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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.

A curve and its polar reciprocal with regard to the fixed conic have the same Halphen transformation.

The rules for the multiplication of quaternions.

Objects which are identical except for a mirror reflection are said to display handedness and to be chiral.

A right-angled parallelepiped with dimensions a×ab×abc, where a, b, and c are integers.

A polynomial function of the elements of a vector x can be uniquely decomposed into a sum of harmonic polynomials times powers of |x|.