# Plane vs. Polygon — What's the Difference?

By Fiza Rafique & Urooj Arif — Updated on May 4, 2024

**Plane is an infinite flat surface with no boundaries, while a polygon is a closed figure formed by straight lines.**

## Difference Between Plane and Polygon

### Table of Contents

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## Key Differences

A plane in geometry is a flat, two-dimensional surface that extends infinitely in all directions, used as a concept in higher mathematics and physics. Whereas, a polygon is a two-dimensional shape made up of a finite number of straight line segments that connect to form a closed circuit.

Planes are theoretical constructs with no edges or vertices, making them fundamental in fields like vector calculus and engineering. On the other hand, polygons are concrete shapes defined by their vertices and sides, commonly studied in basic geometry.

The properties of a plane include being infinitely large and perfectly flat, which makes it ideal for theoretical explorations in spatial analysis. Meanwhile, polygons are described by the number of their sides, such as triangles, quadrilaterals, and pentagons, and have practical applications in computer graphics and architecture.

While a plane itself is not bound by dimensions, it can contain infinite polygons of any size and shape within its expanse. Polygons, however, are confined by their perimeters and are limited to the space they occupy.

Planes serve as a foundation for plotting coordinates and geometric figures in mathematics and physics. In contrast, polygons are used to approximate shapes and forms in more tangible applications like tiling and art.

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## Comparison Chart

### Type

Infinite flat surface

Closed figure formed by straight lines

### Boundaries

None, extends infinitely

Finite, enclosed space

### Dimensions

Two-dimensional

Two-dimensional

### Edges

No edges

Edges formed by straight lines

### Vertices

No vertices

Defined number of vertices

## Compare with Definitions

#### Plane

A flat surface with no thickness or curvature.

Mirrors are assumed to be perfect planes in physics.

#### Polygon

A flat shape with straight sides that are fully closed.

A pentagon is a type of polygon with five sides.

#### Plane

An undefined surface extending infinitely in two dimensions.

The Cartesian plane is used for plotting algebraic equations.

#### Polygon

A multi-sided figure used in mathematical contexts.

Polygons can be regular or irregular based on side lengths.

#### Plane

A tool for smoothing or shaping wood.

The carpenter used a plane to finish the door.

#### Polygon

An area defined for administrative purposes.

The city planned development in a newly marked polygon.

#### Plane

An airplane.

The plane took off at dawn.

#### Polygon

A fundamental element in computer graphics for modeling.

3D models are often made up of numerous small polygons.

#### Plane

A level of existence or thought.

Some theories discuss existence on different planes.

#### Polygon

A shape used in art and design for pattern making.

Mosaic tiles often utilize hexagonal polygons.

#### Plane

(Mathematics) A surface containing all the straight lines that connect any two points on it.

#### Polygon

In geometry, a polygon () is a plane figure that is described by a finite number of straight line segments connected to form a closed polygonal chain (or polygonal circuit). The bounded plane region, the bounding circuit, or the two together, may be called a polygon.

#### Plane

A flat or level surface.

#### Polygon

A plane figure with at least three straight sides and angles, and typically five or more.

#### Plane

A level of development, existence, or achievement

Scholarship on a high plane.

#### Polygon

A closed plane figure bounded by three or more line segments.

#### Plane

An airplane or hydroplane.

#### Polygon

(geometry) A plane figure bounded by edges that are all straight lines.

#### Plane

A supporting surface of an airplane; an airfoil or wing.

#### Polygon

(geometry) The boundary of such a figure.

#### Plane

A carpenter's tool with an adjustable blade for smoothing and leveling wood.

#### Polygon

A figure comprising vertices and (not necessarily straight) edges, alternatingly.

#### Plane

A trowel-shaped tool for smoothing the surface of clay, sand, or plaster in a mold.

#### Polygon

(geometry) Such a figure and its interior, taken as a whole.

#### Plane

The plane tree.

#### Polygon

A plane figure having many angles, and consequently many sides; esp., one whose perimeter consists of more than four sides; any figure having many angles.

#### Plane

(Mathematics) Of or being a figure lying in a plane

A plane curve.

#### Polygon

A closed plane figure bounded by straight sides

#### Plane

Flat; level.

#### Plane

To smooth or finish with a plane

Planed the door.

#### Plane

To remove with a plane

Plane off the rough edges on a board.

#### Plane

To work with a plane.

#### Plane

To rise partly out of the water, as a hydroplane does at high speeds.

#### Plane

To soar or glide.

#### Plane

To travel by airplane.

#### Plane

Of a surface: flat or level.

#### Plane

A level or flat surface.

#### Plane

(geometry) A flat surface extending infinitely in all directions (e.g. horizontal or vertical plane). Category:en:Surfaces

#### Plane

(anatomy) An imaginary plane which divides the body into two portions.

#### Plane

A level of existence or development.

Astral plane

#### Plane

A roughly flat, thin, often moveable structure used to create lateral force by the flow of air or water over its surface, found on aircraft, submarines, etc. (Compare airfoil, hydrofoil.)}}

#### Plane

Any of 17 designated ranges of 2

^{16}(65,536) sequential code points each.#### Plane

A tool for smoothing wood by removing thin layers from the surface.

