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

                                               

Cube and
Cuboid

Some 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 of a cube
Length of an edge of the cube: a.
The length of the diagonals of the faces:
    d = sqrt (2) * a ;
The length of the diagonals through a cube:
    d = sqrt (3) * a ;
The radius of circumsphere:
    R = 1/2*sqrt( 3 ) * a ;
Dimensions of a cuboid
Length of the edges of the cubid: a, b, c.
The length of a diagonal through a cuboid:
d = sqrt ( a2 + b2 + c2 )


Folding of a cube
Diagonals in a cuboid (rectangular parallelepiped)


Folding of a cube

How to make this: The Folding of a Cube Net - 3D Animation with POV-Ray.
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© Friedrich A. Lohmüller, 2010
http://www.f-lohmueller.de