Oct
Octahedron
In geometry, an octahedron (plural: octahedra) is a polyhedron with eight faces. A regular octahedron is a Platonic solid composed of eight equilateral triangles, four of which meet at each vertex.
A regular octahedron is the dual polyhedron of a cube. It is a rectified tetrahedron. It is a square bipyramid in any of three orthogonal orientations. It is also a triangular antiprism in any of four orientations.
An octahedron is the three-dimensional case of the more general concept of a cross polytope.
A regular octahedron is a 3-ball in the Manhattan (ℓ1) metric.
Regular octahedron
Dimensions
If the edge length of a regular octahedron is a, the radius of a circumscribed sphere (one that touches the octahedron at all vertices) is
and the radius of an inscribed sphere (tangent to each of the octahedron's faces) is
while the midradius, which touches the middle of each edge, is
Orthogonal projections
The octahedron has four special orthogonal projections, centered, on an edge, vertex, face, and normal to a face. The second and third correspond to the B2 and A2Coxeter planes.
October
October (
i/ɒktˈoʊbər/ ok-TOH-bər) is the tenth month of the year in the Julian and Gregorian Calendars and one of seven months with a length of 31 days. The eighth month in the old Roman calendar, October retained its name (from the Latin octō meaning "eight") after January and February were inserted into the calendar that had originally been created by the Romans.
October is commonly associated with the season of Autumn in the Northern hemisphere and spring in the Southern hemisphere, where it is the seasonal equivalent to April in the Northern hemisphere and vice versa. In the Western world, October is also commonly associated with Halloween (All Hallows Eve), which initiates the season of Allhallowtide.
