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For the purposes of this build, we need a pentagon (figure with 5 sides), that is regular (all sides have equal length), and it needs to be able to be mounted on a build (like a wreath) by a technic-friction-pin, (the little black ones).

This may be hard to achieve, with the given possible angles. The pentagonal shape must maintain its shape, no warping, etc. It must also be made of "properly fitting pieces."

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Using the same length ratios as in the construction that Philo posted in his answer I created this:

enter image description here enter image description here

It uses length 5, 6 and 7 thin liftarms (5 of each) and 30 half-pins I'm quite happy with it!

Michael Verschaeve
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A solution, using a (quite precise) approximation: enter image description here Granted, it's a bit bulky, but it could be reduced by half using 7.5 stud long stiffeners (eg. using Technic brick 1+ Technic brick 8 +plates)

Link to LDraw file: http://www.brickshelf.com/gallery/Philo/misc2/pentagon/pentagon.ldr

Philo
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  • I see the pentagon outer angle created by triangle with sides 15, 12 and 6 for a 108.21 degree which is indeed a good Approximation, but you could make it a third as small with a 5,4,2 triangle! – Michael Verschaeve Feb 01 '18 at 16:44
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Recently came across this problem again, so I'd like to post another answer (2 answers actually).

I figured out how to create an "exact" pentagram (no approximations) using only swivel plates and turntables (blue in the picture):

FB image smaller

The math very shortly: cos(Pi/5) = (1+sqrt(5))/4 and sqrt(5) can be created with a (2,sqrt(5),3) righthanded triangle.

I posted this in the FB group "LEGO math and patterns", one of the group members mentioned a paper "Mecanno math" by Gerard ’t Hooft which can be found here, which has several elegant solutions, e.g. figure 7 in the paper lists 6 solutions: figure 7 in the paper

It should be straightforward how the Meccano strips can be replaced by Technic liftarms (as the original poster asked).

Another response I got in another FB group is that this constructions works quite well: enter image description here

I tried it and they are correct, the pentagon is rigid and the elements do not seem under undue stress.

enter image description here

Michael Verschaeve
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I would suggest you use 10 of either one of these: 4273 Technic, Axle and Pin Connector Toggle Joint Toothed or 4273a Technic, Axle and Pin Connector Toggle Joint Toothed - Without Slots, together with 5 equal length axles and 5 pins. Creates a sturdy pentagon. Use the pin connector hole to attach the pentagon to other structures.

enter image description here

If you don't want axles, but bricks, you can mount connections onto the bricks to mount these 4273s the same way.

Phil B.
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    It's impossible to create a pentagon with 10 Axle and Pin Connectors. The reason is simple, each angle of a pentagon must be of 108°. But pin connectors can only have the following angles: 90, 112.5, 135, 157.5 and 180°. So it's impossible to create a pentagon with these connectors. – A.L Sep 15 '16 at 20:39
  • You could argue that 112,5 is close enought to 108 degrees. The pentagram is indeed under a bit of stress though, axles are slightly bent – Michael Verschaeve Feb 13 '18 at 11:16
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A right triangle with sides 3 by 1 has as largest angle 71.5650512 and smallest 18.4349488 degrees. That is reasonably close enough to 72 and 18 degrees which can be used to create a pentacle. Lots of right angled connectors or beams you could use then...

Michael Verschaeve
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