Five such regular abstract polyhedra, which can not be realised faithfully, were identified by H. S. M. Coxeter in his book "Regular Polytopes" (1977) and again by J. M. Wills in his paper "The combinatorially regular polyhedra of index 2" (1987). All five have C2×S5 symmetry but can only be realised with half the symmetry, that is C2×A5 or icosahedral symmetry. They are all topologically equivalent to toroids. Their construction, by arranging "n" faces around each vertex, can be repeated indefinitely as tilings of the hyperbolic plane. In the diagrams below, the hyperbolic tiling images have colors corresponding to those of the polyhedra images.