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Build - Polytope

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  • Build - Polytope

    http://en.wikipedia.org/wiki/Truncated_cuboctahedron, http://en.wikipedia.org/wiki/Archimedean_solid. It looks like this:

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    While it might work, it is really big and pretty ugly, just a bad snowman of a speaker. Working it a bit more, I looked at overlapping shapes a bit to make something more compact, with this as a result:

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    Definitely better and might work. Problem is that when I look at the shapes I will need to cut and piece together, it will be a total nightmare. Need to compact things a little more and avoid as many concave joins as possible. Dropping to two joined shapes instead of three was a good improvement and pretty close to workable:

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    The challenge here is how to place the three drivers in a way that will produce good sound and will keep some level of symmetry. My approach is to actually open up part of the hexagons near the bottom and mount the woofer in a baffle that goes across the midpoint of the hex and the bottom of the elongated octagons.

  • #2
    Re: Build - Polytope

    With cutouts for the drivers, the overall shape looks like this:

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    With some generic speakers added to the model, the result will look like this:

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    This pretty much wraps up the basic design steps. The next step is the actual cutting & gluing and cursing of construction. More to follow as I get that part written up.

    Xander

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    • #3
      Re: Build - Polytope

      That is some interesting math, and an interesting design, for sure. Ought to make for an interesting build with reasonably high-level of difficulity.

      I do remember a set of Tanberg speakers from the 70's that were faceted spheres like your first pic. I can't remember how they sounded, but they looked interesting. They were a orange color, too.

      Good luck.
      Andy.

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      • #4
        Re: Build - Polytope

        I am curious about the building process you will use, are all of the edge bevels 22.5 degrees?

        Comment


        • #5
          Re: Build - Polytope

          Part 2 - Construction

          With the design in hand, the next step is the cabinet construction. Transferring the paper layout to the actual boards involved a lot of pencil drawing and double checking of edge lengths. Cutting out the major groups of faces resulted in this:
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          From there a long series of cuts on both table saw and mitre saw to produce the pile of basic faces:

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          Each face now has to be mitred in accordance with how it will connect to adjacent faces. In answer to the question by TN Allen, the dihedral angles depend on the combination of faces:
          • 135 degrees for the octagon-square angle
          • 125 degrees 16 minutes for the octagon-hexagon angle
          • 144 degrees, 44 minutes for the hexagon-square angle

          The set on the saw is (180 - dihedral angle) / 2. So, there are 22.5 degree mitres on each edge between an octagon and a square. An edge between an octagon and a hexagon would be mitred at about 27.5 degrees.

          The cutting and mitering done, the next step was construction of a jig that could hold pieces in place while dryfitting and during the glue process. On consultation with a friend that actually does woodworking for a living, he recommended investing in a biscuit joiner. This was a great investment and in many respects made it possible - I don't know how I would have kept the faces in place during glueing, or gotten the rigidity that comes with all those thirsty biscuits in every edge.

          The jig was built to match the width of the octagons and the squares. The elongated octagons and squares dry fitted in the jig looks like this:

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          The real challenge isn't the elongated center, it is the end caps. I numbered each piece and on each edge marked what piece was adjacent, like this:

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          After cutting the slots for the biscuits, I worked on fitting the end caps together. None of the pieces was exactly correct, so there was a bit of trimming here and there. Note the lines connecting each pair of faces, these were for placing the joiner when cutting slots, but they later came in really handy during gluing - they provided a guide for just how much each piece needed to be moved to get everything into place.

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          • #6
            Re: Build - Polytope

            Glueing the pieces together had to be done all at once. Unlike 90 degree joins, there's no way to add another piece to the end cap once it has dried. Essentially every piece gets glue for the biscuits, glue along the edges, and is loosely fitted to adjacent pieces. Then all of the pieces are squeezed together until everything is in place. After glueing the main chamber together, it looks like this:

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            There really aren't any clamps that work for these angles, so I put bands around the main body like the one shown below (although I actually used several bands, not one), and a weight on the top (not shown) so that all of the faces were under pressure towards each other.

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            I used normal Titebond for the biscuits and construction adhesive along all the edges. The construction adhesive is nice because it doesn't run like the yellow glue, so during the process of glueing and fitting, it doesn't drip all over the place. I did keep the adhesive to the inner part of the edge because I didn't want to spend a lot of time sanding it down later (it is really hard when dry). The view looking from the open bottom towards the top after glueing:

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            While there may glue along all the edges, things aren't perfect. Looking at the outside, there are visible seams between many of the faces. Below is a view of some of the worst. All of these openings will need to be filled and sanded flat.

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            • #7
              Re: Build - Polytope

              The process of filling in seams and getting it all nice and flat starts with pushing Elmers wood filler into all the cracks, letting it dry, and sanding it down. After the first application of filler it looked like this:

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              After sanding this down, the edges were in much better shape, but not good enough to move on. Looking at the edges there are visible flaws.

