Timeline

This is a (partially complete) list of important events in the study of polytopes.

Before year 1 CE

 * The Sumerians were using tessellations in their art as early as the fourth millennium BCE.


 * The Platonic solids are thought to have been discovered sometime in the first millennium BCE.


 * The Archimedean solids were attributed in later manuscripts to the third-century-BCE mathematician Archimedes.

1 - 1800

 * Artwork depicting the Kepler-Poinsot solids can be found as far back as the 15th century.
 * Around 1619, Johannes Kepler recognized the small and great stellated dodecahedron as regular.
 * Kepler also wrote on tessellations in 1619.

1800 - 1900

 * In 1809, Louis Poinsot recognized the great dodecahedron and great icosahedron as regular.
 * Three years later, the list of nonconvex finite regular ("star") polyhedra was proved complete by Augustin Cauchy.


 * Ludwig Schläfli first described the convex regular polychora in the mid-19th century, as well as some of the nonconvex finite ones.
 * Edmund Hess published a list of all of the nonconvex finite regular polychora in 1883. These became known as the Schläfli-Hess polychora.


 * Alicia Boole Stott coined the term "polytope" in the latter half of the 19th century.

1900 - 1990

 * Harold Scott MacDonald Coxeter recieved his Ph.D. in 1931.
 * In 1926, Coxeter and John Flinders Petrie discovered the regular skew apeirohedra: the mucube, muoctahedron, and mutetrahedron.
 * In 1938, he, Petrie, and others published "The Fifty-Nine Icosahedra," a list of the stellations of the icosahedron.
 * Coxeter, J. C. P. Miller, and others published a list of uniform polyhedra in 1954.
 * John Skilling proved the list complete in 1975.
 * Coxeter contributed to the development of Coxeter-Dynkin diagrams, was friends with M. C. Escher, and inspired the work of Buckminster Fuller.


 * Branko Grünbaum received his Ph.D. in 1957. He would author hundreds of papers on discrete geometry and abstract polytopes over the next fifty years.


 * In 1966, Norman Johnson received his Ph.D. under the supervision of H.S.M. Coxeter.
 * In this year, he also published a list of non-uniform convex regular-faced polyhedra, which came to be known as the Johnson solids.
 * Victor Zalgaller proved the list to be complete in 1969.
 * Johnson also gave names to all of the nonconvex uniform polyhedra.


 * In 1970, Bonnie Stewart published "Adventures among the Toroids," in which he found a finite class of regular-faced toroidal polyhedra with uniform convex hulls.


 * In 1971, Father Magnus Wenninger published "Polyhedron Models," the first time that pictures of the uniform polyhedra had been widely published.


 * In the 1980s, Gerd and Roswitha Blind listed the Blind polytopes, a subset of convex regular-faced or "CRF" polytopes.


 * In 1981, Nicolaas Govert de Bruijn published an algebraic theory of the Penrose tiling.

1990 - 2010

 * In 1990, Jonathan Bowers' polychoron search began.


 * In 1996, George Hart began publishing his work on polyhedron models.


 * In 2000, Richard Klitzing published a list of convex segmentochora.


 * In 2005, Wendy Krieger released a paper "Walls and Bridges," which introduced prism, tegum, pyramid, and comb products.


 * By the year 2006, the number of known uniform polychora had risen to 1849, due to the work of Bowers, George Olshevsky, Mason Green, and others.


 * In 2008, Mathieu Dutour Sikirić and Wendy Myrvold determined the number of Blind polytopes created by diminishing the hexacosichoron.

2010 - present

 * In 2014, Higherspace forum users discovered many CRF polychora that unprecedentedly used bilunabirotundae and triangular hebesphenorotundae as cells.


 * In late 2020 and early 2021, Polytope Discord user _Geometer made discoveries that lead to the discovery of hundreds of new uniform polychora.