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Incubator Q&A

Welcome to the staging ground for new communities! Each proposal has a description in the "Descriptions" category and a body of questions and answers in "Incubator Q&A". You can ask questions (and get answers, we hope!) right away, and start new proposals.

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Comments on Closed loop on an icosahedron

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Closed loop on an icosahedron Question

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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 icosahedron.

There are 20 identical tiles:

20 triangular tiles each with an arc joining the centres of 2 of their edges

Here is a net of an icosahedron to arrange the tiles on:

20 triangular faces that can fold into a regular icosahedron

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.

History

1 comment thread

History (2 comments)
History
Peter Taylor‭ wrote 3 days ago

This is very close to the problem which is the origin of the name "Hamiltonian cycle".

trichoplax‭ wrote 3 days ago

Reading through suggests very close. Since that connects all of the dodecahedron vertices using some of the edges, and this connects all of the icosahedron faces using some of the edges, it seems they are equivalent (solutions should be the same shape in either). So that interesting Wikipedia article is probably a spoiler for this puzzle too.

By way of encouragement to anyone considering solving this, the article claims:

it was too easy to become commercially successful