The diagonal of a polyhedron is any line segment connecting two nonadjacent vertices of the polyhedron. Any polyhedron having no diagonals must have a skeleton which is a complete graph (Gardner 1975). The only simple polyhedron with no diagonals is the tetrahedron. The only known toroidal polyhedron with no diagonals is the Császár polyhedron.
Polyhedron Diagonal
See also
Császár Polyhedron, Euler Brick, Polygon Diagonal, Polyhedron, Space Diagonal, TetrahedronExplore with Wolfram|Alpha
References
Gardner, M. "Mathematical Games: On the Remarkable Császár Polyhedron and Its Applications in Problem Solving." Sci. Amer. 232, 102-107, May 1975.Gardner, M. Time Travel and Other Mathematical Bewilderments. New York: W. H. Freeman, 1988.Referenced on Wolfram|Alpha
Polyhedron DiagonalCite this as:
Weisstein, Eric W. "Polyhedron Diagonal." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/PolyhedronDiagonal.html