Concave Polygons vs. Convex Polygons: What's the Difference?

Edited by Sumera Saeed || By Sawaira Riaz || Published on January 27, 2024
Concave polygons have at least one interior angle greater than 180° and inward indentations; convex polygons have all interior angles less than 180°, forming a bulged shape.

Key Differences

Concave polygons exhibit at least one interior angle exceeding 180 degrees, resulting in an inward curve. In contrast, convex polygons feature interior angles that are all less than 180 degrees, creating a consistently outward-facing edge without any indentations.
Sawaira Riaz
Jan 27, 2024
Concave polygons can appear to have a 'caved-in' section due to their inward-facing vertices. Convex polygons, on the other hand, bulge outward, forming a shape where any line segment between two points on the polygon lies entirely inside it.
Sawaira Riaz
Jan 27, 2024
In concave polygons, one or more interior angles are greater than 180 degrees, and they can have vertices pointing inward. Conversely, convex polygons have all interior angles less than 180 degrees and lack inward-pointing vertices.
Sumera Saeed
Jan 27, 2024
Concave polygons are often found in irregular shapes like star polygons, while convex polygons are more common in regular shapes like squares and triangles. This distinction is important in fields like architecture and computer graphics.
Aimie Carlson
Jan 27, 2024
The mathematical characterization of concave polygons involves the presence of non-adjacent vertices, from which a line can be drawn that passes outside the polygon. For convex polygons, any such line will always remain inside the figure.
Sawaira Riaz
Jan 27, 2024

Comparison Chart

Interior Angles

At least one angle > 180°
All angles < 180°
Sawaira Riaz
Jan 27, 2024

Edge Direction

Can have inward indentations
Edges bulge outward
Sumera Saeed
Jan 27, 2024

Line Segment Rule

A line between points may lie outside the shape
All lines between points stay inside
Sawaira Riaz
Jan 27, 2024

Vertex Orientation

Can have vertices pointing inward
No vertices pointing inward
Janet White
Jan 27, 2024

Practical Examples

Star-shaped polygons
Regular shapes like squares and triangles
Sawaira Riaz
Jan 27, 2024

Concave Polygons and Convex Polygons Definitions

Concave Polygons

A polygon not containing the line segment between any two points within it.
A polygon where some internal lines intersect its edges is concave.
Sawaira Riaz
Dec 19, 2023

Convex Polygons

A polygon where the line segment between any two points does not extend outside the shape.
A triangle, with no line extending outside, exemplifies a convex polygon.
Sawaira Riaz
Dec 19, 2023

Concave Polygons

A polygon where a line segment between two points on the polygon can pass outside it.
In a concave polygon, drawing a line between certain points may cross outside the shape.
Sawaira Riaz
Dec 19, 2023

Convex Polygons

A polygon where any line segment between two points lies entirely inside it.
In a convex polygon like a rectangle, all internal lines remain inside.
Sumera Saeed
Dec 19, 2023

Concave Polygons

A polygon that appears to have a 'caved-in' section.
A polygon resembling a crescent moon is concave.
Sawaira Riaz
Dec 19, 2023

Convex Polygons

A polygon with edges that bulge outward.
A circle approximated by a polygon is convex.
Sawaira Riaz
Dec 19, 2023

Concave Polygons

A polygon with one or more inward-pointing vertices.
A polygon with an inward dent forms a concave shape.
Aimie Carlson
Dec 19, 2023

Convex Polygons

A polygon with no vertices pointing inward.
A square, with all outward-facing corners, is a convex polygon.
Sawaira Riaz
Dec 19, 2023

Concave Polygons

A polygon with at least one interior angle greater than 180°.
A star-shaped polygon is a typical concave polygon.
Sawaira Riaz
Dec 19, 2023

Convex Polygons

A polygon with all interior angles less than 180°.
A regular hexagon is a perfect example of a convex polygon.
Sawaira Riaz
Dec 19, 2023

FAQs

Are the edges of convex polygons always outward-facing?

Yes, convex polygons have outward-facing edges without any indentations.
Janet White
Jan 27, 2024

Can a concave polygon have a 'caved-in' appearance?

Yes, concave polygons often have a 'caved-in' appearance due to inward-pointing vertices.
Sawaira Riaz
Jan 27, 2024

What defines a concave polygon?

A concave polygon has at least one interior angle greater than 180° and inward indentations.
Sawaira Riaz
Jan 27, 2024

What happens to a line drawn between two points in a concave polygon?

In a concave polygon, such a line can sometimes pass outside the polygon.
Harlon Moss
Jan 27, 2024

Can a line segment inside a concave polygon lie outside the polygon?

Yes, in concave polygons, some line segments can extend outside the polygon.
Sawaira Riaz
Jan 27, 2024

What is a convex polygon?

A convex polygon has all interior angles less than 180°, with no indentations.
Sumera Saeed
Jan 27, 2024

Is a square a concave or convex polygon?

A square is a convex polygon as all its interior angles are less than 180°.
Janet White
Jan 27, 2024

Can concave polygons form regular shapes?

Generally, concave polygons do not form regular shapes due to their indentations.
Aimie Carlson
Jan 27, 2024

What is an example of a concave polygon?

A star-shaped polygon is an example of a concave polygon.
Harlon Moss
Jan 27, 2024

Can convex polygons have any inward-pointing vertices?

No, convex polygons do not have any inward-pointing vertices.
Janet White
Jan 27, 2024

Are triangles considered convex polygons?

Yes, triangles are convex polygons as all their interior angles are less than 180°.
Janet White
Jan 27, 2024

Is it possible for a convex polygon to have an inward dent?

No, convex polygons cannot have inward dents.
Janet White
Jan 27, 2024

Is a rectangle an example of a convex polygon?

Yes, a rectangle is a convex polygon as it adheres to the angle criteria.
Harlon Moss
Jan 27, 2024

Do concave polygons have more complex mathematical properties than convex ones?

Yes, concave polygons often have more complex mathematical properties due to their inward indentations.
Sawaira Riaz
Jan 27, 2024

Are all regular polygons convex?

Yes, all regular polygons, like squares and equilateral triangles, are convex.
Sawaira Riaz
Jan 27, 2024

Do convex polygons have any interior angles greater than 180°?

No, convex polygons have all interior angles less than 180°.
Harlon Moss
Jan 27, 2024

Are concave polygons common in architecture?

Concave polygons are less common in architecture due to their complex shapes.
Harlon Moss
Jan 27, 2024

What is a distinguishing feature of concave polygons?

A distinguishing feature of concave polygons is their inward-pointing vertices or edges.
Sawaira Riaz
Jan 27, 2024

Can convex polygons be irregular in shape?

Convex polygons can be irregular, but all their angles must still be less than 180°.
Harlon Moss
Jan 27, 2024

Are star-shaped polygons typically concave or convex?

Star-shaped polygons are typically concave due to their inward angles.
Harlon Moss
Jan 27, 2024
Written by
Sawaira Riaz
Sawaira is a dedicated content editor at difference.wiki, where she meticulously refines articles to ensure clarity and accuracy. With a keen eye for detail, she upholds the site's commitment to delivering insightful and precise content.
Edited by
Sumera Saeed
Sumera is an experienced content writer and editor with a niche in comparative analysis. At Diffeence Wiki, she crafts clear and unbiased comparisons to guide readers in making informed decisions. With a dedication to thorough research and quality, Sumera's work stands out in the digital realm. Off the clock, she enjoys reading and exploring diverse cultures.