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Incubator Q&A Closed loop on a side length 1 cube

Place a tile on each face of a cube so that the arcs on the tiles form a single closed loop. You may rotate each tile by any multiple of 90 degrees. The tiles to be used are equal numbers of 2 ki...

1 answer  ·  posted 9d ago by trichoplax‭  ·  last activity 8d ago by will.octagon.gibson‭

Question puzzles grid-puzzles
#5: Post edited by user avatar trichoplax‭ · 2026-09-08T22:30:53Z (9 days ago)
Improve wording
  • Place a tile on each face of a cube so that the arcs on the tiles form a single closed loop.
  • You may rotate each tile by any multiple of 90 degrees.
  • The tiles to be used are equal numbers of 2 kinds of tile:
  • - 3 single arc tiles: [![tile with an arc joining 2 adjacent edges][single arc tile]][single arc tile]
  • - 3 double arc tiles: [![tile with arcs joining 2 pairs of adjacent edges][double arc tile]][double arc tile]
  • Here are 3 of each that can be printed and cut out:
  • [![3 tiles with 2 adjacent edges joined by an arc, and 3 tiles with 2 pairs of adjacent edges joined by arcs][tiles]][tiles]
  • Here is a net of a cube to place the tiles on:
  • [![6 squares that can be folded up to give a cube][cube net]][cube net]
  • Both images can be opened in a separate tab (which will display the tiles and the squares on the cube faces at exactly the same size) if you would like to print them for experimenting or to photograph your solution to post in an answer.
  • [single arc tile]: https://raw.githubusercontent.com/trichoplax/loop-on-a-cube-puzzle/refs/heads/main/single-arc-tile.svg
  • [double arc tile]: https://raw.githubusercontent.com/trichoplax/loop-on-a-cube-puzzle/refs/heads/main/double-arc-tile.svg
  • [tiles]: https://raw.githubusercontent.com/trichoplax/loop-on-a-cube-puzzle/refs/heads/main/tiles-1.svg
  • [cube net]: https://raw.githubusercontent.com/trichoplax/loop-on-a-cube-puzzle/refs/heads/main/cube-net-1.svg
  • Place a tile on each face of a cube so that the arcs on the tiles form a single closed loop.
  • You may rotate each tile by any multiple of 90 degrees.
  • The tiles to be used are equal numbers of 2 kinds of tile:
  • - 3 single arc tiles: [![tile with an arc joining 2 adjacent edges][single arc tile]][single arc tile]
  • - 3 double arc tiles: [![tile with arcs joining 2 pairs of adjacent edges][double arc tile]][double arc tile]
  • Here are 3 of each that can be printed and cut out:
  • [![3 tiles with 2 adjacent edges joined by an arc, and 3 tiles with 2 pairs of adjacent edges joined by arcs][tiles]][tiles]
  • Here is a net of a cube to place the tiles on:
  • [![6 squares that can be folded up to give a cube][cube net]][cube net]
  • Each of the images can be opened in a separate tab (which will display the tiles and the squares on the cube faces at exactly the same size) if you would like to print them for experimenting or to photograph your solution to post in an answer.
  • [single arc tile]: https://raw.githubusercontent.com/trichoplax/loop-on-a-cube-puzzle/refs/heads/main/single-arc-tile.svg
  • [double arc tile]: https://raw.githubusercontent.com/trichoplax/loop-on-a-cube-puzzle/refs/heads/main/double-arc-tile.svg
  • [tiles]: https://raw.githubusercontent.com/trichoplax/loop-on-a-cube-puzzle/refs/heads/main/tiles-1.svg
  • [cube net]: https://raw.githubusercontent.com/trichoplax/loop-on-a-cube-puzzle/refs/heads/main/cube-net-1.svg
#4: Post edited by user avatar trichoplax‭ · 2026-09-08T22:26:05Z (9 days ago)
Explicitly mention rotation
  • Place a tile on each face of a cube so that the arcs on the tiles form a single closed loop.
  • The tiles to be used are equal numbers of 2 kinds of tile:
  • - 3 single arc tiles: [![tile with an arc joining 2 adjacent edges][single arc tile]][single arc tile]
  • - 3 double arc tiles: [![tile with arcs joining 2 pairs of adjacent edges][double arc tile]][double arc tile]
  • Here are 3 of each that can be printed and cut out:
  • [![3 tiles with 2 adjacent edges joined by an arc, and 3 tiles with 2 pairs of adjacent edges joined by arcs][tiles]][tiles]
  • Here is a net of a cube to place the tiles on:
