home

[|pictures of polyhedra]MATHS-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)].

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]) ||
 * Polyhedra**
 * 
 * 
 * 
 * 
 * __Some polyhedrons__**

[|dodecahedron] ([|Regular polyhedron]) || ([|Regular star]) || [|Icosidodecahedron] ([|Uniform]) || [|Great cubicuboctahedron] ([|Uniform star]) || [|Rhombic triacontahedron] ([|Uniform dual]) || [|Elongated pentagonal cupola] ([|Convex regular-faced]) || [|Octagonal prism] ([|Uniform prism]) || || To find more about these shapes click the hyperlinks above.
 * [[image:http://upload.wikimedia.org/wikipedia/commons/thumb/1/18/Icosidodeca%C3%ABder.png/120px-Icosidodeca%C3%ABder.png width="120" height="119" link="http://simple.wikipedia.org/wiki/File:Icosidodeca%C3%ABder.png"]]
 * [[image:http://upload.wikimedia.org/wikipedia/commons/thumb/6/6b/Rhombictriacontahedron.jpg/120px-Rhombictriacontahedron.jpg width="120" height="132" link="http://simple.wikipedia.org/wiki/File:Rhombictriacontahedron.jpg"]]
 * [[image:http://upload.wikimedia.org/wikipedia/commons/thumb/5/59/Octagonal_prism.png/120px-Octagonal_prism.png width="120" height="120" link="http://simple.wikipedia.org/wiki/File:Octagonal_prism.png"]]

Polygons are 2-dimensional shapes. They are made of straight lines, and the shape is "closed" (all the lines connect up). (straight sides) || **Not** a Polygon (has a curve) || **Not** a Polygon (open, not closed) ||
 * [[image:http://www.mathsisfun.com/geometry/images/pentagon-irregular.gif width="110" height="100"]] || [[image:http://www.mathsisfun.com/geometry/images/pentagon-not.gif width="110" height="100"]] || [[image:http://www.mathsisfun.com/geometry/images/pentagon-not2.gif width="110" height="100"]] ||
 * **Polygon**

Simple or Complex
A **simple** polygon has only one boundary, and it doesn't cross over itself. A **complex** polygon intersects itself! (this one's a Pentagon) || Complex Polygon (also a Pentagon) ||
 * [[image:http://www.mathsisfun.com/geometry/images/pentagon-irregular.gif width="110" height="100"]] || [[image:http://www.mathsisfun.com/geometry/images/pentagon-complex.gif width="110" height="100"]] ||
 * Simple Polygon

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//)
 * [[image:http://www.mathsisfun.com/geometry/images/pentagon-irregular.gif width="110" height="100"]] || [[image:http://www.mathsisfun.com/geometry/images/pentagon-concave.gif width="110" height="100"]] ||
 * Convex || Concave ||

Regular or Irregular
If all angles are equal and all sides are equal, then it is **regular**, otherwise it is **irregular**
 * [[image:http://www.mathsisfun.com/geometry/images/pentagon-regular.gif width="110" height="100"]] || [[image:http://www.mathsisfun.com/geometry/images/pentagon-irregular.gif width="110" height="100"]] ||
 * Regular || Irregular ||

More Examples
(a "star polygon") || **Concave Octagon** || **Irregular Hexagon** ||
 * [[image:http://www.mathsisfun.com/geometry/images/star-polygon.gif width="110" height="100"]] || [[image:http://www.mathsisfun.com/geometry/images/concave-octagon.gif width="110" height="100"]] || [[image:http://www.mathsisfun.com/geometry/images/hexagon-irregular.gif width="110" height="100"]] ||
 * **Complex Pentagon**

Names of Polygons
of100** ||  || ~180° ||
 * ||  |||| If it is a Regular Polygon.. ||
 * ~ Name ||~ Sides ||~ Shape ||~ Interior Angle ||
 * Triangle //(or Trigon)// || **3** || [[image:http://www.mathsisfun.com/geometry/images/regular-triangle-sm.gif width="40" height="40"]] || 60° ||
 * Quadrilateral //(or Tetragon)// || **4** || [[image:http://www.mathsisfun.com/geometry/images/regular-quadrilateral-sm.gif width="40" height="40"]] || 90° ||
 * Pentagon || **5** || [[image:http://www.mathsisfun.com/geometry/images/regular-pentagon-sm.gif width="40" height="40"]] || 108° ||
 * Hexagon || **6** || [[image:http://www.mathsisfun.com/geometry/images/regular-hexagon-sm.gif width="40" height="40"]] || 120° ||
 * Heptagon //(or Septagon)// || **7** || [[image:http://www.mathsisfun.com/geometry/images/regular-heptagon-sm.gif width="40" height="40"]] || 128.571° ||
 * Octagon || **8** || [[image:http://www.mathsisfun.com/geometry/images/regular-octagon-sm.gif width="40" height="40"]] || 135° ||
 * Nonagon //(or Enneagon)// || **9** || [[image:http://www.mathsisfun.com/geometry/images/regular-nonagon-sm.gif width="40" height="40"]] || 140° ||
 * Decagon || **10** || [[image:http://www.mathsisfun.com/geometry/images/regular-decagon-sm.gif width="40" height="40"]] || 144° ||
 * Hendecagon //(or Undecagon)// || **11** || [[image:http://www.mathsisfun.com/geometry/images/regular-hendecagon-sm.gif width="40" height="40"]] || 147.273° ||
 * Dodecagon || **12** || [[image:http://www.mathsisfun.com/geometry/images/regular-dodecagon-sm.gif width="40" height="40"]] || 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
 * n-gon || **n** || [[image:http://www.mathsisfun.com/geometry/images/regular-n-gon-sm.gif width="40" height="40"]] || (**n**-2) × 180**°** / **n** ||