Dodecahedron Command

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Dodecahedron( <Point>, <Point>, <Direction> )
Creates a dodecahedron having the segment between two points as an edge.
The other vertices are univocally determined by the given direction, that needs to be:
  • a vector, a segment, a line, a ray orthogonal to the segment, or
  • a polygon, a plane parallel to the segment.
The created dodecahedron will have:
  • a face with the segment as an edge in a plane orthogonal to the given vector/segment/line/ray, or
  • a face with the segment as an edge in a plane parallel to the polygon/plane.
Dodecahedron( <Point>, <Point>, <Point>)
Creates a dodecahedron with three (adjacent) points of the first face. The points have to start a regular pentagon for the dodecahedron to be defined.
Dodecahedron( <Point>, <Point>)
Creates a dodecahedron with two (adjacent) points of the first face, and the third point automatically created on a circle, so that the dodecahedron can rotate around its first edge.
Note: Dodecahedron(A, B) is a shortcut for Dodecahedron(A, B, C) with C = Point(Circle(((1 - sqrt(5)) A + (3 + sqrt(5)) B) / 4, Distance(A, B) sqrt(10 + 2sqrt(5)) / 4, Segment(A, B))).
Note: See also Cube, Tetrahedron, Icosahedron, Octahedron commands.
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