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.
 * He also coined names to all the convex uniform polyhedra, aka Archimedean polyhedra.
 * 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.


 * As early as 1888, Charles Howard Hinton coined the term "tesseract".


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


 * Thorold Gosset discovered the semiregular polytopes 221, 321, and 421 in 1896-1897.



1900 - 1990

 * Max Bruckner published his collections of noble polytopes in 1906.


 * Alicia Boole Stott in 1910 published about what became known as "Stott expansions"
 * 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 - present

 * In 1990, Jonathan Bowers' polychoron search began.
 * Rapsady was found in 1993, the idcossid, dircospid, sidtap, and gidtap regiments in 1997, and the Sabbadipady regiment in 1998.
 * Other polytopists contributed as well. In 1999, George Olshevsky came up with the idea of swirlprisms or swirlchora, which display discretized Hopf fibrations.
 * In 2001-2, Iquipadah was found.


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


 * In 2000, Richard Klitzing published a list of convex segmentochora.
 * It already contained tutcup, the very first example of scaliform polychora.
 * In 2010, he provided a deeper and unifying insight into snubbing, holosnub, and more general alternations.


 * 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, Olshevsky, Mason Green, Hironori Sakamoto, and others.


 * In 2007, Robert Webb released the Stella software, which is extremely useful for exploring uniform polychora and their scaliform relatives.


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


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


 * In 2019, Klitzing brought certain compounds of hexacosichora including Pedisna to Bowers' attention, leading to a large wave of discoveries.


 * In late 2020 and early 2021, Polytope Discord user _Geometer made discoveries that lead to the discovery of hundreds of new uniform polychora.
 * In September 2020, Sidditsphit and Gidditsphit were found, the first uniform polychora since 2006.
 * In early October, Setut and Getut were found.
 * In late October, Pecuexdap and Pecuexidfap were found.
 * In January 2021, several hundred uniform polychora in the Disdi regiment were found, the first being Siggissido.
 * In October 2021, Tesapdid was found by accident.


 * In 2022, the addition of a faceting feature in led to an even larger discovery wave of scaliforms and fissary uniforms including Dexdap. Miratope also allowed many 6D regiments to be counted.
 * _Geometer found the infinite family of uniform polygonal duoprismatic spinoalterprisms during this time.