Gott's Regular Pseudopolyhedrons
J. Richard Gott in 1967 published a larger set of seven infinite skew polyhedra which he called regular pseudopolyhedrons, including the three from Coxeter and four new ones.
Gott relaxed the definition of regularity to allow his new figures. Where Coxeter and Petrie had required that the vertices be symmetrical, Gott required only that they be congruent. Thus, Gott's new examples are not regular by Coxeter and Petrie's definition.
Gott called the full set of regular polyhedra, regular tilings, and regular pseudopolyhedrons as regular generalized polyhedra, representable by a {p,q} Schläfli symbol, with by p-gonal faces, q around each vertex.
A.F. Wells also published a list of pseudopolyhedra in the 1960s, including different forms with the same symbol: {4,5}, {3,7}, {3,8}, {3,10}, {3,12}.
However neither the term "pseudopolyhedron" nor Gott's definition of regularity have achieved wide usage.
Read more about this topic: Infinite Skew Polyhedron
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