The theorem of Möbius tetrads, also simply called Möbius's theorem by Baker (1925, p. 18), may be stated as follows. Let 
, 
, 
, and 
be four arbitrary points in a plane. Draw an arbitrary plane
through each of the six lines through pairs of points 
. The set of three of these planes 
, 
, 
passing through the pairs from three of the original
points meet in a point 
. The theorem of Möbius tetrads then states that
the four points 
,
,
,
and 
lie in a plane (Baker 1992, p. 62).
Möbius Tetrad Theorem
See also
Coplanar, Möbius Tetrahedra, Pappus's Hexagon TheoremExplore with Wolfram|Alpha
References
Baker, H. F. Principles of Geometry, Volume 1: Foundations. Cambridge, England: pp. 61-62, 1922.Baker, H. F. Principles of Geometry, Volume 4: Higher Geometry. Cambridge, England: pp. 18-21, 1925.Möbius, F. A. "Kann von zwei dreiseitigen Pyramiden eine jede in Bezug auf die andere um- und eingeschrieben zugleich heissen?" J. reine angew. Math. 3, 273-278, 1828.National Museum of American History. "Model of Moebius's Theorem by Richard P. Baker, Baker #432a." https://americanhistory.si.edu/collections/search/object/nmah_1087015.National Museum of American History. "Model of Moebius's Theorem, by Richard P. Baker, Baker #432b." https://americanhistory.si.edu/collections/search/object/nmah_1087020.Cite this as:
Weisstein, Eric W. "Möbius Tetrad Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/MoebiusTetradTheorem.html