Symmetric models of the real projective plane

Farran, H.R., Pinto, Maria do Rosario and Robertson, S.A. (1999) Symmetric models of the real projective plane. Beiträge zur Algebra und Geometrie, 40 (1), 195-202.

Abstract

We show that the symmetry group of a stable immersion of the real projective plane P in E³ is either trivial or is cyclic of order 3, and that of a stable map of P in E³ is conjugate to a subgroup of the full tetrahedral group. Thus Boy's surface, in its 'standard' form, is the most symmetrical stable immersion of P in E³, and Steiner's surface is given by the most symmetrical stable map of P in E³. We also construct a smooth embedding of P in E⁴ with symmetry group SO₂ by orthogonal projection of the Veronese surface.

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