Frabjous
lasercut
attached svg file
mathematical
decoration
Frabjous is a fantasy word introduced by Lewis Carroll, and repurposed in this context by George Hart to denote this dodecahedral star sculpture:
https://www.georgehart.com/sculpture/frabjous.html
The pattern I originally found was from here:
https://www.thingiverse.com/thing:724
But it turned out to be hand-traced, so I redrew that in my CAD software with actual symmetry contraints and straight lines.
Pattern to cut out #
Here is a link to the svg. I think this repetition of the shape uses material quite efficiently, but there could be a better “tiling”.
DIY Instructions #
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Cut out 30 pieces. The thickness of the material you choose is important. Too thick and there won’t be enough space to assemble. In the photos it’s 3mm plywood for a tip-to-tip distance of 15cm. I wouldn’t recommend to go thicker at the same scale, so scale up to e.g. 25cm minimum if you have 5mm material. In the assembly instructions, I also made another Frabjous with 5mm thick plywood and 45cm tip-to-tip distance.
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3D print the inside tip, 20 pieces. See below for ideas when you don’t have access to a 3D printer
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Glue pieces together progressively, do not attempt multiple sub-assemblies. Be careful about which part goes under, which over. See Assembly walkthrough.
3D model of inside tip #
Pictured here is the 3x scaled up version for 5mm thickness and 45cm tip-to-tip (tip-to-tip distance is the scaling factor, not the thickness).
You will need 20 of those for one full Frabjous, the 3D model is for the 15cm tip-to-tip design (3mm thickness), so scale it up if needed.
Download here, or on printables.
How to join the tips #
For the wooden models, I used a 3D printed joiner shape and glued the wood pieces on it. But this makes a 3D printer necessary for the construction, even though there are other ideas that can work:
- Sand two opposite edges of every wooden piece at 70°, then glue the pieces together: one flat edge onto one sanded edge
- Use cardboard and make the insert shapes with hotglue
- Cut out equilateral triangle pieces of wood and glue those on the inside of each tip from below
- Make a jig to put three pieces together in one tip (at a 70° angle to eachother), then just glue them. Beware of clearances so that the last tip of the Frabjous can still fit in the jig
Assembly walkthrough #
The Frabjous has a dodecahedral symmetry: if we look at a circle of triple-tips, they are always arranged by five in a circle. If you’re finishing a circle and it only has four or six tips, there is something wrong and you need to backtrack.
We will be leaning on this five-fold symmetry during assembly, for some steps that repeat five times and just need to rotate the in-progress Frabjous by a fifth of a circle between every repetition.
1: Base circle of ten pieces #
Start by making a star-shaped circle base with five pieces. Then add the third piece to complete every tip (5 times).
If you feel unsure, first walk through all the steps just with tape, and glue the pieces only in the final assembly.
Continue in a 5-symmetric pattern around, keeping the under-over pattern like in the picture
Over-under pattern is wrong on this piece! Example of what not to do
Pink arrows are correct: from one piece to the next, they go below. Incorrect orientation: red arrow goes above.
Correct over-under pattern. Every arrow from one to the next piece goes below.
Congratulations, the first ten pieces are holding together!
2: Next ten pieces #
In all five circled tips, add the 2nd/3 and 3rd/3 pieces. Pictured in blue is the start position: 1/3 pieces present in the tip.
In red is the intermediary position: 2/3 pieces placed. Beware of oritentation, one red circled tip has the left-sided 2nd/3 piece and the other red circled has the right-sided 2nd/3 pieces placed. The order doesn’t matter too much because you need to add the 3rd/3 piece as well.
You want to add both all five 2nd/3 pieces and the other five 3rd/3 pieces on the circled tips.
For easier access, flip the whole sculpture over: (else the added pieces need to pierce the floor)
Flipped over, complete all the circled tips to reach 3/3 pieces. Again always keep over-under orientations in mind.
Finished state: two blue circled tips are still visible. All previously circled tips are 3/3 complete.
The green circled tips are created by the added pieces.
3: Complete tips to 3/3 #
Here, add pieces on the green circled tips at the top. In the picture some of the 1/3 and 2/3 pieces are not aligned properly because they were not yet glued and still free to move.
End position: the green tips are completed to 3/3 pieces.
Note: all tips are now present on the star with at least one piece, so you should have used up all the 20 inside-tip 3D printed parts.
4 Finish last circle of five pieces #
The Frabjous is almost finished. You can note that there are five tips with only 1/3 pieces present. Add the 2/3 piece on one of those tips, and it will complete the 3/3 on another opposite tip.
Flip the sculpture upside down for best access.
The difficult part is inserting the piece in position, because they are the last pieces it’s a bit crowded.
You need to insert the piece rotated to face “the wrong way” by 180°, and only rotate it once it’s inside the structure.
Rotate clockwise (corkscrew motion) like the red arrow when in this position
The piece is now rotated and in the correct over-under orientation.
Repeat five times, and you should be finished with the assembly. Congratulations!