An n-dimensional simplex in a euclidean space consists of n + 1 linearly independent points p₀,p₁,...,p_n together with all line segments a₀p₀ + a₁p₁ + . . . + a_np_n where the a_i ≧ 0 and a₀ + a₁ + . . . + a_n = 1; a triangle with its interior and a tetrahedron with its interior are examples.

The eigenvalue of a nucleus or other object with an octupole (pear) shape under an operation consisting of rotation through 180° about an axis perpendicular to the symmetry axis, followed by inversion.