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The Dogic Puzzles are ‎Icosahedrons and these puzzles are extremely rare. Currently, each piece is worth about $500 (USD) on eBay.

There are actually 7 versions of this puzzle; 11 colored, 10 colored (in picture on the right), 12 colors, the most sought when it was mass-produced (in picture on the left), 5 colored, Meffert's first 2 colored, Meffert's second 2 colored, and the 20 colored with all sides having different colors.

For a decade the Dogic had been sought out by many and sold for extremely high prices, so Mefferts produced a lot of Dogics, including all Dogics excluding the 12 and 10 colored versions, for a discount so the price would be more reasonable, but 2 years later they rose to the same high price again. 

In this situation, Mark Segedin decided to design his own Dogic prototypes. Karl-Heinz Diekmann helped print the pieces for Segedin. This is not the only case of making Dogics at home; many have suggested privately remaking this puzzle (even hand making and casting was discussed). Until Segedin created his Dogic, the common opinion is that Dogic puzzles were too hard/too complex to make.

Sources

https://www.youtube.com/watch?v=dwCUlIKe4cY

http://www.twistypuzzles.com/cgi-bin/puzzle.cgi?pkey=2405

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