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permutohedron

polytope whose vertex coordinates are permutations of the vector (1,2,3,...n)
Class type of: isogonal figure, zonotope, integral polytope Q1710083

Facts

6 properties
Instance of
polytope family
Subclass of
isogonal figure, zonotope, integral polytope[3][4][5]
Discoverer or inventor
Pieter Hendrik Schoute[2]
Maintained by WikiProject
WikiProject Mathematics[8]
Studied by
geometric combinatorics[7]
Time of discovery or invention
1911[6]
🏷️ Also known as
en permutation polytope en permutohedron en permutahedron ar متعدد وجوه تبديلي de Permutaeder es permutaedro fr permutoèdre hu permutaéder it permutoedro ja パーミュトヘドロン ja 置換多面体 ko 순열다면체 nl permutoëder ro permutoedru ru перестановочный многогранник ru Пермутоэдр zh 全序多胞形 zh 排列多面體 zh-hans 排列多面体
🔖 Identifiers · 4
Image (Wikimedia Commons)
Permutohedron.svg ↗
Freebase ID
/m/02x30jz
MathWorld ID
Permutohedron
Microsoft Academic ID (discontinued)
152303604

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

🔗 Connections
Discoverer or inventor 1
Pieter Hendrik Schoute
Instance of 1
polytope family
Maintained by WikiProject 1
WikiProject Mathematics
Subclass of 1
isogonal figure
Subtypes 1
truncated octahedron
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Summary

permutohedron is a polytope family[1].

References

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

Direct Wikidata claims

  1. [2] ↑ . wikidata.org.
  2. [3] ↑ . wikidata.org.
  3. [4] ↑ . wikidata.org.
  4. [5] ↑ . wikidata.org.
  5. [6] ↑ . wikidata.org.
  6. [7] ↑ . wikidata.org.
  7. [8] ↑ . wikidata.org.

Class ancestry

  1. [1] ↑ . Wikidata. wikidata.org.

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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). permutohedron. Retrieved November 4, 2026, from https://4ort.xyz/entity/permutohedron
MLA “permutohedron.” 4ort.xyz Knowledge Graph, 4ort.xyz, 4 Nov. 2026, https://4ort.xyz/entity/permutohedron.
BibTeX @misc{4ortxyz_permutohedron_2026, author = {{4ort.xyz Knowledge Graph}}, title = {{permutohedron}}, year = {2026}, url = {https://4ort.xyz/entity/permutohedron}, note = {Accessed: 2026-11-04}}
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