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Johnson solid J_(24).

Johnson solid J_(47).

Johnson solid J_(23).

Johnson solid J_(44).

The vectors +/-a_1, ..., +/-a_n in a three-space form a normalized eutactic star iff Tx=x for all x in the three-space.

The sporadic group HJ, also denoted J_2.

Two nonsingular forms are equivalent over the rationals iff they have the same determinant and the same p-signatures for all p.

Determined the possible values of r and n for which there is an identity of the form (x_1^2+...+x_r^2)(y_1^2+...+y_r^2)=z_1^2+...+z_n^2.

The principal normal indicatrix of a closed space curve with nonvanishing curvature bisects the area of the unit sphere if it is embedded.

A theory of Hamiltonian cycles.