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Place a tile on each face of a regular icosahedron 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 icosahedro...
#1: Initial revision
by
trichoplax
·
2026-09-14T20:51:06Z (4 days ago)
Closed loop on an icosahedron
Place a tile on each face of a [regular icosahedron](https://en.wikipedia.org/wiki/Regular_icosahedron) 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 icosahedron. There are 20 identical tiles: [![20 triangular tiles each with an arc joining the centres of 2 of their edges][tiles]][tiles] Here is a net of an icosahedron to arrange the tiles on: [![20 triangular faces that can fold into a regular icosahedron][icosahedron net]][icosahedron net] ## 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. [tiles]: https://raw.githubusercontent.com/trichoplax/closed-loop-on-tetrahedron-puzzle/refs/heads/main/icosahedron-tiles.svg [icosahedron net]: https://raw.githubusercontent.com/trichoplax/closed-loop-on-tetrahedron-puzzle/refs/heads/main/icosahedron-net.svg