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Hints for formatting the data of your submitted packings



Section 1: Packings of equal and unequal circles in fixed-sized containers with maximum packing density

Circles in a square Circles in a circle Circles in rectangles Circles in an isosceles right triangle Circles in a semicircle Circles in a circular quadrant
Last updated: Last updated: Last updated: Last updated: Last updated: Last updated:
18-Oct-2013 23-Sep-2021 25-Jun-2013 18-Mar-2011 16-Apr-2011 04-Jul-2011
Circles in a square Circles in a circle
Circles in a 1x0.10000 rectangle
Circles in a 1x0.20000 rectangle
Circles in a 1x0.30000 rectangle
Circles in a 1x0.40000 rectangle
Circles in a 1x0.50000 rectangle
Circles in a 1x0.60000 rectangle
Circles in a 1x0.70000 rectangle
Circles in a 1x0.80000 rectangle
Circles in an isosceles right triangle Circles in a semicircle Circles in a circular quadrant
calculation form calculation form calculation form


Circles in a circle (ri = i)     Circles in a circle (ri = i+1/2)     Circles in a circle (ri = i-1/2)     Circles in a circle (ri = i-2/3)     Circles in a circle (ri = i-1/5)     Circles in a circle (benchmark instances)     Packomania's wizard
Last updated: Last updated: Last updated: Last updated: Last updated: Last updated:
21-Oct-2015 27-Oct-2015 17-Jul-2014 01-Jul-2014 27-Jun-2014 17-Jul-2014 08-Sep-2011
Circles in a circle Circles in a circle Circles in a circle Circles in a circle Circles in a circle Circles in a circle


The probably densest irregular packing ever found by computers and humans, of course, like André Müller: ccin200.

Circles in a square (ri = i)     Circles in a square (ri = i+1/2)     Circles in a square (ri = i-1/2)    
Last updated: Last updated: Last updated:
28-Oct-2015 08-Oct-2015 08-May-2013
Circles in a square Circles in a square Circles in a square


Thanks to Neil J. A. Sloane and Ya-Ping Lu who triggered me to resume the work.

Circles in a regular pentagon     Circles in a regular hexagon     Circles in a regular heptagon     Circles in a regular octagon     Circles in a regular nonagon     Circles in a regular decagon     Circles in a regular hendecagon     Circles in a regular dodecagon     Circles in a regular tridecagon     Circles in a regular tetradecagon     Circles in a regular pentadecagon     Circles in a regular hexadecagon     Circles in a regular heptadecagon    
Last updated: Last updated: Last updated: Last updated: Last updated: Last updated: Last updated: Last updated: Last updated: Last updated: Last updated: Last updated: Last updated:
04-Dec-2020 18-Dec-2020 05-Dec-2020 05-Dec-2020 05-Dec-2020 05-Dec-2020 07-Dec-2020 07-Dec-2020 07-Dec-2020 08-Dec-2020 14-Dec-2020 14-Dec-2020 10-Dec-2020
Circles in an regular pentagon Circles in an regular hexagon Circles in an regular heptagon Circles in an regular octagon Circles in an regular nonagon Circles in an regular decagon Circles in an regular hendecagon Circles in an regular dodecagon Circles in an regular tridecagon Circles in an regular tetradecagon Circles in an regular pentadecagon Circles in an regular hexadecagon Circles in an regular heptadecagon


Section 2: Packings of equal and unequal circles in variable-sized containers with maximum packing density

Circles in rectangles with variable aspect ratio     Circular open dimension problem (CODP)
Last updated: Last updated:
10-Dec-2011 01-Nov-2012
Circles in rectangles with variable aspect ratio Circular open dimension problem (CODP)




Section 3: Packings of equal spheres in fixed-sized containers with maximum packing density

Spheres in a cube
Last updated:
29-Jun-2018
Spheres in a cube




Section 4: Literature

Literature