4-simplex

four-dimensional analogue of the tetrahedron

Facts

13 properties
Followed by
5-simplex[9]
Different from
pentatope, regular pentachoron, pentachoron[16][17][18]
Has facet polytope
regular tetrahedron[13]
Has part(s) of the class
vertex, edge, face, cell[20][21][22][23]
Has vertex figure
regular tetrahedron[15]
Main subject
regular pentachoron, pentachoron[11][12]
Maintained by WikiProject
WikiProject Mathematics[25]
Schläfli symbol
{3,3,3}[24]
🏷️ Also known as
en tetrahedral hyperpyramid en 5-cell en 4-simplex en pentachoron en pentahedroid en pentatope ar خماسي الخلايا cs 4-simplex cs 5nadstěn cs Pentachoron de vierdimensionales Hypertetraeder de vierdimensionale Hyperpyramide de Pentatop de Fünfzell de 5-Zeller de 5-Zell de 4-Simplex es hiperpirámide de cuatro dimensiones es 4-simplejo es 4-símplex
🔖 Identifiers · 5
Image (Wikimedia Commons)
Schlegel wireframe 5-cell.png ↗
Bowers acronym
pen
Freebase ID
/m/02kb2x
MathWorld ID
Pentatope
Microsoft Academic ID (discontinued)
5913903

Report an error or request removal Lineage (PROV-JSON)

🔗 Connections
Has part(s) of the class 4
← Has vertex figure 2
Dual to 1
Followed by 1
Followed by (predecessor) 1
Follows 1
Has facet polytope 1
Has vertex figure 1
Instance of 1
Maintained by WikiProject 1
Studied by 1
Subclass of 1
← Dual to 1
← Has facet polytope 1
← Model item 1
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Summary

4-simplex is a 4-polytope[1]. 4-simplex is a type of simplex[2], uniform 1ₖ₂ polytope[3], A4 polytope[4], and pentatope[5].

References

Programmatic citations — every numbered marker resolves to a verifiable graph row below.

Direct Wikidata claims

  1. [6] ↑ . wikidata.org.
  2. [7] ↑ . wikidata.org.
  3. [8] ↑ . wikidata.org.
  4. [9] ↑ . wikidata.org.
  5. [2] ↑ . wikidata.org.
  6. [3] ↑ . wikidata.org.
  7. [4] ↑ . wikidata.org.
  8. [5] ↑ . wikidata.org.
  9. [10] ↑ . wikidata.org.
  10. [11] ↑ . wikidata.org.
  11. [12] ↑ . wikidata.org.
  12. [13] ↑ . wikidata.org.
  13. [14] ↑ . wikidata.org.
  14. [15] ↑ . wikidata.org.
  15. [16] ↑ . wikidata.org.
  16. [17] ↑ . wikidata.org.
  17. [18] ↑ . wikidata.org.
  18. [19] ↑ . wikidata.org.
  19. [20] ↑ . wikidata.org.
  20. [21] ↑ . wikidata.org.
  21. [22] ↑ . wikidata.org.
  22. [23] ↑ . wikidata.org.
  23. [24] ↑ . wikidata.org.
  24. [25] ↑ . wikidata.org.

Class ancestry

  1. [1] ↑ . Wikidata. wikidata.org.

📑 Cite this page

Use these citations when quoting this entity in research, articles, AI prompts, or wherever provenance matters. We aggregate Wikidata + Wikipedia + authoritative open-data sources; the stitched, scored, cross-referenced view is what 4ort.xyz contributes.

APA 4ort.xyz Knowledge Graph. (2026). 4-simplex. Retrieved November 2, 2026, from https://4ort.xyz/entity/pentachoron
MLA “4-simplex.” 4ort.xyz Knowledge Graph, 4ort.xyz, 2 Nov. 2026, https://4ort.xyz/entity/pentachoron.
BibTeX @misc{4ortxyz_pentachoron_2026, author = {{4ort.xyz Knowledge Graph}}, title = {{4-simplex}}, year = {2026}, url = {https://4ort.xyz/entity/pentachoron}, note = {Accessed: 2026-11-02}}
LLM prompt According to 4ort.xyz Knowledge Graph (aggregator of Wikidata, Wikipedia, and authoritative open-data sources): 4-simplex — https://4ort.xyz/entity/pentachoron (retrieved 2026-11-02)

Canonical URL: https://4ort.xyz/entity/pentachoron · Last refreshed:

Edit History

Rolling log of changes to this entity's Wikidata record. Values shown reflect the current state of each edited property — follow the history link to see the precise diff for any edit.

  1. 2d ago · Infovarius · 2026-11-02 view diff on Wikidata ↗
    Instance of → 4-polytope, Wikimedia article covering multiple topics, type of polychoron
    Claims rich → —
    "/* wbsetclaim-create:1||1 */ Instance of: type of polychoron, Copying from tesseract"
  2. 29d ago · MsynBot bot · 2026-10-07 view diff on Wikidata ↗
    Sitelink count → 13
    Wikipedia languages → ['commons', 'de', 'en', 'es', 'it', 'ja', 'pt', 'ro', 'ru', 'simple', 'sl', 'uk'
    Claims rich → —
    Name → —
    "/* wbeditentity-update:0| */ add badge sitelink to redirect to zhwiki sitelink; see [[Wikidata:Sitelinks to redirects]] for details #msynbotTask10"
  3. 7w ago · A2569875 · 2026-09-14 view diff on Wikidata ↗
    Main subject → regular pentachoron, pentachoron
    Subclass of → simplex, uniform 1ₖ₂ polytope, A4 polytope +2
    "/* wbsetclaim-create:2||1 */ Subclass of: pentachoron"
  4. 9w ago · A2569875 · 2026-09-03 view diff on Wikidata ↗
    Instance of → 4-polytope, Wikimedia article covering multiple topics, type of polychoron
    "/* wbsetclaim-create:2||1 */ Instance of: Wikimedia article covering multiple topics"
  5. 9w ago · A2569875 · 2026-09-02 view diff on Wikidata ↗
    Follows → regular tetrahedron
    Instance of → —
    Has facet polytope → regular tetrahedron
    Maintained by WikiProject → WikiProject Mathematics
    + 12 other properties edited (see Wikidata diff for full list)
    "/* wbsetclaim-create:2||1 */ Different from: pentachoron"
Live feed via Wikidata EventStreams. New edits appear within minutes of being made on Wikidata.