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Planigon

In geometry, a planigon is a convex polygon that can fill the plane with only copies of itself (isotopic to the fundamental units of monohedral tessellations). In the Euclidean plane there are 3 regular planigons; equilateral triangle, squares, and regular hexagons; and 8 semiregular planigons; and 4 demiregular planigons which can tile the plane only…

History, Measurement & Standards

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Overview

History

Construction

Derivation of all possible planigons

Number of Dual Uniform Tilings

Higher Dual Uniform Tilings

  • Here 3-4-6-12 tiling

Fractalizing Dual k-Uniform Tilings

Miscellaneous

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Map overview Semantic statistics

Planigon

Nodes60
Edges59
Triples79
Avg. degree1.97
Density0.033333
Components1

How this topic connects Entity context

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Planigon

Top relations

related to history · 17
Planigon → Alekseĭ Vasilʹevich, Archimedean, Branko Grünbaum, Catalan, Each, Fritz Laves, In, John Conway, Laves, Shubnikov, The, The Laves, Their, They're, This, Three, Tilings
related to References · 8
Planigon → Akad, Alexander Korobov, Delone, Izv, Mat, Nauk SSSR Ser, September, Theory
related to Regular Vertices · 7
Planigon → All, All Laves, Grünbaum, In, In Tilings, Laves, Patterns
related to Big Fractalization · 6
Planigon → By, DB, DC, In, S2TC, The
related to Planigons in the plane · 5
Planigon → By, If, In, Laves Tiling, Only
related to Optimized Tilings · 4
Planigon → Also, Catalaves, Finally, If
related to Other Edge-Edge Construction Comparisons · 4
Planigon → All, Other, Pictured, Rotates
related to Circle Packing · 3
Planigon → Below, Each, Optimized Tilings
related to Large Fractalization · 3
Planigon → To, V3, V32
related to Number of Dual Uniform Tilings · 3
Planigon → Every, If, Such

Important terminology Word statistics

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Important terminology

tilings regular planigons dual vertex uniform tiling edges laves displaystyle polygons vertices number two plane types shown k-uniform tiles must

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Planigonis aconvex polygon that can fill the plane with only copies of itself0.90text
Planigonrelated to 2-Dual-UniformThere0.60section
Planigonrelated to 2-Dual-UniformKrotenheerdt Duals0.60section
Planigonrelated to 3-Dual-UniformThere0.60section
Planigonrelated to 3-Dual-UniformKrotenheerdt Duals0.60section
Planigonrelated to 4-Dual-UniformThere0.60section
Planigonrelated to 4-Dual-UniformKrotenheerdt Duals0.60section
Planigonrelated to 5-Dual-UniformThere0.60section
Planigonrelated to 5-dual-uniform 4-Catalaves tilingsChanges0.60section
Planigonrelated to Affine Linear ExpansionsBelow0.60section
Planigonrelated to Affine Linear ExpansionsThe0.60section
Planigonrelated to Big FractalizationBy0.60section

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    Min side: 3
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