  The Witting configuration with 40 complex rays was suggested as a possible
reformulation of Penrose model with two spin-3/2 systems based on geometry of
dodecahedron and used for analysis of nonlocality and contextuality in quantum
mechanics. Yet another configuration with 120 quantum states is considered in
presented work. Despite of different number of states both configurations can
be derived from complexification of 240 minimal vectors of 8D real lattice
corresponding to root system of Lie algebra $E_8$. An analysis of properties of
suggested configuration of quantum states is provided using many analogies with
properties of Witting configuration.
