and re sewing or even remaking a panel so not appropriate as a solution here.To do it mathematically is crazy and the stuff of Uni Maths or derived from making a CAD model of a sphere and panelling from there. None of these approaches are of much use to the OP and a childrens parcel wrapper.KISS

author: RobK_NL
author_rank: Frequent Contributor
timestamp: November 29, 2018, 08:52:09 am
content: It probably won't pass FIFA muster, but as a surprise gift made by an 8 year old it's pretty decent I would say.Thanks again for all the help guys.

author: Brumby
author_rank: Unknown
timestamp: November 29, 2018, 11:15:24 am
content: That's a great job! The geometry looks spot on.Well done.

author: Fred27
author_rank: Unknown
timestamp: November 29, 2018, 02:34:43 pm
content: That looks really good (unless you've hidden the bits that don't line up round the back).

author: RobK_NL
author_rank: Frequent Contributor
timestamp: November 29, 2018, 03:18:44 pm
content: Quote from: Fred27 on November 29, 2018, 02:34:43 pmOf course I did, what do you think?

author: bw2341
author_rank: Regular Contributor
timestamp: November 29, 2018, 08:07:35 pm
content: That looks awesome! I'm sure your kid's friend will love it.

author: bw2341
author_rank: Regular Contributor
timestamp: November 29, 2018, 08:10:14 pm
content: Quote from: Brumby on November 29, 2018, 06:45:12 amHere’s my reasoning. Line AA’ is what I used to count off the length. It’s the same length as line BB’. Since they form a parallelogram, line CC’ (which is midway between AA’ and BB’) is the same length too.Paper is a loose and floppy material, but you can roll it up on one axis into a cylinder with no kinks or creases. If you size the pattern so that the length of CC’ matches the circumference of the sphere, it will fit exactly.Of course, this is only approximate as only line CC’ is in direct contact with the sphere. When you try to curve the half-hexagon flaps down to the surface, you can’t make them lie flat without kinking or creasing the paper. Still, it should let you mark the vertices more accurately than any other method.If the paper cylinder is twisted 120 degrees at the centre point of a hexagon, the same strip can be used to mark off more vertices. Twist another 120 degrees and the final vertices can be found.Accounting for curvature in one axis is better than ignoring it and pretending that paper can stay flat and rigid. Yes, the vertices won’t match the points projected from the truncated icosahedron, but they will be very close. If you only mark the vertices from the pattern and use a flexible ruler to mark the edges, you won’t be able to tell by eye that the angles are off and that the edges aren’t all the same length.

author: coppercone2
author_rank: Super Contributor
timestamp: November 29, 2018, 08:15:21 pm
content: you misnamed the thread

author: RobK_NL
author_rank: Frequent Contributor
timestamp: November 29, 2018, 09:49:50 pm
content: Is that a rugby ball?

author: Brumby
author_rank: Unknown
timestamp: November 30, 2018, 12:32:06 am
content: Quote from: RobK_NL on November 29, 2018, 09:49:50 pmI'd duck, if I were you.