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Put a letter on each face of an icosahedron such that a five-letter word can be read clockwise around each vertex. Specifically, these words:

ENDOW
ERODE
LANES
NAMED
RESTS
ROLLS
SEEMS
SEWER
SLOTS
SMALL
STORE
WORSE

Every word in the above list will appear around exactly one vertex.

Some letters might appear on multiple faces.



As an illustration of how it might look, notice how the word ENDOW can be read clockwise around the vertex:

icosahedron_with_word_around_vertex



If you don't have a 3-D model of an icosahedron to work on, you might consider printing out the planar graph of an icosahedron. Just keep in mind that the 20th face stands outside the graph.

icosahedron_planar_graph

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    $\begingroup$ This isn't much of a puzzle for us, but it was impressive to come up with the idea and list of words. It's a shame we don't have a recognized alternate color alphabet (why don't we?) so that all the letters are 'right side up' from every perspective. $\endgroup$
    – Mike Serfas
    Commented Jul 19, 2022 at 9:14
  • $\begingroup$ @MikeSerfas — Thank you. I try to come up with a range of puzzles for various skill levels and conceptual abilities. Someone who is not a natural spatial thinker might find this puzzle to be very challenging and enjoyable. You're right, a lot of heavy computation went into making this! $\endgroup$
    – SlowMagic
    Commented Jul 19, 2022 at 13:00

2 Answers 2

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How about like this

enter image description here Note the S outside the graph that is adjacent to the three borders.

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Note that every pair of adjacent faces appear in two words, reversed in one compared to the other.
This word list contains unique enough words that the placements are all forced.
(E.g. After placing Endow as a starting word, only Named can cover the other vertex common to ND. etc.)

And the following unique solution falls out: Icosohedron net with letters

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  • $\begingroup$ Beautiful presentation. Unfortunately, there are two correct answers, so I have to award it to the one with the earliest timestamp. But you certainly get an upvote! $\endgroup$
    – SlowMagic
    Commented Jul 19, 2022 at 19:10

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