###### 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 DodecahedronSome 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 dodecahedron Length of an edge of the dodecahedron: a. The radius of circumsphere: R = a / 4 * sqrt( 3 ) * ( 1 + sqrt(5) ) ; The radius of edgesphere (tangent to edges): Re = a / 4 * ( 3 + sqrt(5) ) ; The radius of the insphere: Ri = a / 2 * sqrt( ( 25 + 10*sqrt(5))/10 ); The angle between two faces: ~116.57° Face_Angle = degrees( acos(-1/5*sqrt(5)) ); The angle between two edges: ~ ~121.72° Face_Edge_Angle = degrees( acos( -sqrt( (5-sqrt(5))/10 ) ) );
Flolding of a regular dodecahedron
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 © Friedrich A. Lohmüller, 2011 http://www.f-lohmueller.de