Editing Simplex (section)

== History ==
The concept of a simplex was known to [[William Kingdon Clifford]], who wrote about these shapes in 1886 but called them "prime confines". 
[[Henri Poincaré]], writing about [[algebraic topology]] in 1900, called them "generalized tetrahedra".
In 1902 [[Pieter Hendrik Schoute]] described the concept first with the [[Latin]] superlative ''simplicissimum'' ("simplest") and then with the same Latin adjective in the normal form ''simplex'' ("simple").<ref>{{citation|url=http://jeff560.tripod.com/s.html|title=Simplex|work=Earliest Known Uses of Some of the Words of Mathematics|first=Jeff|last=Miller|access-date=2018-01-08}}</ref>

The '''regular simplex''' family is the first of three [[regular polytope]] families, labeled by [[Donald Coxeter]] as {{math|''α''<sub>''n''</sub>}}, the other two being the [[cross-polytope]] family, labeled as {{math|''β''<sub>''n''</sub>}}, and the [[hypercube]]s, labeled as {{math|''γ''<sub>''n''</sub>}}. A fourth family, the [[hypercubic honeycomb|tessellation of {{mvar|n}}-dimensional space by infinitely many hypercubes]], he labeled as {{math|''δ''<sub>''n''</sub>}}.{{sfn|Coxeter|1973|loc=§7.2|pp=120-124}}