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 35 hexominoes]][The 35 hexominoes Wikimedia page]
### The 11 nets of a cube[^2]
[![The 11 nets of a cube]][The 11 nets of a cube Wikimedia page]
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.
```text
#.....
####..
#.....
......
......
......
.#....
.#....
.#....
###...
......
......
...#..
####..
...#..
......
......
......
###...
.#....
.#....
.#....
......
......
.##...
.#....
.#....
##....
......
......
...#..
####..
#.....
......
......
......
##....
.#....
.#....
.##...
......
......
#.....
####..
...#..
......
......
......
##....
.###..
.#....
......
......
......
#.....
###...
.#....
.#....
......
......
..#...
###...
.#....
.#....
......
......
.#....
.###..
##....
......
......
......
.#....
.#....
###...
#.....
......
......
..##..
###...
..#...
......
......
......
.#....
.#....
###...
..#...
......
......
..#...
###...
..##..
......
......
......
##....
.##...
..##..
......
......
......
#.....
##....
.##...
..#...
......
......
..##..
.##...
##....
......
......
......
..#...
.##...
##....
#.....
......
......
###...
..###.
......
......
......
......
..###.
###...
......
......
......
......
#.....
#.....
##....
.#....
.#....
......
.#....
.#....
##....
#.....
#.....
......
.#....
###...
.#....
.#....
......
......
.#....
.#....
###...
.#....
......
......
..#...
####..
..#...
......
......
......
.#....
####..
.#....
......
......
......
.#....
###...
..##..
......
......
......
..#...
.##...
##....
.#....
......
......
##....
.###..
..#...
......
......
......
.#....
.##...
##....
#.....
......
......
#.....
##....
.##...
.#....
......
......
..##..
###...
.#....
......
......
......
..#...
.###..
##....
......
......
......
.#....
##....
.##...
..#...
......
......
#.....
##....
.#....
.##...
......
......
..##..
###...
#.....
......
......
......
##....
.#....
.##...
..#...
......
......
.##...
.#....
##....
#.....
......
......
##....
.###..
...#..
......
......
......
#.....
###...
..##..
......
......
......
..#...
.##...
.#....
##....
......
......
...#..
.###..
##....
......
......
......
...#..
####..
..#...
......
......
......
.##...
##....
.#....
.#....
......
......
##....
.##...
.#....
.#....
......
......
.#....
####..
#.....
......
......
......
#.....
####..
.#....
......
......
......
.#....
.#....
##....
.##...
......
......
.#....
.#....
.##...
##....
......
......
..#...
####..
...#..
......
......
......
.#....
.##...
##....
.#....
......
......
.#....
####..
..#...
......
......
......
..#...
####..
.#....
......
......
......
.#....
##....
.##...
.#....
......
......
.#....
.##...
.#....
##....
......
......
.#....
##....
.#....
.##...
......
......
.##...
.#....
##....
.#....
......
......
##....
.#....
.##...
.#....
......
......
#.....
####..
..#...
......
......
......
..#...
####..
#.....
......
......
......
...#..
####..
.#....
......
......
......
.#....
####..
...#..
......
......
......
```
### Not cube nets
The 152 hexominoes that cannot be folded into a cube.
```text
..#...
#####.
......
......
......
......
#####.
..#...
......
......
......
......
.#....
.#....
##....
.#....
.#....
......
#.....
#.....
##....
#.....
#.....
......
.##...
###...
.#....
......
......
......
##....
###...
.#....
......
......
......
.#....
###...
##....
......
......
......
.#....
###...
.##...
......
......
......
##....
.####.
......
......
......
......
####..
...##.
......
......
......
......
#.....
##....
.#....
.#....
.#....
......
...##.
####..
......
......
......
......
.#....
.#....
.#....
##....
#.....
......
#.....
#.....
#.....
##....
.#....
......
.#....
##....
#.....
#.....
#.....
......
.####.
##....
......
......
......
......
.#....
##....
###...
......
......
......
#.....
###...
##....
......
......
......
###...
##....
.#....
......
......
......
##....
###...
#.....
......
......
......
###...
.##...
.#....
......
......
......
.##...
###...
..#...
......
......
......
..#...
###...
.##...
......
......
......
.#....
.##...
###...
......
......
......
###...
..#...
..##..
......
......
......
..#...
..#...
###...
#.....
......
......
..#...
###...
#.....
#.....
......
......
#.....
###...
..#...
..#...
......
......
.###..
.#....
##....
......
......
......
#.....
#.....
###...
..#...
......
......
..##..
..#...
###...
......
......
......
##....
.#....
.###..
......
......
......
####..
##....
......
......
......
......
.#....
.#....
##....
##....
......
......
..##..
####..
......
......
......
......
#.....
#.....
##....
##....
......
......
##....
##....
.#....
.#....
......
......
##....
####..
......
......
......
......
##....
##....
#.....
#.....
......
......
####..
..##..
......
......
......
......
####..
.#....
.#....
......
......
......
..#...
..#...
####..
......
......
......
..#...
..#...
###...
..#...
......
......
#.....
#.....
###...
#.....
......
......
#.....
###...
#.....
#.....
......
......
####..
..#...
..#...
......
......
......
.#....
.#....
####..
......
......
......
..#...
###...
..#...
..#...
......
......
####..
#.#...
......
......
......
......
.#....
##....
.#....
