Joining pentagons

Dear all

Looks as though my brain has finally turned to mush. Pretty sure I could have worked this out with pen and pencil 50 years ago.

Kids grow up. They abandon the trampoline. The 2" steel poles that supported the trampoline are inevitably too good to abandon and so you pack them up and transport them across a few house moves in the certainty that you will use them creatively.

Numerous Norman Wisdom slips, trips falls and surfing across the garage floor episodes later the time has come to weld them into something of no practical value.

This is where the problem starts. Confidently convinced SWMBO that I could create a tubular duodecahedron using my new found welding skills and even more developed 'grinding the mistakes off' abilities. So ten tubular pentagons sharing vertices in a 3D configuration.

For the life of me I can't work out how to plot the cut lines or intersections on the end of each tube. If it was smaller section or wood I could rig up a drilling jig but gashing out 2" tube takes more grunt than the kit I have available. I do have a mill and a couple of lathes but set up for the cuts is dependent on working out the geometry which is defeating me. Hence a preference for paper templates, saw and grinder.

Enough rambling. Some assumptions.

• Each component part should be identical so I once the mark out is set it should be a relatively simple question of gashing the 30 pieces required with basic saw and grinder. Surely any pentagon viewed individually attaches to another identically? Or there a consideration around top and bottom halves that throws that assumption out?
• A simple pentagon wooden framework as a base will allow the parts to be held relative to each for assembly. The base layer first then flip that on its side/at an angle to add each upright in turn.
• Do that for a top and bottom and the two halves will join seamlessly with no need to bodge and hammer them into shape. What could go wrong?

It seems an interesting exercise but I can't for the life of me work out how to project the angles for the various intersects and then develop the bit of high tech paper to wrap around each end.

Creating a single pentagon in one plane is easy enough - diagonal cuts - and it would be possible to do a top and bottom that way but it will be inelegant to then tie in the other components 'overlapping' the corners. If that is the only realist route to success I will pursue that but ideally I'd like it to look decent so that I can dump it in the garden and call it 'art.' Then I can re-fill the space created in the workshop with more scrap to trip over . . . it keeps me nimble.

Finally the question! Is there an online tool that I can use to do the required projection?

Many thanks in anticipation. I ask more questions than I ever answer and always appreciate the help given. Once this is out of the way I have a few more queries lined up. Will post a picture of it once done.

Andrew Smith

This is not an answer to your question.

This is a link to a dome calculator. - extraordinarily good time waster. Used in a past life to design a dome.

I also found this but I cannot speak as to its utility. [specifically about dodecahedron math]

Regards.

Frank C

Edited By Chuck Taper on 28/03/2023 10:13:38

**LINK**

https://www.cuemath.com/geometry/dodecahedron/

MichaelG.

I think you might have two too many sides in your mind, which is making the thinking difficult.

If you look at the picture here:

https://upload.wikimedia.org/wikipedia/commons/3/33/Dodecahedron.png

every vertex of the shape has _three_ members meeting. Hence, you can think of a primitive shape as a non-regular tetrahedron and you need to know the tube shape for the apex. You know the side length of the pentagon, hence you know the side length of the triangular tetrahedron base.

Rig up a similar tetrahedron made from broom handles or wooden dowels, sand to a good fit, wrap a piece of paper around the end and trace the profile and then scale up on a photocopier.

Making a start, the shape is a Pentagonal Dodecahedron. (Image from FreeCAD's Pyramids and Polyhedrons Workbench, which is an optional download from Tools->Addon Manager)

The angle at each pentagon's corner is 108°.

The dihedral angle between adjacent pentagons is 116.565°

So I think the exam question is: 'If the edges are replaced by 2" diameter tube, what shape should be cut into the end of each tube so that each group of three will butt together exactly so the weld doesn't have to fill any large gaps.'

Two is easy, have to think about three!

Dave

Start by making three pentagonal templates from sheet material, MDF is cheap. Assemble the structure so you have a common corner. This gives you the geometry and once you have all the tube cut to length so each piece fits on the outside of the jig you can then trim the ends so they join neatly when on the inside. If you cut the corner out you can use the jig to align the tubes for welding by placing them on the inside an tacking up.

