Eutactic star

In Euclidean geometry, a eutactic star is a geometrical figure in a Euclidean space. A star is a figure consisting of any number of opposing pairs of vectors (or arms) issuing from a central origin. A star is eutactic if it is the orthogonal projection of plus and minus the set of standard basis vectors (i.e., the vertices of a cross-polytope) from a higher-dimensional space onto a subspace. Such stars were called "eutactic" – meaning "well-situated" or "well-arranged" – by Schläfli (1901, p. 134) because, for a common scalar multiple, their vectors are projections of an orthonormal basis.