The isogonal polyhedra have had many discovers throughout history.
The platonic solids are described by Plato although he is not the first discoverer of them. The tetrahedron, cube and dodecahedron were attributed to Pythagorus and the octahedron and icosahedron were attributed to Theaetetus.
The archimedean solids are described by Archimedes.
In 1619, Kepler was the first person to catalogue the 11 uniform tilings of the plane. They had probably all been individually discovered long before this.
Johannes Kepler. Harmonice Mundi. Linz, 1619
Coxeter and Petrie discovered the three infinite regular polyhedra and proved that there are no more.
H. S. M. Coxeter. Regular skew polyhedra in three and four dimensions, and their topological analogues. Proceedings of the London Mathematical Society (2), volume 43, pages 33-62, 1937
ApSimon discovered three new infinite polyhedra.
Hugh ApSimon. Three Facially-Regular polyhedra. Canadian Journal of Mathematics, volume 2, pages 326-330, 1950
Gott published seven infinite polyhedra, three of which are the same as Coxeter’s.
J. R. Gott, III. Pseudopolyhedrons. The American Mathematical Monthly, volume 74, pages 497-504, 1967
These authors published many new polyhedra. Their lists included many (but not all) of the cylindrical polyhedra and the corrugated tilings. Also they discovered many of the infinite archimedean polyhedra. Because of the large number of these polyhedra, they have been broken down into five sublists.
A. Wachman, M. Burt and M. Kleinmann, Infinite Polyhedra, Technion, Haifa, 1974.
Wells’ collection includes many previous discoveries, but also includes some or his own.
A. F. Wells, Three-Dimensional Nets and Polyhedra, Wiley, 1977
Webber found three new corrugated tilings.
A. F. Wells, Three-Dimensional Nets and Polyhedra, Wiley, 1977
Hughes Jones found all polyhedra whose faces are triangles and with vertices given by the octet honeycomb. In doing so, he discovered a number of new polyhedra.
R, Hughes Jones, Enumerating uniform polyhedral surfaces with triangular faces, Discrete Mathematics, volume 138, pages 281–292, 1995
Goodman-Strauss and Sullivan found all the 46 cubic polyhedra.
C. Goodman-Strauss and J. M. Sullivan, Cubic polyhedra. Discrete Geometry: in Honor of W. Kuperberg's 60th Birthday, A. Bezdek, ed. Dekker, New York, 2003, pages 305–330.
Gillispie and Grünbaum found all 15 of the 45 cubic polyhedra.
Steven B. Gillispie, Branko Grünbaum, The {4,5} isogonal sponges on the cubic lattice. Electronic Journal of Combinatorics volume 16 issue 1, article R22, 2009
These are the polyhedra that I have discovered myself. I wrote software that searched for polyhedra. This software rediscovered all known polyhedra as well as discovering these new ones, although I had already found many by other means.
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