Infinite Rubik's Cube
23
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Is there an infinite analog to the Rubik's Cube? What does its solution-algorithm look like? For illustration, consider the Rubik's cube with infinite tiles to a side, on all sides, with sides of finite length.
combinatorics group-theory puzzle
edited Jan 8 at 1:56
David G. Stork
11k41432
asked Jan 8 at 1:54
DohlemanDohleman
395212
$endgroup$
add a comment |
23
$begingroup$
Is there an infinite analog to the Rubik's Cube? What does its solution-algorithm look like? For illustration, consider the Rubik's cube with infinite tiles to a side, on all sides, with sides of finite length.
combinatorics group-theory puzzle
edited Jan 8 at 1:56
David G. Stork
11k41432
asked Jan 8 at 1:54
DohlemanDohleman
395212
$endgroup$
1
$begingroup$
Problems might just be slices at real valued intervals through the cube rotated iteratively until a confused state is reached and then solving it.
$endgroup$
– Dohleman
Jan 8 at 1:58
2
$begingroup$
You might want to look up Thompson's groups $F$, $T$ and $V$, and also the Brin-Thompson groups $nV$. They are not exactly what you are looking for, but I think they might be close. Certainly, they are "slices" of the interval $[0, 1)$, and the groups $nV$ are slices of the $n$-cube $[0, 1)^n$. They also have rather pleasing graphical representations.
$endgroup$
– user1729
Jan 8 at 11:55
2
$begingroup$
You have to say what you mean. For example, it is the cube $[-1,1]^3$, but rotations can be made fixing any subset of one of the axes: rotate the planes corresponding to that subset, fix the rest of the planes
$endgroup$
– GEdgar
Jan 18 at 11:42
2
$begingroup$
I wonder how an infinite rubik's cube can have finite sides?
$endgroup$
– Michael Wang
Jan 21 at 3:14
add a comment |
23
23
23
6
$begingroup$
Is there an infinite analog to the Rubik's Cube? What does its solution-algorithm look like? For illustration, consider the Rubik's cube with infinite tiles to a side, on all sides, with sides of finite length.
combinatorics group-theory puzzle
edited Jan 8 at 1:56
David G. Stork
11k41432
asked Jan 8 at 1:54
DohlemanDohleman
395212
$endgroup$
Is there an infinite analog to the Rubik's Cube? What does its solution-algorithm look like? For illustration, consider the Rubik's cube with infinite tiles to a side, on all sides, with sides of finite length.
combinatorics group-theory puzzle
combinatorics group-theory puzzle
edited Jan 8 at 1:56
David G. Stork
11k41432
asked Jan 8 at 1:54
DohlemanDohleman
395212
edited Jan 8 at 1:56
David G. Stork
11k41432
asked Jan 8 at 1:54
DohlemanDohleman
395212
edited Jan 8 at 1:56
David G. Stork
11k41432
edited Jan 8 at 1:56
David G. Stork
11k41432
edited Jan 8 at 1:56
David G. Stork
11k41432
11k41432
asked Jan 8 at 1:54
DohlemanDohleman
395212
asked Jan 8 at 1:54
DohlemanDohleman
395212
asked Jan 8 at 1:54
DohlemanDohleman
395212
395212
1
$begingroup$
Problems might just be slices at real valued intervals through the cube rotated iteratively until a confused state is reached and then solving it.
$endgroup$
– Dohleman
Jan 8 at 1:58
2
$begingroup$
You might want to look up Thompson's groups $F$, $T$ and $V$, and also the Brin-Thompson groups $nV$. They are not exactly what you are looking for, but I think they might be close. Certainly, they are "slices" of the interval $[0, 1)$, and the groups $nV$ are slices of the $n$-cube $[0, 1)^n$. They also have rather pleasing graphical representations.
$endgroup$
– user1729
Jan 8 at 11:55
2
$begingroup$
You have to say what you mean. For example, it is the cube $[-1,1]^3$, but rotations can be made fixing any subset of one of the axes: rotate the planes corresponding to that subset, fix the rest of the planes
$endgroup$
– GEdgar
Jan 18 at 11:42
2
$begingroup$
I wonder how an infinite rubik's cube can have finite sides?
