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Closed loop on an octahedron Question
Place a tile on each face of a regular octahedron so that the arcs on the tiles form a single closed loop.
You may rotate the tiles provided they align with the triangular faces of the octahedron.
There are 8 identical tiles:
Here is a net of an octahedron to arrange the tiles on:
Printing
Each image can be opened in a separate tab (which will display the tiles at exactly the right size to place on the net) to allow printing so you can experiment or photograph your solution.
1 answer
The following users marked this post as Works for me:
| User | Comment | Date |
|---|---|---|
| trichoplax | (no comment) | Sep 15, 2026 at 14:38 |
Solution
Process
An easy observation is that every triangle has an edge which the line does not pass through, so we're really tiling with four diamonds:
I placed the red diamond arbitrarily due to symmetry. Since the top half of the red diamond couldn't be part of a cycle of length 4 around the vertex I placed the blue diamond to break that cycle. The other two diamonds are now forced.
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