Descriptions and Examples for the POV-Ray Raytracer by Friedrich A. Lohmüller
Elementary Geometry for Raytracing
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Home
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  - 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 Octahedron
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
Length of octahedron edge: a.
The radius of circumsphere:
R = a / 2 * sqrt( 2 );

The radius of edgesphere (tangent to edges):
Re = a / 2;

The radius of the insphere:
Ri= a / 6 * sqrt( 6 );

The angle between two faces: ~ 109,471°
Face_Angle = degrees(acos(-1/3));

The angle between two edges:
Edge_Angle = 90°


Inside of a regular octahedron:
3 squares.


Folding of a regular octahedron
top

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