To find more about these shapes click the hyperlinks above.

Polygons are 2-dimensional shapes. They are made of straight lines, and the shape is "closed" (all the lines connect up).

Polygon
(straight sides)

Not a Polygon
(has a curve)

Not a Polygon
(open, not closed)

Types of Polygons

Simple or Complex

A simple polygon has only one boundary, and it doesn't cross over itself. A complex polygon intersects itself!

Simple Polygon
(this one's a Pentagon)

Complex Polygon
(also a Pentagon)

Concave or Convex

A convex polygon has no angles pointing inwards. More precisely, no internal angles can be more than 180°.
If there are any internal angles greater than 180° then it is concave. (Think: concave has a "cave" in it)

Convex

Concave

Regular or Irregular

If all angles are equal and all sides are equal, then it is regular, otherwise it is irregular

## pictures of polyhedraMATHS-WIKI and MATH-WIKI

Maths-wiki and Math-wiki is a collaborative wiki space created and maintained by mathematics students from UK and US.

This, and the pages that follow from this one, are made by the teams from two mathematics and science specialist schools. The schools are Simon Langton Grammar School for Boys in Canterbury, UK (The Langton Institute for Young Mathematicians) and Illinois Mathematics and Science Academy, US (IMSA).

Polyhedrais a geometrical shape. It has flat faces, and straight edges.

Dodecahedron

(Regular polyhedron)

Small stellated dodecahedron

(Regular star)

Icosidodecahedron

(Uniform)

Great cubicuboctahedron

(Uniform star)

Rhombic triacontahedron

(Uniform dual)

Elongated pentagonal cupola

(Convex regular-faced)

Octagonal prism

(Uniform prism)

Square antiprism

(Uniform antiprism)

Some polyhedronsdodecahedron

(Regular polyhedron) ||

(Regular star) ||

Icosidodecahedron

(Uniform)

Great cubicuboctahedron

(Uniform star)

Rhombic triacontahedron

(Uniform dual)

Elongated pentagonal cupola

(Convex regular-faced)

Octagonal prism

(Uniform prism)

Polygons are 2-dimensional shapes. They are made of straight lines, and the shape is "closed" (all the lines connect up).

Polygon(straight sides)

Nota Polygon(has a curve)

Nota Polygon(open, not closed)

## Types of Polygons

## Simple or Complex

Asimplepolygon has only one boundary, and it doesn't cross over itself. Acomplexpolygon intersects itself!(this one's a Pentagon)

(also a Pentagon)

## Concave or Convex

Aconvexpolygon has no angles pointing inwards. More precisely, no internal angles can be more than 180°.If there are any internal angles greater than 180° then it is

concave. (Think: concave has a "cave" in it)## Regular or Irregular

If all angles are equal and all sides are equal, then it isregular, otherwise it isirregular## More Examples

Complex Pentagon(a "star polygon")

Concave OctagonIrregular Hexagon## Names of Polygons

(or Trigon)3(or Tetragon)456(or Septagon)78(or Enneagon)910(or Undecagon)11121314151617181920304050607080901001,00010,0001,000,00010 to the powerof100

nn-2) × 180°/n