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### Solutions for Meta - Rlyeh

Throughout the course of the puzzle hunt, teams were awarded a Meta piece each time they solved a puzzle. This year the pieces took the form of triangles with glyphs on their edges and coloured dots in their corners. When the Meta file was released, twelve pentagons were revealed with similar markings, along with a tablet listing various Lovecraftian Elder Ones.

At the end of the hunt, when the meta had not been solved, in an effort to supply a hint without having to recode the live site, we posted this not-quite-an-Epilogue, which contained one of the triangles with a letter drawn on it, and mentioned a 32-sided shape. These solutions won't assume knowledge of the hint however.

The logical thing to do with the 20 triangles is to try arranging them into an icosahedron, and the obvious joining method seems to be matching edges so that their symbols form letters. There is a unique way of doing this, and the net of the formed icosahedron looks as follows:

The orientation of the above net is a natural one, since holding the shape in this position keeps all the letters in an upright (or readable) position. The letters in the top and bottom "rows" seem to ring around their respective levels, while the "middle row" zig-zags around the centre in an alternating direction - the letters read either south-east or south-west. Similarly the vertical joins are all orientated correctly, and could be read normally from top to bottom.

Of the letters themselves, the vast majority are vowels and so they certainly don't seem to anagram or even sub-anagram to give anything useful. Instead the intuitive leap here is to realise each edge-letter represents the middle letter of a three-letter word, whose first and third letters are supplied by the adjacent faces. This interpretation is inspired by the fact the faces themselves are currently empty, and it makes sense we'd want to add letters (as opposed to, say, numbers) to them.

Filling out the faces in this way is slightly tricky, but starting at the K shouldn't make things too difficult. For example, the only common three-letters words with middle K are EKE, SKI, and SKY. EKE's first E must start a word with EU_, which has no common candidates, while SKY would require a word fitting YL_. Working in this way should give us a fairly complete net, with only a few ambiguities left over, depending on one's opinion of what words are common and what three-letter strings count as words. For now though we won't worry about ambiguities and leave the icosahedron as complete as we can make it. (Note the hint gave us one of the ambiguous letters which also helps fill out more of the shape, since the A in AIR is then forced (assuming no words satisfy _OF for FIR).)

Now let's turn our attention to the pentagons. Using analogous reasoning, we can combine these to make a unique dodecahedron, again matching edges but this time to make numbers. What numbers then can we place on the faces so that these edge-numbers make sense? In the icosahedron, the edge-letters represented the middles of words. Perhaps here the edge-numbers represent averages of numbers? Checking a few cases reveals this to definitely be the case, and we can quickly fill out the dodecahedron like so:

It's worth noting here that the numbers we get for the pentagonal faces can all correspond to puzzles in this year's hunt, where 1.2 represents Act I Scene 2, etc. Each of the matching twelve puzzles are linked in that in their story text, an Elder One's epithet is mentioned. These turn out to be:

 Puzzle Epipthet Elder One I.2 Harbinger of Doom Mappo no Ryujin I.3 The Shining Hunter Iod II.1 The Wind Walker Ithaqua II.2 The Burrower Beneath Shudde M'ell II.4 The Living Flame Cthugha III.2 The Sound of the Deep Waters Ghisguth IV.1 The Ever-Consuming Xinlurgash IV.2 The Thing in the Pit Ythogtha IV.4 The Call of Cthulhu Cthulhu V.1 Devourer of Stars Ammutseba V.2 The Fiery Messenger Zindarak V.3 The King in Yellow Hastur

Conveniently, all these names are mentioned in the supplied tablet. So we have an ordering of gods, which map to puzzle numbers, which map to pentagon faces. But where does the icosahedron come in? The other thing we haven't used here is the presence of coloured dots on the corners of all our shapes. Trying to create a new icosahedron or dodecahedron by matching coloured vertices doesn't seem to work, but what if we combine all 32 shapes? This matching works, and uniquely gives us a 32-faced icosidodecahedron.

(Note in this image we've removed the ambiguous triangle letters, which can be done after discovering the next step.) Now we can finally use the ordering supplied by the tablet. It seems logical that this ordering gives a traversal of the shape, and that we should travel the shortest distance from the centre of each pentagon. If two pentagons share a vertex, travelling between them means passing over that vertex. However if they do not, since at no point does one have to travel to the opposite face, the traversal in this case is always over the two triangles adjacent to each that meet at a vertex.

Note every time we pass over a triangle, we cross over its letter. If we read out all such letters, we get the message DREAMS IN CULT CHANTS. Recalling the dual theme of this year's story, it seems we want the word for "dreams" as chanted by the cult of Cthulhu. This turns out to be the word fhtagn.

Design Notes: This puzzle was mostly designed because we wanted to use the interesting fact that there exists a polyhedron made up of the faces of an icosahedron and a dodecahedron - the two biggest Platonic solids. Because one of these shapes has 20 faces, it lends itself nicely to being made of Meta pieces, and so this is what we ran with.

Unforunately the edges did not match up as flush as we would have liked, because we forgot to factor in line thickness. We trust the letters/numbers on the edges were still clear enough to be understood.

Judging by the solve rate, this puzzle turned out much harder than expected. We were aware some of the letters in the icosahedron step were ambiguous, but trusted there were enough guaranteed letters to make the final message readable. The rule for the dodecahedron numbers was also sligtly difficult to hit upon, but we figured eagle-eyed solvers would have realised the story references already and would be on the lookout for the twelve puzzles to be represented somewhere on the twelve pentagons. These were really the only two logic-leaping steps, since everything else was either essentially a jigsaw or following a list of orders. Unfortunately we couldn't see any unartificial way to hint at these two letter/number-adding steps though - apologies to all those who were stumped!