n=11 square packing
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€1.18 – €1.44 net (excluding VAT)
For file: jscad (75)_0.4n_0.2mm_PLA_MINIIS_54m.gcode
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Average indicative estimate: €1.31 excluding VAT (range midpoint).
- Weight reported by the author
- 25 g
- Print time reported by the author
- 54 min
- Source material
- PLA
- Estimate material
- PLA
- Estimate printer
- Bambu Lab P1S - 0.4 nozzle
- Estimate process
- 0.20mm Standard
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n=11 is the smallest number for which no optimal square packing is known.
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Updated at source:
Model information
- Source
- Printables
- Category
- Puzzles & Brain-teasers
- License
- Creative Commons — Attribution
n=11 is smallest number for which no optimal square packing
https://web.archive.org/web/20180505055454/http://www.combinatorics.org/files/Surveys/ds7/ds7v5-2009/ds7.html#previousresults
https://en.wikipedia.org/wiki/Square_packing#In_a_square
is known. The best known packing as shown in photo has outer square size of 3.877084 times the size of a unit square. I tried with bigger values before, because I was not sure whether 3D print would be exact enough to fit. The final value I used is 3.8771, and the 11 squares fit inside. It is a tight fit, so if a factor lass than 3.877084 is possible, then with a different arrangement.
I created the model with JSCAD, here is share link you can use to open the model in your browser:
"use strict"
const jscad = require('@jscad/modeling')
const { subtract } = jscad.booleans
const { cuboid } = jscad.primitives
const { translate } = jscad.transformsconst l=15
const s=8
const t=3
const f=3.8771
function main() {
var ret = []
for(var j=0; j<4; ++j)
for(var i=0; i<6; ++i) {
if (j==0 || i==0 || (i==5 && j<3))
ret.push(translate([-70 + i*(l+s),j*(l+s),0],cuboid({size: [l,l,t]})))
}
ret.push(subtract(
translate([-10 , 55, 0],cuboid({size: [fl+2l,fl+2l,t]})),
translate([-10 , 55, 0],cuboid({size: [fl,fl,t]})),
))
return ret
}
module.exports = { main }