All Questions
Tagged with packing-problem 3d
10
questions
4
votes
1
answer
139
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Longest path/snake in 2D and 3D space
Recently I was reminded of an old blogpost I wrote about packing a snake-like path into 2D space (https://www.royvanrijn.com/blog/2019/01/longest-path/).
I never bothered to research this; try to find ...
- 249
1
vote
1
answer
299
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Height of square pyramid stacking of spheres with different radii
What is the total height of a system consisting of 4 spheres of radius $x$ on top of which is a sphere of radius $y$? (Such that the top sphere is in the 'crevice' of the others, as seen when packing ...
- 13
1
vote
0
answers
24
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Densest 3D packing of tori (toruses)
I have a 3D torus, say with radii $R$ (around the hole) and $r$ (thickness), where $R \gg r$. What is the densest packing, to fill a rectangular block with as many identical tori as possible?
Tori ...
- 113
2
votes
0
answers
124
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Packing of consecutive cubes
Using the Ponting Square Packing, squares of size 1-49 can be packed in a 7x7 array so that the 25 interior squares are completely surrounded.
Another way to look at the above squares is with the ...
- 21.4k
0
votes
2
answers
841
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Volume of air in the box (packing problem)
Suppose I have a box with dimensions $L \times W \times H$.
What is the volume of air in the box, if I pack balls with radii $r$?
With increase of radius, does volume of air decrease?
- 2,319
3
votes
0
answers
101
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Orthogonally packing consecutive integer cubes 1x1x1 -nxnxn inside the smallest integer cube.
For small n, the problem of orthogonally packing consecutively sized integer cubes 1x1x1 - nxnxn inside the smallest integer cube CxCxC is trivial. By inspection, the sizes of two largest cubes n and ...
- 344
3
votes
1
answer
755
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Prove that a triangulated hexagon will have an equal number of double-triangle tiles in each direction.
Good afternoon!
I got the problem below from my tutor, which should help with thinking about problems.
A regular hexagon is drawn on isometric paper, with each triangle having side length 1. Two of ...
- 31
2
votes
2
answers
2k
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Maximal number of cubes in a given pyramid
I have a pyramid whose base is a square of side length $a=120$, and whose height is also $a=120$. The projection of the summit of the pyramid on the square basis coincides with the center of the ...
- 6,362
0
votes
2
answers
153
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Unusual 3D Packing Problem
I made up this interesting problem playing with wire sculptures:
If I have a $10 \times 10 \times 10$ clear box and inside I can put wireframe unit cubes, what's the maximum number of unit edges (or ...
- 10.8k
1
vote
0
answers
152
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3D Space Covering-Problem
Given a finite amount of "slots" in 3D space, e.g.
$$S = [(1,2,3),(1,3,3),(1,4,3),(1,3,4)] \in \mathbb{N}^3.$$
I'm trying to find an efficient algorithm to determine a minimal set of (rectangular) ...
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