  • [![6 squares that can be folded up to give a cube][cube net]][cube net]
  • Both images can be opened in a separate tab (which will display the tiles and the squares on the cube faces at exactly the same size) if you would like to print them for experimenting or to photograph your solution to post in an answer.
  • [single arc tile]: https://raw.githubusercontent.com/trichoplax/loop-on-a-cube-puzzle/refs/heads/main/single-arc-tile.svg
  • [double arc tile]: https://raw.githubusercontent.com/trichoplax/loop-on-a-cube-puzzle/refs/heads/main/double-arc-tile.svg
  • [tiles]: https://raw.githubusercontent.com/trichoplax/loop-on-a-cube-puzzle/refs/heads/main/tiles-1.svg
  • [cube net]: https://raw.githubusercontent.com/trichoplax/loop-on-a-cube-puzzle/refs/heads/main/cube-net-1.svg
  • Place a tile on each face of a cube so that the arcs on the tiles form a single closed loop.
  • You may rotate each tile by any multiple of 90 degrees.
  • The tiles to be used are equal numbers of 2 kinds of tile:
  • - 3 single arc tiles: [![tile with an arc joining 2 adjacent edges][single arc tile]][single arc tile]
  • - 3 double arc tiles: [![tile with arcs joining 2 pairs of adjacent edges][double arc tile]][double arc tile]
  • Here are 3 of each that can be printed and cut out:
  • [![3 tiles with 2 adjacent edges joined by an arc, and 3 tiles with 2 pairs of adjacent edges joined by arcs][tiles]][tiles]
  • Here is a net of a cube to place the tiles on:
  • [![6 squares that can be folded up to give a cube][cube net]][cube net]
  • Both images can be opened in a separate tab (which will display the tiles and the squares on the cube faces at exactly the same size) if you would like to print them for experimenting or to photograph your solution to post in an answer.
  • [single arc tile]: https://raw.githubusercontent.com/trichoplax/loop-on-a-cube-puzzle/refs/heads/main/single-arc-tile.svg
  • [double arc tile]: https://raw.githubusercontent.com/trichoplax/loop-on-a-cube-puzzle/refs/heads/main/double-arc-tile.svg
  • [tiles]: https://raw.githubusercontent.com/trichoplax/loop-on-a-cube-puzzle/refs/heads/main/tiles-1.svg
  • [cube net]: https://raw.githubusercontent.com/trichoplax/loop-on-a-cube-puzzle/refs/heads/main/cube-net-1.svg
#3: Post edited by user avatar trichoplax‭ · 2026-09-08T22:14:29Z (9 days ago)
Mention tiles and squares are identical sizes when opened in a separate tab
  • Place a tile on each face of a cube so that the arcs on the tiles form a single closed loop.
  • The tiles to be used are equal numbers of 2 kinds of tile:
  • - 3 single arc tiles: [![tile with an arc joining 2 adjacent edges][single arc tile]][single arc tile]
  • - 3 double arc tiles: [![tile with arcs joining 2 pairs of adjacent edges][double arc tile]][double arc tile]
  • Here are 3 of each that can be printed and cut out:
  • [![3 tiles with 2 adjacent edges joined by an arc, and 3 tiles with 2 pairs of adjacent edges joined by arcs][tiles]][tiles]
  • Here is a net of a cube to place the tiles on:
  • [![6 squares that can be folded up to give a cube][cube net]][cube net]
  • Both images can be opened in a separate tab if you would like to print them for experimenting or to photograph your solution to post in an answer.
  • [single arc tile]: https://raw.githubusercontent.com/trichoplax/loop-on-a-cube-puzzle/refs/heads/main/single-arc-tile.svg
  • [double arc tile]: https://raw.githubusercontent.com/trichoplax/loop-on-a-cube-puzzle/refs/heads/main/double-arc-tile.svg
  • [tiles]: https://raw.githubusercontent.com/trichoplax/loop-on-a-cube-puzzle/refs/heads/main/tiles-1.svg
  • [cube net]: https://raw.githubusercontent.com/trichoplax/loop-on-a-cube-puzzle/refs/heads/main/cube-net-1.svg
  • Place a tile on each face of a cube so that the arcs on the tiles form a single closed loop.
  • The tiles to be used are equal numbers of 2 kinds of tile:
  • - 3 single arc tiles: [![tile with an arc joining 2 adjacent edges][single arc tile]][single arc tile]
  • - 3 double arc tiles: [![tile with arcs joining 2 pairs of adjacent edges][double arc tile]][double arc tile]
  • Here are 3 of each that can be printed and cut out:
