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Prof.\ Susan Landau
Dept.\ of Mathematics
Wesleyan University
Middletown, CT 06457
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Dear Professor Landau:

	Thanks for your report {\it Shrinking Lattice Polyhedra}.  I
assume it's dated 1987 from the number 87-05.

	I didn't get very far with the problem myself --- only
the two dimensional case, getting the same algorithm.  I didn't
know enough about quaternion algebra to do the three and
four dimensional cases.

	The problem arose, I don't remember exactly how, from
another problem that may interest you.  D. J. Newman's problem
book asks whether an equilateral triangle can have its vertices
lattice points in the plane.  His proof that it can't is peculiar to the
equilateral triangle, but one can give a general answer for a plane
polygonal figure where one allows similarities transformations.
Namely, that all the angles have rational tangents is necessary
and sufficient.

	As far as I know, such problems are unsolved for higher
dimensions.  In three dimensions, equilateral triangles are
possible, e.g.\ the points 100, 010 and 001.
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Sincerely,
John McCarthy
Professor
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