What does simplex mean?
A simplex is a mathematical or geometric structure of the simplest possible type for a given dimension. A point is a zero-dimensional simplex, a line segment is one-dimensional, a triangle is two-dimensional, and a tetrahedron is three-dimensional. More generally, a simplex in n dimensions is the convex hull of n plus one affinely independent points. The word also has established uses in telecommunications, where simplex communication travels in only one direction at a time, and in cryptography and information systems, where it can describe a simple, unencrypted, or one-way arrangement. In mathematics, simplex is a formal term with precise technical properties; outside mathematics, its meaning depends more on context. It is especially useful because it connects a familiar sequence of geometric shapes with a general framework used throughout geometry, optimization, and related mathematical fields.
A geometric figure or mathematical structure consisting of the convex hull of a finite set of affinely independent points; in n dimensions, it has n plus one vertices.
"A triangle is a two-dimensional simplex."
The mathematical sense is technical. In telecommunications, a simplex is a system permitting communication in one direction only.
Denoting a simple, one-way, or unencrypted mode or arrangement.
"The radio operates in simplex mode."
This use is especially common in telecommunications, cryptography, and computing, though the precise meaning depends on the technical context.
The plural is usually written with -es in mathematical writing.
"The simplices share a common face in this configuration."
In mathematics, a simplex is the simplest possible space of a given dimension: a point, line, triangle, or tetrahedron.
Reviewed by Deb Chak, Editor. AI-assisted content curated by RJS Tech Solutions LLP.
Where does simplex come from?
The word simplex comes from Latin simplex, meaning “single” or “simple,” from the root simplex, simplic-, which is also the source of English simple. The mathematical sense developed in the geometric tradition, where a simplex is the simplest object of a specified dimension. The telecommunications sense refers to one-way rather than two-way communication and follows the same underlying contrast between single and multiple directions.
Related word forms
How simplex is actually used
In mathematics, the term is technical and precise. In telecommunications, simplex denotes one-way communication; in cryptography and related contexts, it may also describe a comparatively simple or unencrypted arrangement.
Easily confused with simplex
A simplex is a simple geometric or mathematical structure, whereas a complex is a mathematical structure that includes interacting components and can have more complicated topology.