Net or not?

−0

Given a hexomino, indicate whether it is a net of a cube.

Input

A 6 by 6 grid containing exactly 6 filled squares.
The 6 filled squares will be in a single edge connected set (a hexomino).
The topmost row and leftmost column will never be empty (the hexomino will be as far up and left as it can go).
The grid is represented as 6 newline separated strings of 6 characters, with # for a filled square and . for an empty square.

Output

One of 2 distinct values to indicate whether the hexomino can be folded to give a cube.

The hexominoes

A hexomino is an edge connected subset of the square tiling, composed of exactly 6 squares.

Up to rotation and reflection, there are 35 edge connected hexominoes, 11 of which are nets of a cube.

The 35 hexominoes^[1]

The 11 nets of a cube^[2]

Your code must also accept inputs that are rotations and reflections of these. There are a total of 216 hexominoes including all rotations by a multiple of 90 degrees and reflections, 64 of which are cube nets. The test cases include all of these.

Test cases

Cube nets

The 64 hexominoes that can be folded into a cube.

#.....
####..
#.....
......
......
......

.#....
.#....
.#....
###...
......
......

...#..
####..
...#..
......
......
......

###...
.#....
.#....
.#....
......
......

.##...
.#....
.#....
##....
......
......

...#..
####..
#.....
......
......
......

##....
.#....
.#....
.##...
......
......

#.....
####..
...#..
......
......
......

##....
.###..
.#....
......
......
......

#.....
###...
.#....
.#....
......
......

..#...
###...
.#....
.#....
......
......

.#....
.###..
##....
......
......
......

.#....
.#....
###...
#.....
......
......

..##..
###...
..#...
......
......
......

.#....
.#....
###...
..#...
......
......

..#...
###...
..##..
......
......
......

##....
.##...
..##..
......
......
......

#.....
##....
.##...
..#...
......
......

..##..
.##...
##....
......
......
......

..#...
.##...
##....
#.....
......
......

###...
..###.
......
......
......
......

..###.
###...
......
......
......
......

#.....
#.....
##....
.#....
.#....
......

.#....
.#....
##....
#.....
#.....
......

.#....
###...
.#....
.#....
......
......

.#....
.#....
###...
.#....
......
......

..#...
####..
..#...
......
......
......

.#....
####..
.#....
......
......
......

.#....
###...
..##..
......
......
......

..#...
.##...
##....
.#....
......
......

##....
.###..
..#...
......
......
......

.#....
.##...
##....
#.....
......
......

#.....
##....
.##...
.#....
......
......

..##..
###...
.#....
......
......
......

..#...
.###..
##....
......
......
......

.#....
##....
.##...
..#...
......
......

#.....
##....
.#....
.##...
......
......

..##..
###...
#.....
......
......
......

##....
.#....
.##...
..#...
......
......

.##...
.#....
##....
#.....
......
......

##....
.###..
...#..
......
......
......

#.....
###...
..##..
......
......
......

..#...
.##...
.#....
##....
......
......

...#..
.###..
##....
......
......
......

...#..
####..
..#...
......
......
......

.##...
##....
.#....
.#....
......
......

##....
.##...
.#....
.#....
......
......

.#....
####..
#.....
......
......
......

#.....
####..
.#....
......
......
......

.#....
.#....
##....
.##...
......
......

.#....
.#....
.##...
##....
......
......

..#...
####..
...#..
......
......
......

.#....
.##...
##....
.#....
......
......

.#....
####..
..#...
......
......
......

..#...
####..
.#....
......
......
......

.#....
##....
.##...
.#....
......
......

.#....
.##...
.#....
##....
......
......

.#....
##....
.#....
.##...
......
......

.##...
.#....
##....
.#....
......
......

##....
.#....
.##...
.#....
......
......

#.....
####..
..#...
......
......
......

..#...
####..
#.....
......
......
......

...#..
####..
.#....
......
......
......

.#....
####..
...#..
......
......
......

Not cube nets

The 152 hexominoes that cannot be folded into a cube.

..#...
#####.
......
......
......
......

#####.
..#...
......
......
......
......

.#....
.#....
##....
.#....
.#....
......

#.....
#.....
##....
#.....
#.....
......

.##...
###...
.#....
......
......
......

##....
###...
.#....
......
......
......

.#....
###...
##....
......
......
......

.#....
###...
.##...
......
......
......

##....
.####.
......
......
......
......

####..
...##.
......
......
......
......

#.....
##....
.#....
.#....
.#....
......

...##.
####..
......
......
......
......

.#....
.#....
.#....
##....
#.....
......

#.....
#.....
#.....
##....
.#....
......

.#....
##....
#.....
#.....
#.....
......

.####.
##....
......
......
......
......

.#....
##....
###...
......
......
......

#.....
###...
##....
......
......
......

###...
##....
.#....
......
......
......

##....
###...
#.....
......
......
......

###...
.##...
.#....
......
......
......

.##...
###...
..#...
......
......
......

..#...
###...
.##...
......
......
......

.#....
.##...
###...
......
......
......

###...
..#...
..##..
......
......
......

..#...
..#...
###...
#.....
......
......

..#...
###...
#.....
#.....
......
......

#.....
###...
..#...
..#...
......
......

.###..
.#....
##....
......
......
......

#.....
#.....
###...
..#...
......
......

..##..
..#...
###...
......
......
......

##....
.#....
.###..
......
......
......

####..
##....
......
......
......
......

.#....
.#....
##....
##....
......
......

..##..
####..
......
......
......
......

#.....
#.....
##....
##....
......
......

##....
##....
.#....
.#....
......
......

##....
####..
......
......
......
......

##....
##....
#.....
#.....
......
......

