Dodecahedron Command

Dodecahedron( <Regular pentagon> )

Creates a dodecahedron having the given regular pentagon as base.

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.

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))).

See also Cube, Tetrahedron, Icosahedron, Octahedron commands.