Dodecahedron Class Documentation
Overview
References
Class Documentation
Bases: Polyhedron
Dodecahedron Class
calc_angle_dihedral()
staticmethod
Face-edge-face angle, i.e., "dihedral angle" (approx. 116.565)
calc_angle_solid_vertex()
staticmethod
Solid angle at a vertex subtended by a face (approx. 2.96174 steradians)
calc_angle_subtended(a)
staticmethod
Vertex-Center-Vertex angle calc_face_angle_face_edge_face The angle between lines from the dodecahedron center to any two vertices. It is also the angle between Plateau borders at a vertex. In chemistry it is called the tetrahedral bond angle. This angle (in radians) is also the length of the circular arc on the unit sphere resulting from centrally projecting one edge of the dodecahedron to the sphere.
(approx. 41.810)
calc_area(a)
staticmethod
Formula to calculate area of Dodecahedron
~ 20.645728807 * a * a
calc_radius_circumsphere(a)
staticmethod
Radius of circumsphere the radius of a circumscribed sphere (one that touches the Dodecahedron at all vertices)
~ 1.401258538 * a
calc_radius_insphere(a)
staticmethod
Radius of insphere that is tangent to faces The radius of an inscribed sphere (tangent to each of the Dodecahedron's faces) is
~ 1.113516364 * a
calc_radius_midsphere(a)
staticmethod
Radius of midsphere that is tangent to edges
while the midradius, which touches the middle of each edge, is
~ 1.309016994 * a
calc_volume(a)
staticmethod
Formula to calculate volume of Dodecahedron
vertices()
staticmethod
Vertices Static Method
The following Cartesian coordinates define the 20 vertices of a regular dodecahedron centered at the origin and suitably scaled and oriented:
Vertex coordinates:
Position 1 ( ±1, ±1, ±1) ( 0, ±1/ϕ, ±ϕ) (±1/ϕ, ±ϕ, 0) ( ±ϕ, 0, ±1/ϕ)
or:
Position 2 ( ±1, ±1, ±1) ( 0, ±ϕ, ±1/ϕ) ( ±ϕ, ±1/ϕ, 0) (±1/ϕ, 0, ±ϕ)