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              After a second round of filling and sanding, the result is much better:

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              Almost there. However, if you look along the edge up and to the right of the corner, you can see a defect in the edge. The final round to touch these up only involved the affected areas, like this:

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              After getting the top and sides into shape, I added the bottom and went through the same filling and sanding procedure.

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              • #8
                Re: Build - Polytope

                The base that goes under the the woofer was the final piece to construct. Fortunately, the same jig used for the main body could be reused for the base:

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                A bit of tidying up was needed on the bottom of the main body. I connected it to the rest of the body using glue and screws. (remember the problem about joining mitered pieces after the fact?) As the screws went in at angle in order to go through the bottom and into the adjacent faces, part of the heads were sticking out. A few minutes with a Dremel cured that and made for a kind of pretty display.

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                At this point, the main body of the speaker is together. While I'm sure I should have cut the holes for the drivers before assembly, it just didn't happen that way. So, it was time for drawing lines and circles. I started by getting axes drawn as cleanly as possible. Using diagonals across faces was a good way to double check.

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                Using those lines and figuring offsets so that each driver would be centered, I ended up with circles and more importantly center points that could be used for routing.

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                The cutting of the holes was definitely stressful. Since I had already invested quite a bit of time in construction, an error here would be really unpleasant. I used a pretty standard circle cutting jig. Note: it doesn't fit on my good router, but does fit on the low end plunge router I got from Lowes because it and a table together were only $75. I think the bits I used for cutting cost more than the router.

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                • #9
                  Re: Build - Polytope

                  ..... Wow. That is really awesome. Just the box is impressive, none the less the fact that the boxes will be speakers. :applause:

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                  • #10
                    Re: Build - Polytope

                    Nearly done with the construction. After using the router & jig, cutting once for the flush mount and a second time for the hole. Of course all three drivers are different sizes (even the 10" aren't quite the same) and different thicknesses. All in all the circle cutting jig worked. A view of the cabinets, upside down so you can see the woofer cutout:

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                    Just a couple more things to do. The first is layout of the ports and the plate where the connections will go. I used tau (the golden mean, limit of ratio of successive Fibonacci #'s, ...) to determine the vertical placement of the centers of both. Not that is makes any real difference, but I needed some scheme for the measurement.

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                    I cut the holes for the ports using a Forstner bit. They are really nice for making clean holes. The flat drill bits always seem to shred the back side of the hole.

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                    I didn't do the cutout for the terminal place. Parts Express sent me only one of them (I ordered 4) and apparently discontinued the line. I would have preferred none to just one. Not happy about that. I did leave 1/16" drill holes at the corners of opening so I wouldn't have to measure again after the paint goes on. Within the outline of the terminal place I drilled holes for the Speakon connectors so I could do some testing while waiting for replacements.

                    I fitted the base using screws to make the (temporary) attachment. The base needs to be removable in order to be able to remove the woofer. I haven't figured out a better way to make the attachment. They turn out to be pretty unobtrusive since they are on the bottom and most people won't have their heads down there.

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                    Right side up and assembled, the bare cabinet looks like this:

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                    Next up is painting. If I'd know what an onerous task it would be I might have just stopped here.

                    Xander

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                    • #11
                      Re: Build - Polytope

                      Why not use 'hanger hooks' From Walmart meant for coats, hats, etc? 3 or 4 on the underside would keep it stable, and still allow for driver removal without removing the base.

                      Later,
                      Wolf
                      "Wolf, you shall now be known as "King of the Zip ties." -Pete00t
                      "Wolf and speakers equivalent to Picasso and 'Blue'" -dantheman
                      "He is a true ambassador for this forum and speaker DIY in general." -Ed Froste
                      "We're all in this together, so keep your stick on the ice!" - Red Green aka Steve Smith

                      *InDIYana event website*

                      Photobucket pages:
                      http://photobucket.com/Wolf-Speakers_and_more

                      My blog/writeups/thoughts here at PE:
                      http://techtalk.parts-express.com/blog.php?u=4102

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                      • #12
                        Re: Build - Polytope

                        Wow...great work. Amazing craftsmanship there!! I'd like to be able to do a nice 45-deg miter....is that asking too much?
                        Bryan K.

                        Midwest Audio Club

                        Speedster | Sub Attach | The Wildeman | Sean's NLA Towers | COGAR, COUGAR II and COGAR JR | Triton | Lithium | J-Boom | Trym MLTL | Docere MLTL

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                        • #13
                          Re: Build - Polytope

                          What a lot of work! Well done!

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                          • #14
                            Re: Build - Polytope

                            Originally posted by Wolf View Post
                            Why not use 'hanger hooks' From Walmart meant for coats, hats, etc? 3 or 4 on the underside would keep it stable, and still allow for driver removal without removing the base.

                            Later,
                            Wolf
                            Just went and looked at them - that is a great idea. I may try building a second base and see if it will work. The purpose of the fastener is to maintain a connection, not for structural strength. The base has to be strong, but the connection between the two parts just has to be enough to keep them together.

                            Xander

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                            • #15
                              Re: Build - Polytope

                              Awesome project. I wish I had a shred of woodworking ability.

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