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3-d grid hunting (Posted on 2004-03-25) Difficulty: 2 of 5
Find two regular tetrahedra that share a face placed in a way such that each vertex has integer coordinates.

See The Solution Submitted by Tristan    
Rating: 3.1667 (6 votes)

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Solution Solution | Comment 2 of 7 |
I started with the tetrahedron with vertices (0,0,0), (1,1,0), (1,0,1) and (0,1,1). The symmetrical image of (0,0,0) with regard to the opposite face turns out to be (4/3, 4/3, 4/3), so multyplying everything by 3 gets:

(0,0,0), (3,3,0), (3,0,3), (0,3,3)

and

(4,4,4), (3,3,0), (3,0,3), (0,3,3)


  Posted by e.g. on 2004-03-25 14:56:25
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