I just stumbled across a way to build a 7-way radial symmetry in LEGO.
A technique for building 7-way radial symmetry in LEGO. The blue 2×2 plates are connected to each other using plate hinges in a ring, and when I built that I noticed the ring looked like the right diameter to go around a 4×4 round piece. The hinges actually protrude a little into the center, but by sandwiching the two 4×4 rounds together and filling the space inside with a round 2×2 plate and seven (leaving one stud open) 1×1 round plates, you can make it all fit nicely. And since the 4×4 rounds and 2×2 round plate have axle holes, it can easily be connected to any Technic mechanism.
If you stick an axle in the middle it twirls like a top – it’s very well balanced.
LDraw code after the break:
0 FILE seven-symmetery.ldr
0 Seven Symmetry
0 Name: seven-symmetery.ldr
0 Author: William R. Ward
0 License: public domain
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1 0 0 8 0 1 0 0 0 1 0 0 0 1 6222.DAT
0 STEP
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1 25 -30 0 -10 1 0 0 0 1 0 0 0 1 4073.DAT
1 25 -10 0 30 1 0 0 0 1 0 0 0 1 4073.DAT
1 25 10 0 30 1 0 0 0 1 0 0 0 1 4073.DAT
1 25 30 0 10 1 0 0 0 1 0 0 0 1 4073.DAT
1 25 30 0 -10 1 0 0 0 1 0 0 0 1 4073.DAT
1 25 -10 0 -30 1 0 0 0 1 0 0 0 1 4073.DAT
1 0 0 0 0 1 0 0 0 1 0 0 0 1 4032.DAT
0 STEP
1 0 0 0 0 1 0 0 0 1 0 0 0 1 ring.ldr
0 STEP
1 0 0 -24 0 1 0 0 0 1 0 0 0 1 6222.DAT
0
0 FILE seventh.ldr
0 Seventh
0 Name: seventh.ldr
0 Author: William R. Ward
0 License: public domain
0 ROTATION CENTER 0 0 0 1 "Custom"
0 ROTATION CONFIG 0 0
1 1 62 0 0 1 0 0 0 1 0 0 0 1 3022.DAT
1 1 42 8 -20 1 0 0 0 1 0 0 0 1 2430.DAT
1 1 42 8 -20 -0.62349 0 -0.781831 0 1 0 0.781831 0 -0.62349 2429.DAT
0
0 FILE ring.ldr
0 Ring
0 Name: ring.ldr
0 Author: William R. Ward
0 License: public domain
0 ROTATION CENTER 0 0 0 1 "Custom"
0 ROTATION CONFIG 0 0
1 0 0 0 0 1 0 0 0 1 0 0 0 1 seventh.ldr
1 0 0 0 0 0.62349 0 0.781831 0 1 0 -0.781831 0 0.62349 seventh.ldr
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1 0 0 0 0 -0.222519 0 -0.974928 0 1 0 0.974928 0 -0.222519 seventh.ldr
1 0 0 0 0 -0.900971 0 -0.433879 0 1 0 0.433879 0 -0.900971 seventh.ldr
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0
Very clever discovery.
I have a new
LEGO® community site: Brick Collections
and would be delighted to have you submit your work.
Stephen
I also built a neat (IMO) 7 way symmetry in my Souther Star Wheel, you can see it here: http://www.flickr.com/photos/roscohead/6975695697/in/pool-lego_math
The hub is based on sin(pi/14) being very close to 2/9, and is made of 14 isosceles triangles 4/9/9 studs.