  • [![3 tiles with 2 adjacent edges joined by an arc, and 3 tiles with 2 pairs of adjacent edges joined by arcs][tiles]][tiles]
  • Here is a net of a cube to place the tiles on:
  • [![6 squares that can be folded up to give a cube][cube net]][cube net]
  • Both images can be opened in a separate tab (which will display the tiles and the squares on the cube faces at exactly the same size) if you would like to print them for experimenting or to photograph your solution to post in an answer.
  • [single arc tile]: https://raw.githubusercontent.com/trichoplax/loop-on-a-cube-puzzle/refs/heads/main/single-arc-tile.svg
  • [double arc tile]: https://raw.githubusercontent.com/trichoplax/loop-on-a-cube-puzzle/refs/heads/main/double-arc-tile.svg
  • [tiles]: https://raw.githubusercontent.com/trichoplax/loop-on-a-cube-puzzle/refs/heads/main/tiles-1.svg
  • [cube net]: https://raw.githubusercontent.com/trichoplax/loop-on-a-cube-puzzle/refs/heads/main/cube-net-1.svg
#2: Post edited by user avatar trichoplax‭ · 2026-09-08T21:10:35Z (9 days ago)
Show individual tiles for clarity
  • Place a tile on each face of a cube so that the arcs on the tiles form a single closed loop.
  • The tiles to be used are equal numbers of 2 kinds of tile:
  • - 3 single arc tiles
  • - 3 double arc tiles
  • [![3 tiles with 2 adjacent edges joined by an arc, and 3 tiles with 2 pairs of adjacent edges joined by arcs][tiles]][tiles]
  • Here is a net of a cube to place the tiles on:
  • [![6 squares that can be folded up to give a cube][cube net]][cube net]
  • Both images can be opened in a separate tab if you would like to print them for experimenting or to photograph your solution to post in an answer.
  • [tiles]: https://raw.githubusercontent.com/trichoplax/loop-on-a-cube-puzzle/refs/heads/main/tiles-1.svg
  • [cube net]: https://raw.githubusercontent.com/trichoplax/loop-on-a-cube-puzzle/refs/heads/main/cube-net-1.svg
  • Place a tile on each face of a cube so that the arcs on the tiles form a single closed loop.
  • The tiles to be used are equal numbers of 2 kinds of tile:
  • - 3 single arc tiles: [![tile with an arc joining 2 adjacent edges][single arc tile]][single arc tile]
  • - 3 double arc tiles: [![tile with arcs joining 2 pairs of adjacent edges][double arc tile]][double arc tile]
  • Here are 3 of each that can be printed and cut out:
  • [![3 tiles with 2 adjacent edges joined by an arc, and 3 tiles with 2 pairs of adjacent edges joined by arcs][tiles]][tiles]
  • Here is a net of a cube to place the tiles on:
  • [![6 squares that can be folded up to give a cube][cube net]][cube net]
  • Both images can be opened in a separate tab if you would like to print them for experimenting or to photograph your solution to post in an answer.
  • [single arc tile]: https://raw.githubusercontent.com/trichoplax/loop-on-a-cube-puzzle/refs/heads/main/single-arc-tile.svg
  • [double arc tile]: https://raw.githubusercontent.com/trichoplax/loop-on-a-cube-puzzle/refs/heads/main/double-arc-tile.svg
  • [tiles]: https://raw.githubusercontent.com/trichoplax/loop-on-a-cube-puzzle/refs/heads/main/tiles-1.svg
  • [cube net]: https://raw.githubusercontent.com/trichoplax/loop-on-a-cube-puzzle/refs/heads/main/cube-net-1.svg
#1: Initial revision by user avatar trichoplax‭ · 2026-09-08T20:01:04Z (9 days ago) 
Closed loop on a side length 1 cube
Place a tile on each face of a cube so that the arcs on the tiles form a single closed loop.

The tiles to be used are equal numbers of 2 kinds of tile:
- 3 single arc tiles
- 3 double arc tiles

[![3 tiles with 2 adjacent edges joined by an arc, and 3 tiles with 2 pairs of adjacent edges joined by arcs][tiles]][tiles]

Here is a net of a cube to place the tiles on:

[![6 squares that can be folded up to give a cube][cube net]][cube net]

Both images can be opened in a separate tab if you would like to print them for experimenting or to photograph your solution to post in an answer.

[tiles]: https://raw.githubusercontent.com/trichoplax/loop-on-a-cube-puzzle/refs/heads/main/tiles-1.svg

[cube net]: https://raw.githubusercontent.com/trichoplax/loop-on-a-cube-puzzle/refs/heads/main/cube-net-1.svg
puzzles grid-puzzles