####..
..##..
......
......
......
......

####..
.#....
.#....
......
......
......

..#...
..#...
####..
......
......
......

..#...
..#...
###...
..#...
......
......

#.....
#.....
###...
#.....
......
......

#.....
###...
#.....
#.....
......
......

####..
..#...
..#...
......
......
......

.#....
.#....
####..
......
......
......

..#...
###...
..#...
..#...
......
......

####..
#.#...
......
......
......
......

.#....
##....
.#....
##....
......
......

#.#...
####..
......
......
......
......

#.....
##....
#.....
##....
......
......

##....
.#....
##....
.#....
......
......

.#.#..
####..
......
......
......
......

####..
.#.#..
......
......
......
......

##....
#.....
##....
#.....
......
......

...#..
...#..
####..
......
......
......

####..
...#..
...#..
......
......
......

..#...
..#...
..#...
###...
......
......

###...
..#...
..#...
..#...
......
......

###...
#.....
#.....
#.....
......
......

#.....
#.....
#.....
###...
......
......

#.....
#.....
####..
......
......
......

####..
#.....
#.....
......
......
......

.##...
##....
.##...
......
......
......

#.#...
###...
.#....
......
......
......

##....
.##...
##....
......
......
......

.#....
###...
#.#...
......
......
......

##....
##....
.##...
......
......
......

#.....
###...
.##...
......
......
......

..#...
###...
##....
......
......
......

.##...
###...
#.....
......
......
......

.##...
##....
##....
......
......
......

##....
.##...
.##...
......
......
......

##....
###...
..#...
......
......
......

.##...
.##...
##....
......
......
......

#.....
##....
###...
......
......
......

..#...
.##...
###...
......
......
......

###...
.##...
..#...
......
......
......

###...
##....
#.....
......
......
......

######
......
......
......
......
......

#.....
#.....
#.....
#.....
#.....
#.....

.###..
##....
.#....
......
......
......

.#....
###...
#.....
#.....
......
......

.#....
###...
..#...
..#...
......
......

..#...
..#...
###...
.#....
......
......

###...
..##..
..#...
......
......
......

.#....
##....
.###..
......
......
......

..#...
..##..
###...
......
......
......

#.....
#.....
###...
.#....
......
......

#.#...
###...
#.....
......
......
......

#.#...
###...
..#...
......
......
......

#.....
###...
#.#...
......
......
......

##....
.#....
###...
......
......
......

..#...
###...
#.#...
......
......
......

###...
.#....
##....
......
......
......

.##...
.#....
###...
......
......
......

###...
.#....
.##...
......
......
......

###...
###...
......
......
......
......

##....
##....
##....
......
......
......

#####.
....#.
......
......
......
......

....#.
#####.
......
......
......
......

#####.
#.....
......
......
......
......

##....
#.....
#.....
#.....
#.....
......

.#....
.#....
.#....
.#....
##....
......

#.....
#.....
#.....
#.....
##....
......

##....
.#....
.#....
.#....
.#....
......

#.....
#####.
......
......
......
......

#.....
#.#...
###...
......
......
......

###...
#.....
##....
......
......
......

###...
#.#...
#.....
......
......
......

###...
..#...
.##...
......
......
......

##....
#.....
###...
......
......
......

###...
#.#...
..#...
......
......
......

..#...
#.#...
###...
......
......
......

.##...
..#...
###...
......
......
......

###...
.###..
......
......
......
......

.#....
##....
##....
#.....
......
......

#.....
##....
##....
.#....
......
......

.###..
###...
......
......
......
......

##....
.##...
..#...
..#...
......
......

###...
..##..
...#..
......
......
......

..#...
..#...
.##...
##....
......
......

.##...
##....
#.....
#.....
......
......

.###..
##....
#.....
......
......
......

#.....
##....
.###..
......
......
......

#.....
#.....
##....
.##...
......
......

...#..
..##..
###...
......
......
......

.##...
####..
......
......
......
......

#.....
##....
##....
#.....
......
......

.#....
##....
##....
.#....
......
......

####..
.##...
......
......
......
......

##....
.#....
##....
#.....
......
......

##....
#.....
##....
.#....
......
......

##.#..
.###..
......
......
......
......

.###..
##.#..
......
......
......
......

#.##..
###...
......
......
......
......

.#....
##....
#.....
##....
......
......

###...
#.##..
......
......
......
......

#.....
##....
.#....
##....
......
......

.#....
##....
.#....
.#....
.#....
......

...#..
#####.
......
......
......
......

#.....
#.....
#.....
##....
#.....
......

.#....
#####.
......
......
......
......

.#....
.#....
.#....
##....
.#....
......

#####.
...#..
......
......
......
......

#.....
##....
#.....
#.....
#.....
......

#####.
.#....
......
......
......
......

#..#..
####..
......
......
......
......

##....
.#....
.#....
##....
......
......

####..
#..#..
......
......
......
......

##....
#.....
#.....
##....
......
......

Scoring

This is a code golf challenge. Your score is the number of bytes in your code. Lowest score for each language wins.

Explanations are optional, but I'm more likely to upvote answers that have one.

Thanks to The 35 hexominoes Wikimedia page. ↩︎
Thanks to The 11 nets of a cube Wikimedia page. ↩︎

code-golf math

posted 5 months ago

CC BY-SA 4.0

trichoplax‭

1050 reputation 83 17 132 472

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is a duplicate

This question has been asked before and has already been answered. It should be marked as a duplicate.

Please enter the URL of the proposed duplicate in the details field below.

not constructive

This question cannot be answered in a way that is helpful to anyone. It's not possible to learn something from possible answers, except for the solution for the specific problem of the asker.

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