Octahedron Class Documentation
Overview
References
Class Documentation
Bases: Polyhedron
Octahedron Class
Regular unit Octahedron.
calc_angle_dihedral()
staticmethod
Face-edge-face angle, i.e., "dihedral angle" (approx. 109.471)
calc_angle_solid_vertex()
staticmethod
Solid angle at a vertex subtended by a face (approx. 1.35935 steradians)
calc_angle_subtended()
staticmethod
angles beta subtended by an edge from the center for the Platonic solids (Cundy and Rollett 1989, Table II following p. 144). 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. 90.000)
calc_area(a)
staticmethod
Calculate Area Static Method
Formula to calculate the area of a Octahedron.
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
edge_length |
float | int
|
The radius of the Octahedron. |
required |
Returns:
| Name | Type | Description |
|---|---|---|
area |
float
|
The area of the Octahedron. |
calc_radius_circumsphere(a)
staticmethod
Radius of circumsphere If the edge length of a regular octahedron is a, the radius of a circumscribed sphere (one that touches the octahedron at all vertices).
~ 0.707 * 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 octahedron's faces)
~ 0.408 * 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
calc_volume(a)
staticmethod
Calculate Volume Static Method
Formula to calculate the volume of a Octahedron Thus the volume is four times that of a regular tetrahedron with the same edge length, while the surface area is twice (because we have 8 rather than 4 triangles).
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
a |
float | int
|
The edge length of the Octahedron. |
required |
Returns:
| Name | Type | Description |
|---|---|---|
area |
float
|
The area of the Octahedron. |
vertices()
staticmethod
Vertices Static Method
Vertex coordinates: (±1, 0, 0) ( 0, ±1, 0) ( 0, 0, ±1)