K382


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	X(1), X(2), X(3), X(4), X(6), X(7), X(354), X(672), X(955), X(991), X(5728), X(14547), X(14548), X(14549), X(43672) other points below

K382 is the only (undecomposed) cubic passing through I, G, O, H, K and Ge (Gergonne point) i.e. six centers of the ETC Top 10. See also K696 and Table 30.

The following table gives alignments and other points on the cubic.

Xi	Xj	Xk / pt	notes/1st baryc.	Search
1	2	1	G is the tangential of I	*
1	3	354		*
1	4	14547		*
1	6	5728		*
1	7	991		*
1	672		a(a^4b - a^3b^2 - a^2b^3 + ab^4 + a^4c + a^3bc - 2a^2b^2c - ab^3c + b^4c - a^3c^2 - 2a^2bc^2 - 4ab^2c^2 - b^3c^2 - a^2c^3 - abc^3 - b^2c^3 + ac^4 + bc^4)/(2bc + ab + ac - a^2)	1.5149423271
1	995		ugly	0.39759327634
2	3	4		*
2	6	14548		*
2	7	672		*
2	354		a(a^2+b^2+c^2-2ab-2ac)/(-a^2+ab+ac+2bc)	-0.26879818663
2	955	5728		*
2	991	43672		*
3	6	991		*
3	7	OGe	(3a^2b-2ab^2-b^3+3a^2c+4abc+b^2c-2ac^2+bc^2-c^3)/(a^2b-b^3+a^2c+2abc+b^2c+bc^2-c^3)	1.8270354007
3	672		a^2(ab+ac-b^2-c^2)/(-a^3+a^2b-ab^2+b^3+a^2c-2abc-b^2c-ac^2-b*c^2+c^3)	-12.113065373
3	955		ugly	1.794898451968
4	6	HK	ugly	-31.019596589
4	7	5728		*
4	354		ugly	1.533666290999
4	672		ugly	-4.8466314073
4	955		ugly	1.198832957781
4	991	14549		*
6	7		ugly	2.4103172619
6	354		a(a^5 - a^4b - ab^4 + b^5 - a^4c - 2a^3bc + 2a^2b^2c + 2ab^3c - b^4c + 2a^2bc^2 + 6ab^2c^2 + 2abc^3 - ac^4 - bc^4 + c^5)/(a^2 + b^2 + c^2 - 2ab - 2a*c)	18.74219943685
6	672	14547		*
6	955		ugly	1.769623144772
7	354	14548		*
7	955		ugly	-0.4068239559082
354	672	14549		*
354	955	HK	ugly	-31.019596589
354	991		a^2(a^2 - b^2 - 4bc - c^2)/(-a^5 + 2a^4b - 2a^2b^3 + ab^4 + 2a^4c + 2a^3bc - 5a^2b^2c + b^4c - 5a^2bc^2 - 2ab^2c^2 - b^3c^2 - 2a^2c^3 - b^2c^3 + ac^4 + b*c^4)	1.658226689587
672	955		ugly	1.664615036028
672	991		ugly	-0.880651271322
955	991	14547		*