It may be a more interesting shape to build from pentagons and hexagons. A friend and I did an observatory dome this way with fabricated panels in fibreglass.

regards Martin

Thanks for the suggestions gents.

Arranging the intersection between a single apex is simple enough.

I am probably over thinking things but while the geometry of each individual joint is identical the relationship of those joints relative to each edge is offset to accommodate the closure of the shape. The 'notch' nibbled out of one end of the tube will be replicated at the other BUT that complementary notch will be offset both around the axis of the tube and also angled to accommodate the additional offset required to close the shape in three dimensions.

It is the relative angle of rotation along the axis plus the lean out to achieve the flared sides that have frazzled my brain.

Thanks again. I will revert to trial and error as the grey cells aren't firing for me.

Thanks Martin

That might be my salvation. Will that just invite straight cuts in each plane rather than faffing with projecting curves?

Surely it does??? That would be a simple jig to knock up.

A

Just looking at the image Dave so kindly provided if you draw a line from a corner to the midpoint of the opposite side for the three faces that should get you the angles of the 3 cuts you need. If you put a hacksaw cut down each line square to the face that would get you a saw guide. With a little inventiveness you should be able to clamp each piece of tube to the inside of the jig and trim the ends.
regards Martin

The whole thing could be done using only a straight edge with 2 marks to define the edge length, thus escaping the metric or imperial argument.

Looking at Dave's image, which I have previously looked at on the net several times, it is now obvious how to go about this.

Thanks for the inspiration everyone. Wouldn't have seen the wood for the trees without your nudging. I think a plan has formed.

Regards

Andrew

You could buy some balls then it's just straight cuts to the tubes rather than working out the compound angles to cope cut the tubes at

Just a thought [although I do rather likeJason’s idea] …

a 2” hole-saw, guided by a 3D jig representing one ‘corner’ should do the end-trimming nicely.

MichaelG.

Nice idea Jason, and my wife would appreciate the artistry as much as I would appreciate the time saving. But I suspect the cost of balls required would prove prohibitive (can you get 2" steel balls?) My daughters magnet sets worked on the same principle.

Thanks for the thought Michael. My initial idea was along those lines but guiding a drill accurately enough to get it cutting on the periphery of a tube at an angle invited more engineering than I wanted for a quicky.

I'll opt for what will essentially be a saw dog with splayed legs to create the alignment for the saw cuts at the end of each member. Some basic guides for the blade, maybe studding, and a happy few hours of sawing before I cover everything in spatter. Almost excited at the prospect now.

Truly grateful. The fog is clearing - and may well have cleared completely. The only thing unresolved is my cack handedness.

50mm hollow steel balls from eBay if I am allowed to post the link.

John

F H Brundle supply all sorts of steel items including Hemispheres and balls. A link to their web page (if thats OK).

Aimed at the trade but will supply to individuals, F H Brundle

Also do full balls Link Full Balls

Need to add VAT and delivery might cost but unit pricing is good.

Michael

Edited By Michael Cottle on 28/03/2023 15:50:23

It's 2 straight cuts at each end, you just have to rotate the tube by some angle to make the second pair of cuts. The problem is what's the angle, and it will take a geometry guru to work that one out.

.

Trying to get my head around how those would be used with 2” tubes

MichaelG.

.

… useful range of sizes

MichaelG.

The pricing from FH Brundle invites a redesign - and a few more flights of fancy as to what might be achievable over the coming weeks.

If the geometry guru Duncan alludes to should show up I am still interested in working out a way to set out angles without resorting to building a jig. By 'working out a way' I of course mean 'receiving a tailor made solution that overcomes my incompetence at what should be a relatively simple exercise.'

I'm not sure it can be done with a pair of compound cuts at each end whether straight or done with a hole saw. There is the little matter of a curved external "corner" that would be best done by letting in a triangular piece of flat sheet and then building up some weld over the top before dressing it back. All options I have tried with just cutting the tube leave a nasty lump or a hole.