##....
......
......
#.#...
####..
......
......
......
......
#.....
##....
#.....
##....
......
......
##....
.#....
##....
.#....
......
......
.#.#..
####..
......
......
......
......
####..
.#.#..
......
......
......
......
##....
#.....
##....
#.....
......
......
...#..
...#..
####..
......
......
......
####..
...#..
...#..
......
......
......
..#...
..#...
..#...
###...
......
......
###...
..#...
..#...
..#...
......
......
###...
#.....
#.....
#.....
......
......
#.....
#.....
#.....
###...
......
......
#.....
#.....
####..
......
......
......
####..
#.....
#.....
......
......
......
.##...
##....
.##...
......
......
......
#.#...
###...
.#....
......
......
......
##....
.##...
##....
......
......
......
.#....
###...
#.#...
......
......
......
##....
##....
.##...
......
......
......
#.....
###...
.##...
......
......
......
..#...
###...
##....
......
......
......
.##...
###...
#.....
......
......
......
.##...
##....
##....
......
......
......
##....
.##...
.##...
......
......
......
##....
###...
..#...
......
......
......
.##...
.##...
##....
......
......
......
#.....
##....
###...
......
......
......
..#...
.##...
###...
......
......
......
###...
.##...
..#...
......
......
......
###...
##....
#.....
......
......
......
######
......
......
......
......
......
#.....
#.....
#.....
#.....
#.....
#.....
.###..
##....
.#....
......
......
......
.#....
###...
#.....
#.....
......
......
.#....
###...
..#...
..#...
......
......
..#...
..#...
###...
.#....
......
......
###...
..##..
..#...
......
......
......
.#....
##....
.###..
......
......
......
..#...
..##..
###...
......
......
......
#.....
#.....
###...
.#....
......
......
#.#...
###...
#.....
......
......
......
#.#...
###...
..#...
......
......
......
#.....
###...
#.#...
......
......
......
##....
.#....
###...
......
......
......
..#...
###...
#.#...
......
......
......
###...
.#....
##....
......
......
......
.##...
.#....
###...
......
......
......
###...
.#....
.##...
......
......
......
###...
###...
......
......
......
......
##....
##....
##....
......
......
......
#####.
....#.
......
......
......
......
....#.
#####.
......
......
......
......
#####.
#.....
......
......
......
......
##....
#.....
#.....
#.....
#.....
......
.#....
.#....
.#....
.#....
##....
......
#.....
#.....
#.....
#.....
##....
......
##....
.#....
.#....
.#....
.#....
......
#.....
#####.
......
......
......
......
#.....
#.#...
###...
......
......
......
###...
#.....
##....
......
......
......
###...
#.#...
#.....
......
......
......
###...
..#...
.##...
......
......
......
##....
#.....
###...
......
......
......
###...
#.#...
..#...
......
......
......
..#...
#.#...
###...
......
......
......
.##...
..#...
###...
......
......
......
###...
.###..
......
......
......
......
.#....
##....
##....
#.....
......
......
#.....
##....
##....
.#....
......
......
.###..
###...
......
......
......
......
##....
.##...
..#...
..#...
......
......
###...
..##..
...#..
......
......
......
..#...
..#...
.##...
##....
......
......
.##...
##....
#.....
#.....
......
......
.###..
##....
#.....
......
......
......
#.....
##....
.###..
......
......
......
#.....
#.....
##....
.##...
......
......
...#..
..##..
###...
......
......
......
.##...
####..
......
......
......
......
#.....
##....
##....
#.....
......
......
.#....
##....
##....
.#....
......
......
####..
.##...
......
......
......
......
##....
.#....
##....
#.....
......
......
##....
#.....
##....
.#....
......
......
##.#..
.###..
......
......
......
......
.###..
##.#..
......
......
......
......
#.##..
###...
......
......
......
......
.#....
##....
#.....
##....
......
......
###...
#.##..
......
......
......
......
#.....
##....
.#....
##....
......
......
.#....
##....
.#....
.#....
.#....
......
...#..
#####.
......
......
......
......
#.....
#.....
#.....
##....
#.....
......
.#....
#####.
......
......
......
......
.#....
.#....
.#....
##....
.#....
......
#####.
...#..
......
......
......
......
#.....
##....
#.....
#.....
#.....
......
#####.
.#....
......
......
......
......
#..#..
####..
......
......
......
......
##....
.#....
.#....
##....
......
......
####..
#..#..
......
......
......
......
##....
#.....
#.....
##....
......
......
```
## 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.
[^1]: Thanks to [The 35 hexominoes Wikimedia page].
[^2]: Thanks to [The 11 nets of a cube Wikimedia page].
[hexomino]: https://en.wikipedia.org/wiki/Hexomino
[The 35 hexominoes]: https://upload.wikimedia.org/wikipedia/commons/0/02/All_35_free_hexominoes.svg
[The 35 hexominoes Wikimedia page]: https://en.wikipedia.org/wiki/File:All_35_free_hexominoes.svg
[The 11 nets of a cube]: https://upload.wikimedia.org/wikipedia/commons/c/cd/The_11_cubic_nets.svg
[The 11 nets of a cube Wikimedia page]: https://en.wikipedia.org/wiki/File:The_11_cubic_nets.svg
[code golf challenge]: https://codegolf.codidact.com/categories/49/tags/4274 "The code-golf tag"
