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

## Regular OctahedronSome 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 www.f-lohmueller.de