Faces: 48
Outside vertices: 12
Other vertices: 14 (I believe)
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$\begingroup$ Am I seeing the shape correctly to think that this is essentially three $8$-sided dice merged? $\endgroup$– abiessuDec 8, 2017 at 14:41
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$\begingroup$ @abiessu I thought so, but apparently not. Well, not regular ones, at least. $\endgroup$– ArthurDec 8, 2017 at 14:46
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$\begingroup$ @Arthur: ah, so close. At least I can say I was in the ballpark... $\endgroup$– abiessuDec 8, 2017 at 14:50
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$\begingroup$ 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...) $\endgroup$– JPhi1618Dec 8, 2017 at 16:24
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$\begingroup$ 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 $\endgroup$– Mario CarneiroDec 10, 2017 at 1:52
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1 Answer
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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.
answered Dec 8, 2017 at 14:44