The most common statement known as Steiner's theorem (Casey 1893, p. 329) states that the Pascal lines of the hexagons 123456, 143652, and 163254 formed by interchanging the vertices at positions 2, 4, and 6 are concurrent (where the numbers denote the order in which the vertices of the hexagon are taken). The 20 points of concurrence so generated are known as Steiner points.
Another theorem due to Steiner lets lines 
and 
join a variable point on a conic
section to two fixed points on the same conic section.
Then 
and 
are projectively related.
A third "Steiner's theorem" states that if two opposite edges of a tetrahedron move on two fixed skew lines in any way whatsoever but remain fixed in length, then the volume of the tetrahedron remains constant (Altshiller-Court 1979, p. 87).
