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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 1 of 7
okay... playing around on the back of a napkin...

it occurs to me that...

two tetrahedrons... one at:
(0,0,0)
(0,12,12)
(12,0,12)
(12,12,0)

and the other at
(0,12,12)
(12,0,12)
(12,12,0)
(16,16,16)

of course they both share the face:
(0,12,12)
(12,0,12)
(12,12,0)

and the tetrahedrons have an edge of length 12√2.

We can also shift, scale, and rotate this around to produce an infinite number of others....


  Posted by SilverKnight on 2004-03-25 14:50:21
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