###### Descriptions and Examples for the POV-Ray Raytracerby Friedrich A. Lohmüller Elementary Geometry for Raytracing
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- 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 ## 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 