Descriptions and Examples for the POV-Ray Raytracer by Friedrich A. Lohmüller
Elementary Geometry for Raytracing
Italiano Italiano
Français français
Deutsch Deutsch

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 Dodecahedron Some 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
top

© Friedrich A. Lohmüller, 2011
http://www.f-lohmueller.de