Let 
be a primitive
polytope with eight vertices. Then there is a unimodular map that maps 
to the polyhedron whose vertices are (0, 0, 0), (1, 0, 0),
(0, 1, 0), (0, 0, 1), (0, 1, 1), (1, 
, 
),
(1, 
, 
), and (1, 
, 
)
with 
,
, and 
. Furthermore, any primitive polyhedron with fewer than
eight vertices can be embedded in one with eight vertices.
Howe's Theorem
See also
Primitive PolytopeExplore with Wolfram|Alpha
References
Khan, M. R. "A Counting Formula for Primitive Tetrahedra in
."
Amer. Math. Monthly 106, 525-533, 1999.Scarf, H. E.
"Integral Polyhedra in Three Space." Math. Oper. Res. 10,
403-438, 1985.Referenced on Wolfram|Alpha
Howe's TheoremCite this as:
Weisstein, Eric W. "Howe's Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/HowesTheorem.html