- POV-Ray Tutorial
- Geometrical Basics
Law of cosines
Cube & Cuboid
- Geometric 3D Animations
In the following we write for the square root of a number
Some useful geometrical facts.
Folding of a Rhombicuboctahedron
the expression "sqrt(ZAHL)"
conforming to the syntax used in POV-Ray.
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)));