Is 'reentering polygon' the same as 'concave polygon'?

Yes, they are synonyms. 'Concave polygon' is the more common term in many contexts.

Can a triangle be a reentering polygon?

No. The sum of interior angles in a triangle is 180°, so no single angle can exceed 180°. Only polygons with four or more sides can be reentering.

Why is it called 'reentering'?

The term visualises the polygon's boundary: at a reentrant angle, the boundary line appears to turn and go back into the interior space of the shape, 're-entering' it.

Where would I encounter this term professionally?

Most commonly in computer graphics (3D modelling, game engines), geographic information systems (GIS), computational geometry research, CAD software, and urban/land surveying.

Is “reentering polygon” formal?

Reentering polygon is usually technical/academic in register.

How do you pronounce “reentering polygon”?

Reentering polygon: in British English it is pronounced /ˌriːɛnˈtɪərɪŋ ˈpɒlɪɡən/, and in American English it is pronounced /ˌriɛnˈtɪrɪŋ ˈpɑːliɡɑːn/. Tap the audio buttons above to hear it.

reentering polygon: meaning, definition, pronunciation and examples

UK/ˌriːɛnˈtɪərɪŋ ˈpɒlɪɡən/US/ˌriɛnˈtɪrɪŋ ˈpɑːliɡɑːn/

Technical/Academic

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Quick answer

What does “reentering polygon” mean?

In geometry, a polygon that has at least one interior angle greater than 180 degrees, causing the shape to 'dent inwards' rather than being fully convex.

Audio

Pronunciation

Definition

Meaning and Definition

In geometry, a polygon that has at least one interior angle greater than 180 degrees, causing the shape to 'dent inwards' rather than being fully convex.

Any shape or metaphorical construct that folds back into its own interior space; used in geometry, computer graphics, urban planning (e.g., oddly shaped plots), and sometimes metaphorically to describe recursive or self-referential processes.

Dialectal Variation

British vs American Usage

Differences

No significant lexical or spelling differences. 'Re-entering' with a hyphen is slightly more common in British English writing, but 'reentering' is standard in technical contexts.

Connotations

Identically technical in both dialects.

Frequency

Equally low-frequency and specialised in both regions, confined to geometry, computer science, and related fields.

Grammar

How to Use “reentering polygon” in a Sentence

[the/some] reentering polygon [has/contains] [a reentrant angle/an indentation][to identify/calculate] [the area of] a reentering polygon

Vocabulary

Collocations

strong

concave polygonreentrant angleinterior angleconvex hull

medium

complex polygonsimple polygonshape geometrypolygon clipping

weak

calculate areagraphics algorithmspatial analysismathematical definition

Examples

Examples of “reentering polygon” in a Sentence

verb

British English

The algorithm must identify where the polygon boundary re-enters the convex hull.
The path re-enters the shaded area at vertex D.

American English

The software flags any polygon that reenters its own bounding box.
The property line reenters from the western fence.

Usage

Meaning in Context

Business

Rarely used. Possibly in very specialised contexts like real estate for describing oddly shaped land parcels.

Academic

Standard term in geometry, computer graphics, computational geometry, and GIS (Geographic Information Systems) research papers and textbooks.

Everyday

Virtually never used in everyday conversation.

Technical

Precise term in CAD software, game engine development, geographic mapping, and algorithm design for spatial data.

Vocabulary

Synonyms of “reentering polygon”

Strong

concave polygon

Neutral

concave polygonnon-convex polygon

Weak

complex polygonself-intersecting polygon (Note: not exactly the same)

Vocabulary

Antonyms of “reentering polygon”

convex polygonregular polygon (if also convex)

Watch out

Common Mistakes When Using “reentering polygon”

Confusing it with a 'self-intersecting polygon' (like a pentagram), which is different.
Using 'reentering' to describe any complex shape, rather than specifically one with an interior angle > 180°.
Misspelling as 're-entering polygon' (acceptable but less common in technical docs).

FAQ

Frequently Asked Questions

: Yes, they are synonyms. 'Concave polygon' is the more common term in many contexts.
: No. The sum of interior angles in a triangle is 180°, so no single angle can exceed 180°. Only polygons with four or more sides can be reentering.
: The term visualises the polygon's boundary: at a reentrant angle, the boundary line appears to turn and go back into the interior space of the shape, 're-entering' it.
: Most commonly in computer graphics (3D modelling, game engines), geographic information systems (GIS), computational geometry research, CAD software, and urban/land surveying.
: In geometry, a polygon that has at least one interior angle greater than 180 degrees, causing the shape to 'dent inwards' rather than being fully convex.
: Reentering polygon is usually technical/academic in register.
: Reentering polygon: in British English it is pronounced /ˌriːɛnˈtɪərɪŋ ˈpɒlɪɡən/, and in American English it is pronounced /ˌriɛnˈtɪrɪŋ ˈpɑːliɡɑːn/. Tap the audio buttons above to hear it.

Phrases

Idioms & Phrases

“None”

Learning

Memory Aids

Mnemonic

Imagine a star-shaped cookie cutter. If you trace your finger around its edge, your finger has to go back INTO the space of the star to get to the next point. That 'going back in' is 're-entering'.

Conceptual Metaphor

A SITUATION IS A SHAPE: 'Our negotiation has become a reentering polygon, looping back on issues we thought were settled.'

Practice

Quiz

Fill in the gap

A polygon must have at least one interior angle measuring more than 180 degrees.

Multiple Choice

What is the defining characteristic of a reentering polygon?