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

                                               

Cuboctahedron  
Some useful geometrical facts.

Folding of aCuboctahedron
Folding of a Cuboctahedron
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 an edge: a.
The radius of circumsphere:
R = a ;

The radius of edgesphere (tangent to edges):
Re = a/2 * sqrt(3);

The angle between square and triange: ~ 125,26°
Face_Angle = degrees(acos(-1/sqrt(3)));

The angle between edges: 120°
Edge_Angle = degrees(acos(-1/2))


Inside of a cuboctahedron:
4 regular hexagons.

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