I read somewhere that using a compass and a straight edge you can't make a seven sided polygon (heptagon).  That led me down a rabbit hole of playing with the polygon tool in Aspire to prove or disprove that mathematically  proven fact.  Along the way I discovered a few other neat facts about five and seven and 9 sided polygon that help me make these patterns.  The vector patterns are made by spinning a shape by a known amount that is double the number of sides on the polygon used.  Some layer tracing was used to isolate areas after the spinning, but that didn't take too long. 

 

The last image was done using a star shape.  I imagined a small feature wall tiled with unique variations of this technique, with all tiles unique.  All of the above renders show the results using a 120 degree V-bit and the VCarve toolpath.   Not sure what dimensionally stable and uniform material these could be cut in that wouldn't warp or expand/contract.   I remember some color paper board we had samples of to play with a couple decades ago which might work.   Have no idea what it is called or where to get it though.  

4D

Edited August 2, 20232 yr by 4DThinker

I've written up how I produced these patterns on my blog.  It is fairly easy, particularly using the drafting features in Aspire. 

https://4dfurniture.blogspot.com/2023/08/polygons-and-pattern-work.html

Possibilities are practically endless.

4D

A practical application for these patterns could be carved drawer or door fronts for cabinetry.   I've shrunk and stretched a pattern to fit on a 15" x 4" drawer front as one example.

Something to add a little detail to what is usually a boring surface.  Center 1/2" diameter area cropped out for a knob.   These patterns are vertical and could be left as recessed carves or inlaid with a contrasting color of wood using the V-Carve inlay technique. 

4D

What a great idea! I will have to read that write up. Thanks for sharing!

Smaller versions, using  a 60 degree V bit might be nice décor for coasters or trivets. For coasters I'd still fill the patterns with epoxy.  

This example started out with a nine-side polygon.  I replaced every 3rd edge with a concave V before spinning it nine time in 360 degrees.  After the first render I replaced the outer square edges with an arc to relate better to the round coaster shape.

4D

Perhaps a little nice final touch would be a small chamfered edge. Then add a recessed adhesive backed cork bottom to keep then from sliding around.