###### Descriptions and Examples for the POV-Ray Raytracerby Friedrich A. Lohmüller Elementary Geometry for Raytracing
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Home
- POV-Ray Tutorial

- Geometrical Basics
for Raytracing

Right-angled Triangle
Pythagorean Theorem
Trigonometry Basics
Law of cosines
Equilateral Triangle
Regular Polygon
Polyhedron
Tetrahedron
Octahedron
Cube & Cuboid
Dodecahedron
Icosahedron
Cuboctahedron
Truncated Octahedron
Rhombicuboctahedron
Truncated Icosahedron
Circles
Tangent circles
Internal Tangents
External Tangents

- Geometric 3D Animations

## Regular IcosahedronSome useful geometrical facts

In the following we write for the square root of a number the expression "sqrt(ZAHL)"
conforming to the syntax used in POV-Ray.

 Dimensions of a regular icosahedron Length of an edge of the icosahedron: a. The radius of circumsphere: R = a / 4 * sqrt( 10 + 2*sqrt(5) ); The radius of edgesphere (tangent to edges): Re = a / 4 *( 1 + sqrt(5) ); The radius of the insphere: Ri = a / 12 * sqrt(3)* ( 3 + sqrt(5) ); The angle between two faces: ~138.19° Face_Angle = degrees(acos(-1/3*sqrt(5))); The angle between two edges: 108° Face_Edge_Angle = degrees(acos(1/4*(1 - sqrt(5))));

Flolding of a regular icosahedron
Inside the regular icosahedron
Inside the regular icosahedron
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 © Friedrich A. Lohmüller, 2009 www.f-lohmueller.de