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

    Right-angled Triangle
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    Law of cosines
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    Regular Polygon
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      Octahedron
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      Dodecahedron
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      Cuboctahedron
      Truncated Octahedron
      Rhombicuboctahedron
      Truncated Icosahedron
    Circles
      Tangent circles
      Internal Tangents
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   - Geometric 3D Animations

                                             

Rhombicuboctahedron
(small Rhombicuboctahedron)
Some useful geometrical facts.

Folding of a Rhombicuboctahedron
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 / 2 * sqrt( 5 + 2*sqrt(2));

The radius of edgesphere (tangent to edges):
Re = a / 2 * sqrt( 4 + 2*sqrt(2) );

Coordinates of the corners:
all permutations of ( +/-1, +/-1, +/-(1+sqrt(2)) );

The angle between square and square: 135°
SS_Angle = degrees(acos(-1/sqrt(2)));

The angle between square and triangle: ~144,74°
ST_Angle = degrees(acos(-sqrt(2/3)));

The angle between edges: 135°
Edge_Angle = degrees(acos(-1/sqrt(2)));

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