#### Plane

An airplane; an aeroplane.

#### Plane

(entomology) Any of various nymphalid butterflies, of various genera, having a slow gliding flight.

#### Plane

(entomology) The butterfly Bindahara phocides, family Lycaenidae, of Asia and Australasia.

#### Plane

(countable) A deciduous tree of the genus Platanus.

#### Plane

(Northern UK) A sycamore.

#### Plane

To smooth (wood) with a plane.

#### Plane

To move in a way that lifts the bow out of the water.

#### Plane

To glide or soar.

#### Plane

Any tree of the genus Platanus.

#### Plane

A surface, real or imaginary, in which, if any two points are taken, the straight line which joins them lies wholly in that surface; or a surface, any section of which by a like surface is a straight line; a surface without curvature.

#### Plane

An ideal surface, conceived as coinciding with, or containing, some designated astronomical line, circle, or other curve; as, the plane of an orbit; the plane of the ecliptic, or of the equator.

#### Plane

A block or plate having a perfectly flat surface, used as a standard of flatness; a surface plate.

#### Plane

A tool for smoothing boards or other surfaces of wood, for forming moldings, etc. It consists of a smooth-soled stock, usually of wood, from the under side or face of which projects slightly the steel cutting edge of a chisel, called the iron, which inclines backward, with an apperture in front for the escape of shavings; as, the jack plane; the smoothing plane; the molding plane, etc.

#### Plane

Without elevations or depressions; even; level; flat; lying in, or constituting, a plane; as, a plane surface.

#### Plane

To make smooth; to level; to pare off the inequalities of the surface of, as of a board or other piece of wood, by the use of a plane; as, to plane a plank.

#### Plane

To efface or remove.

He planed away the names . . . written on his tables.

#### Plane

Figuratively, to make plain or smooth.

What student came but that you planed her path.

#### Plane

Of a boat, to lift more or less out of the water while in motion, after the manner of a hydroplane; to hydroplane.

#### Plane

An aircraft that has a fixed wing and is powered by propellers or jets;

The flight was delayed due to trouble with the airplane

#### Plane

(mathematics) an unbounded two-dimensional shape;

We will refer to the plane of the graph as the X-Y plane

Any line joining two points on a plane lies wholly on that plane

#### Plane

A level of existence or development;

He lived on a worldly plane

#### Plane

A power tool for smoothing or shaping wood

#### Plane

A carpenter's hand tool with an adjustable blade for smoothing or shaping wood;

The cabinetmaker used a plane for the finish work

#### Plane

Cut or remove with or as if with a plane;

The machine shaved off fine layers from the piece of wood

#### Plane

Travel on the surface of water

#### Plane

Make even or smooth, with or as with a carpenter's plane;

Plane the top of the door

#### Plane

Having a horizontal surface in which no part is higher or lower than another;

A flat desk

Acres of level farmland

A plane surface

## Common Curiosities

#### Can a polygon exist within a plane?

Yes, polygons of any shape and size can exist within the infinite expanse of a plane.

#### What is the role of vertices in polygons?

Vertices are the points where the sides of a polygon meet and are crucial for defining the shape of the polygon.

#### What is a plane in geometry?

A plane is a flat, two-dimensional surface that extends infinitely in all directions.

#### What is the difference between a plane and a polygon in terms of boundaries?

A plane has no boundaries and extends infinitely, whereas a polygon has a closed boundary formed by straight lines.

#### Are all polygons planar figures?

Yes, all polygons are planar figures as they lie on a single flat plane.

#### Can a plane have any physical existence?

No, a plane is an idealized concept used in mathematics and does not have a physical form.

#### How is a polygon defined?

A polygon is defined as a two-dimensional geometric figure with a finite number of straight sides that enclose a space.

#### Are there different types of polygons?

Yes, there are many types of polygons, ranging from triangles to polygons with many sides, categorized as regular (equal sides and angles) or irregular.

#### Why are planes important in mathematics?

Planes are important for theoretical studies and for plotting geometric figures and coordinates.

#### How do the dimensions of a plane and a polygon compare?

Both a plane and a polygon are two-dimensional, but a plane is unbounded while a polygon is bounded.

#### How do planes and polygons differ in their applications?

Planes are mainly theoretical and used in higher mathematics and physics, while polygons have practical applications in various fields like architecture and computer graphics.

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Written by

Fiza RafiqueFiza Rafique is a skilled content writer at AskDifference.com, where she meticulously refines and enhances written pieces. Drawing from her vast editorial expertise, Fiza ensures clarity, accuracy, and precision in every article. Passionate about language, she continually seeks to elevate the quality of content for readers worldwide.

Co-written by

Urooj ArifUrooj is a skilled content writer at Ask Difference, known for her exceptional ability to simplify complex topics into engaging and informative content. With a passion for research and a flair for clear, concise writing, she consistently delivers articles that resonate with our diverse audience.