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Everything about Simplex

Multi-dimensional generalization of triangle

In geometry, a simplex is a generalization of the notion of a triangle or tetrahedron to arbitrary dimensions. The simplex is so-named because it represents the simplest possible polytope in any given dimension. For example,a 0-dimensional simplex is a point, a 1-dimensional simplex is a line segment, a 2-dimensional simplex is a triangle, a 3-dimensional simplex is a tetrahedron, and a 4-dimensional simplex is a 5-cell. Wikipedia →

🧭 Start here: a 6-step reading path

  1. Read the overview: SimplexA 5-minute orientation
  2. Skim a recent paper: Acyclovir resistance in herpes simplex viruses: Prevalence and therapeutic alternativesInfluential work since 2022
  3. Pick up a classic book: Herpes SimplexThe most-reprinted book on the subject
  4. Read the landmark paper: A Simplex Method for Function MinimizationCited 24,015 times
  5. Go sideways: Schläfli orthoschemeA closely related topic
  6. Go sideways: Simplicial homologyA closely related topic

📖 Definitions

Adjective Having a single structure; not composite or complex; undivided, unitary.

Adjective Of an eye: (supposedly) having pigment on only the posterior surface of the iris and not the anterior surface, and thus appearing blue; this was later found to be inaccurate, as eye colour is due to the amount of pigment in the anterior surface of the iris; also, of eye pigmentation: present only on the posterior surface of the iris; and of a person: having eyes with this form of pigmentation.

Adjective Of a circuit or device: involving signals which travel in one direction at a time; unidirectional.

Adjective Of a polyploid organism: having one dominant allele at a given locus on all homologous chromosomes.

🗂️ The subject at a glance

  1. History
  2. Elements
  3. Symmetric graphs of regular simplices
  4. Standard simplex
  5. Cartesian coordinates for a regular n-dimensional simplex in Rn
  6. Geometric properties
  7. Algebraic topology
  8. Algebraic geometry
  9. Applications

🏆 Landmark papers (most cited)

🆕 Influential since 2022

📚 Books worth reading

Ranked by number of editions on Open Library, a rough measure of how lasting a book is.

🔗 Related topics