18
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Faces: 48

Outside vertices: 12

Other vertices: 14 (I believe) Object

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  • $\begingroup$ Am I seeing the shape correctly to think that this is essentially three $8$-sided dice merged? $\endgroup$
    – abiessu
    Dec 8, 2017 at 14:41
  • $\begingroup$ @abiessu I thought so, but apparently not. Well, not regular ones, at least. $\endgroup$
    – Arthur
    Dec 8, 2017 at 14:46
  • $\begingroup$ @Arthur: ah, so close. At least I can say I was in the ballpark... $\endgroup$
    – abiessu
    Dec 8, 2017 at 14:50
  • $\begingroup$ And if anyone wanted to know, and didn't already, this is a common wooden star puzzle. (Amazon link just because all the others I found had spoilers on how to solve it...) $\endgroup$
    – JPhi1618
    Dec 8, 2017 at 16:24
  • $\begingroup$ See this video for examples of puzzles based on this figure, tessellations of the star, and folding a cube into two stars! youtube.com/watch?v=gWgXlvIlpzM $\endgroup$ Dec 10, 2017 at 1:52

1 Answer 1

28
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The object is the first stellation of the rhombic dodecahedron. This is sometimes known as Escher's solid, for its use in a study for his Stars, though the final picture uses a compound of three regular octahedra rather than the squashed ones of this question's solid.

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