Dimensions of a regular dodecahedron
Length of an edge of the dodecahedron: a. |
The radius of circumsphere:
R = a / 4 * sqrt( 3 ) * ( 1 + sqrt(5) ) ;
The radius of edgesphere (tangent to edges):
Re = a / 4 * ( 3 + sqrt(5) ) ;
The radius of the insphere:
Ri = a / 2 * sqrt( ( 25 + 10*sqrt(5))/10 );
The angle between two faces: ~116.57°
Face_Angle =
degrees( acos(-1/5*sqrt(5)) );
The angle between two edges: ~ ~121.72°
Face_Edge_Angle =
degrees( acos( -sqrt( (5-sqrt(5))/10 ) ) );
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Flolding of a regular dodecahedron
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