If line , line ,
and collinear . Pappus's hexagon
theorem is self-dual .
The Levi graph of the configuration corresponding
to the theorem is the Pappus graph .
See also Brianchon's Theorem ,
Cayley-Bacharach Theorem ,
Hexagon ,
Pappus's
Centroid Theorem ,
Pappus Chain ,
Pappus
Configuration ,
Pappus Graph ,
Pappus's
Harmonic Theorem ,
Möbius Tetrahedra ,
Pascal's Theorem
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References Coxeter, H. S. M. "Self-Dual Configurations and Regular Graphs." Bull. Amer. Math. Soc. 56 , 413-455, 1950. Coxeter,
H. S. M. The
Beauty of Geometry: Twelve Essays. Coxeter,
H. S. M. and Greitzer, S. L. "Pappus's Theorem." §3.5
in Geometry
Revisited. Eves,
H. "Pappus' Theorem." §6.2.6 in A
Survey of Geometry, rev. ed. Johnson, R. A. "Theorem of Pappus." §388
in Modern
Geometry: An Elementary Treatise on the Geometry of the Triangle and the Circle. Ogilvy, C. S.
Excursions
in Geometry. Pappas, T.
"Pappus' Theorem & the Nine Coin Puzzle." The
Joy of Mathematics. Wells, D. The
Penguin Dictionary of Curious and Interesting Geometry. Referenced on Wolfram|Alpha Pappus's Hexagon Theorem
Cite this as:
Weisstein, Eric W. "Pappus's Hexagon Theorem."
From MathWorld https://mathworld.wolfram.com/PappussHexagonTheorem.html
Subject classifications
,
,
and 
are three points on one line, 
, 
, and 
are three points on another line,
and 
meets 
at 
,
meets 
at 
,
and 
meets 
at 
,
then the three points 
, 
, and 
are collinear. Pappus's hexagon
theorem is self-dual.
configuration corresponding
to the theorem is the Pappus graph.
