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K911

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X(1), X(3), X(381), X(1340), X(1341), X(3576)

excenters

extraversions of X(3576)

foci of the Steiner inellipse

infinite points of K003

K911 is a stelloid as in Table 63.

It has three asymptotes parallel to those of the McCay cubic K003 and concurring at X(5054). It is tangent at X(3) to the Euler line hence X(381) is the tangential of X(3).

The polar conic (H) of X(3) is a rectangular hyperbola passing through X(3), X(54), X(110), X(182), X(1147), X(1385), X(2574), X(2575), the vertices of the Circum-Normal triangle.

The polar conic of X(381) is also a rectangular hyperbola passing through X(3), X(381), X(575), X(2574), X(2575).

These two hyperbolas are obviously homothetic to the Jerabek hyperbola.

More generally, the polar conic of any point on the Euler line is a rectangular hyperbola passing through X(3), X(2574), X(2575) and another unlisted point with SEARCH = 2.26084735242638. These are the poles of the Euler line in K911.