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).

Polyhedra
is 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 polyhedrons

dodecahedronexternal image 120px-Dodecahedron.svg.png
(Regular polyhedron) || external image 120px-Small_stellated_dodecahedron.png
(Regular star) ||
external image 120px-Icosidodeca%C3%ABder.png
Icosidodecahedron
(Uniform)
external image 120px-Great_cubicuboctahedron.png
Great cubicuboctahedron
(Uniform star)
external image 120px-Rhombictriacontahedron.jpg
Rhombic triacontahedron
(Uniform dual)
external image 120px-Elongated_pentagonal_cupola.png
Elongated pentagonal cupola
(Convex regular-faced)
external image 120px-Octagonal_prism.png
Octagonal prism
(Uniform prism)
external image 120px-Square_antiprism.png
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).
external image pentagon-irregular.gif
external image pentagon-not.gif
external image pentagon-not2.gif
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!
external image pentagon-irregular.gif
external image pentagon-complex.gif
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)
external image pentagon-irregular.gif
external image pentagon-concave.gif
Convex
Concave

Regular or Irregular

If all angles are equal and all sides are equal, then it is regular, otherwise it is irregular
external image pentagon-regular.gif
external image pentagon-irregular.gif
Regular
Irregular

More Examples

external image star-polygon.gif
external image concave-octagon.gif
external image hexagon-irregular.gif
Complex Pentagon
(a "star polygon")
Concave Octagon
Irregular Hexagon

Names of Polygons



If it is a Regular Polygon..
Name
Sides
Shape
Interior Angle
Triangle (or Trigon)
3
external image regular-triangle-sm.gif
60°
Quadrilateral (or Tetragon)
4
external image regular-quadrilateral-sm.gif
90°
Pentagon
5
external image regular-pentagon-sm.gif
108°
Hexagon
6
external image regular-hexagon-sm.gif
120°
Heptagon (or Septagon)
7
external image regular-heptagon-sm.gif
128.571°
Octagon
8
external image regular-octagon-sm.gif
135°
Nonagon (or Enneagon)
9
external image regular-nonagon-sm.gif
140°
Decagon
10
external image regular-decagon-sm.gif
144°
Hendecagon (or Undecagon)
11
external image regular-hendecagon-sm.gif
147.273°
Dodecagon
12
external image regular-dodecagon-sm.gif
150°
Triskaidecagon
13

152.308°
Tetrakaidecagon
14

154.286°
Pentadecagon
15

156°
Hexakaidecagon
16

157.5°
Heptadecagon
17

158.824°
Octakaidecagon
18

160°
Enneadecagon
19

161.053°
Icosagon
20

162°
Triacontagon
30

168°
Tetracontagon
40

171°
Pentacontagon
50

172.8°
Hexacontagon
60

174°
Heptacontagon
70

174.857°
Octacontagon
80

175.5°
Enneacontagon
90

176°
Hectagon
100

176.4°
Chiliagon
1,000

179.64°
Myriagon
10,000

179.964°
Megagon
1,000,000

~180°
Googolgon
10 to the power
of100


~180°
n-gon
n
external image regular-n-gon-sm.gif
(n-2) × 180° / n