A sextic primal in five dimensions

Abstract

In a recent tract (Baker (1)) there is described in considerable detail a configuration of forty-five points which are nodes of a quartic primal in four dimensions. The geometry of this primal is very fascinating; among its interesting properties is the fact that a number of well-known geometrical configurations, which usually arise as unrelated phenomena, here all appear in connexion with the one figure. The interest of the primal, of course, lies chiefly in the large number of collineations which leave it invariant. The group G* of these collineations is considered in a paper by Burkhardt (2), in which are given explicit expressions for five algebraically independent functions of the five variables, which are left invariant by the operations of the group. The simplest of these invariants is of the fourth order, and when equated to zero represents the quartic primal which is the subject of Baker's tract.