$endgroup$
– Michael Wang
Jan 21 at 3:14
add a comment |
1
$begingroup$
Problems might just be slices at real valued intervals through the cube rotated iteratively until a confused state is reached and then solving it.
$endgroup$
– Dohleman
Jan 8 at 1:58
2
$begingroup$
You might want to look up Thompson's groups $F$, $T$ and $V$, and also the Brin-Thompson groups $nV$. They are not exactly what you are looking for, but I think they might be close. Certainly, they are "slices" of the interval $[0, 1)$, and the groups $nV$ are slices of the $n$-cube $[0, 1)^n$. They also have rather pleasing graphical representations.
$endgroup$
– user1729
Jan 8 at 11:55
2
$begingroup$
You have to say what you mean. For example, it is the cube $[-1,1]^3$, but rotations can be made fixing any subset of one of the axes: rotate the planes corresponding to that subset, fix the rest of the planes
$endgroup$
– GEdgar
Jan 18 at 11:42
2
$begingroup$
I wonder how an infinite rubik's cube can have finite sides?
$endgroup$
– Michael Wang
Jan 21 at 3:14
1
1
$begingroup$
Problems might just be slices at real valued intervals through the cube rotated iteratively until a confused state is reached and then solving it.
$endgroup$
– Dohleman
Jan 8 at 1:58
$begingroup$
Problems might just be slices at real valued intervals through the cube rotated iteratively until a confused state is reached and then solving it.
$endgroup$
– Dohleman
Jan 8 at 1:58
2
2
$begingroup$
You might want to look up Thompson's groups $F$, $T$ and $V$, and also the Brin-Thompson groups $nV$. They are not exactly what you are looking for, but I think they might be close. Certainly, they are "slices" of the interval $[0, 1)$, and the groups $nV$ are slices of the $n$-cube $[0, 1)^n$. They also have rather pleasing graphical representations.
$endgroup$
– user1729
Jan 8 at 11:55
$begingroup$
You might want to look up Thompson's groups $F$, $T$ and $V$, and also the Brin-Thompson groups $nV$. They are not exactly what you are looking for, but I think they might be close. Certainly, they are "slices" of the interval $[0, 1)$, and the groups $nV$ are slices of the $n$-cube $[0, 1)^n$. They also have rather pleasing graphical representations.
$endgroup$
– user1729
Jan 8 at 11:55
2
2
$begingroup$
You have to say what you mean. For example, it is the cube $[-1,1]^3$, but rotations can be made fixing any subset of one of the axes: rotate the planes corresponding to that subset, fix the rest of the planes
$endgroup$
– GEdgar
Jan 18 at 11:42
$begingroup$
You have to say what you mean. For example, it is the cube $[-1,1]^3$, but rotations can be made fixing any subset of one of the axes: rotate the planes corresponding to that subset, fix the rest of the planes
$endgroup$
– GEdgar
Jan 18 at 11:42
2
2
$begingroup$
I wonder how an infinite rubik's cube can have finite sides?
$endgroup$
– Michael Wang
Jan 21 at 3:14
$begingroup$
I wonder how an infinite rubik's cube can have finite sides?
$endgroup$
– Michael Wang
Jan 21 at 3:14
add a comment |
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1
$begingroup$
Problems might just be slices at real valued intervals through the cube rotated iteratively until a confused state is reached and then solving it.
$endgroup$
– Dohleman
Jan 8 at 1:58
2
$begingroup$
You might want to look up Thompson's groups $F$, $T$ and $V$, and also the Brin-Thompson groups $nV$. They are not exactly what you are looking for, but I think they might be close. Certainly, they are "slices" of the interval $[0, 1)$, and the groups $nV$ are slices of the $n$-cube $[0, 1)^n$. They also have rather pleasing graphical representations.
$endgroup$
– user1729
Jan 8 at 11:55
2
$begingroup$
You have to say what you mean. For example, it is the cube $[-1,1]^3$, but rotations can be made fixing any subset of one of the axes: rotate the planes corresponding to that subset, fix the rest of the planes
$endgroup$
– GEdgar
Jan 18 at 11:42
2
$begingroup$
I wonder how an infinite rubik's cube can have finite sides?
$endgroup$
– Michael Wang
Jan 21 at 3:14