In geometry, a simplex (plural: simplexes or simplices) is a generalization of the notion of a triangle or tetrahedron to arbitrary dimensions.
Specifically, a k-simplex is a k-dimensional polytope which is the convex hull of its k + 1 vertices.
More formally, suppose the k + 1 points are affinely independent, which means
are linearly independent.
Then, the simplex determined by them is the set of points
For example, a 2-simplex is a triangle, a 3-simplex is a tetrahedron, and a 4-simplex is a 5-cell. A single point may be considered a 0-simplex, and a line segment may be considered a 1-simplex. A simplex may be defined as the smallest convex set containing the given vertices.
A regular simplex is a simplex that is also a regular polytope. A regular n-simplex may be constructed from a regular (n − 1)-simplex by connecting a new vertex to all original vertices by the common edge length.
In topology and combinatorics, it is common to “glue together” simplices to form a simplicial complex. The associated combinatorial structure is called an abstract simplicial complex, in which context the word “simplex” simply means any finite set of vertices.
Simplex is Latin for "simple, pure, plain" and may refer to:
Not to be confused with American Simplex
Crane-Simplex was a car manufacturer, operating in New York City and New Brunswick, New Jersey, at the beginning of the 20th century.
The Smith and Mabley Manufacturing Co. of New York City was founded by Carleton Raymond Mabley (1878-1963) and his brother-in-law Albert Proctor Smith to import European cars for sale in America. They built their first car in 1904, which was called the S&M Simplex, largely from imported Mercedes parts. The company went bankrupt in 1906 and in 1907 the firm's assets were absorbed into the Simplex Automobile Co. Herman Broesel, passionate about racing, purchased the company and redesigned the "Simplex" so it could reach speeds of 90 mph (140 km/h). The firm became Crane-Simplex after purchase of the Crane Motor Car Company of Bayonne, New Jersey, which had been founded by Henry Middleton Crane, in 1915. The Crane-Simplex Company was purchased in 1920 by the Mercer Automobile Company but by 1922 ownership had passed to Henry Crane, who then failed to realise an ambition to revive the marque.
Some people wake up on Monday mornings
Barring maelstroms and red flare warnings
With no explosions and no surprises
Perform a series of exercises
Hold your fire
Take your place around an open fire
Before your neurons declare a crisis
Before your trace Serotonin rises
Before you're reading your coffee grounds
And before a pundit can make a sound
And before you're reading your list of vices
Perform the simplest exercises
So here we are at the end
The war is over
There's nothing left to defend
No cliffs of Dover
So let us put down our pens
And this concludes the test
Our minds are scattered about
From hell to breakfast
Hold your fire
Take your place around an open fire