Twisted Fano spaces i.e. linear spaces with the parameters of
PG(3, 2) which contain a pencil of Fano subplanes are completely classified and characterized. In particular, it is proved that
twisted Fano spaces are exactly all the linear completions of systems of triangle perspectives with point degree 4.
Keywords Veblen configuration - Multi-Veblen configuration - System of triangle perspectives - Twisted Fano space - Fano projective plane - Partial Steiner triple system
Mathematics Subject Classification (2000) 05B30 - 51E30
Communicated by Dina Ghinelli.