polygon
Let an agent handle polygons by sides, angles, regularity, convexity and area, and link extended notions appropriately.
Research draft, second pass
A second pass drafted this model: the structure a model of this thing needs, and what is known about it in the world. The line under this one says how the second half was obtained - researched against sources, or recalled without web access, in which case nothing here was read anywhere and every claim is a lead to verify. Unreviewed either way.
written by Claude from model knowledge without web access - no source was read, every claim is a lead to verify
Researched by: Claude
Purpose and description
Let an agent handle polygons by sides, angles, regularity, convexity and area, and link extended notions appropriately.
A plane figure bounded by a finite chain of straight line segments closing in a loop, such as triangles, quadrilaterals, pentagons and hexagons; extended notions include apeirogons and polyominoes built from squares.
What it is for: Geometry, design, computer graphics, mapping and tiling.
It can be compute area and perimeter; classify by sides and angles; triangulate for graphics; tile the plane with suitable polygons.
Distinguishing features
Straight sides, closed
Interior angle sum (n - 2) x 180 degrees
Regular, convex or concave
Self-intersecting forms exist
What it looks like
Closed flat shapes with straight sides.
How it is recognised
Number of sides
Names such as hexagon
Polyominoes are shapes made of squares
Related models
is a kind of - category
includes - example
forms faces of - solids
is used in - applications
In practice
Families and kinds
triangles
quadrilaterals
regular polygons
star polygons
polyominoes (related)
Standards and regulation
OGC Simple Features for polygons in GIS
Failure modes and hazards
Area errors for self-intersecting polygons
Winding-order errors in GIS
Also called
+179
Where this came from
wikidata · CC0 1.0
Drafted structure
Bundle to layer to finding to question, as the second pass will find it: 4 bundles · 8 layers · 8 findings · 16 questions.
Shape Which polygon.
Sides define it.
Sides
Count.
Sides
Sides.
- How many sides does it have? measurement
- Is it regular? boundary
Convexity
Convex or concave.
Convexity
Convexity.
- Is it convex, concave or self-intersecting? definition
- How does that affect calculations? boundary
Measures Area and angles.
Formulas apply.
Area
Formula.
Area
Area.
- What is its area? measurement
- Which formula is used? definition
Angles
Interior sum.
Angles
Angles.
- What are its interior angles? measurement
- What is their sum? measurement
Computing Graphics and GIS.
Polygons are data.
Graphics
Triangulation.
Graphics
Graphics.
- How is it triangulated for rendering? action
- Is winding order consistent? boundary
GIS
Geometries.
GIS
GIS polygons.
- Is the polygon valid under the GIS standard? boundary
- In which coordinate system? definition
Tiling Patterns.
Some polygons tile.
Tiles
Tessellation.
Tiles
Tiling.
- Can this polygon tile the plane? boundary
- In which pattern? definition
Related shapes
Polyominoes.
Related
Related shapes.
- Is a polyomino or apeirogon meant instead? boundary
- Which entry fits? action
What the second pass must settle
- Should polygon types be separate entries?
- How should GIS polygons be linked?
- How should polyominoes be split off?