Descriptions and Examples for the POV-Ray Raytracer by Friedrich A. Lohmüller
Elementary Geometry for Raytracing
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    Right-angled Triangle
    Pythagorean Theorem
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    Law of cosines
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    Regular Polygon
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      Octahedron
      Cube & Cuboid
      Dodecahedron
      Icosahedron
      Cuboctahedron
      Truncated Octahedron
      Rhombicuboctahedron
      Truncated Icosahedron
    Circles
      Tangent circles
      Internal Tangents
      External Tangents
     
     
     
     
     
     
     
     
     
   - Geometric 3D Animations

                                             

Truncated Icosahedron
Buckminsterfullerene
buckyball, C60.
Some useful geometrical facts.
Truncated Icosahedron
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.
Radius of circumsphere (vertices):
Rc = a / 4 * sqrt( 58 + 18*sqrt(5));

Radius of edgesphere (tangent to edges):
Re = 3/4 * a * ( 1 + sqrt(5) );

Angle between hexagon and hexagon: ~138,2°
HH_Angle =
degrees(acos(-1/3*sqrt(5)));

Angle between hexagon and pentagon: ~142,6°
HP_Angle =
degrees(acos(-sqrt((5+2*sqrt(5))/15)));
Truncated Icosahedron net
Truncated Icosahedron
Folding of a Truncated Icosahedron
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© Friedrich A. Lohmüller, 2013
www.f-lohmueller.de