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Regular Icosahedron
Some useful geometrical facts |
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In the following we write for the square root of a number the expression "sqrt(ZAHL)"
conforming to the syntax used in POV-Ray.
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Dimensions of a regular icosahedron
Length of an edge of the icosahedron: a. |
The radius of circumsphere:
R = a / 4 * sqrt( 10 + 2*sqrt(5) );
The radius of edgesphere (tangent to edges):
Re = a / 4 *( 1 + sqrt(5) );
The radius of the insphere:
Ri = a / 12 * sqrt(3)* ( 3 + sqrt(5) );
The angle between two faces: ~138.19°
Face_Angle =
degrees(acos(-1/3*sqrt(5)));
The angle between two edges: 108°
Face_Edge_Angle =
degrees(acos(1/4*(1 - sqrt(5))));
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Flolding of a regular icosahedron
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Inside the regular icosahedron
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Inside the regular icosahedron
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