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Orthogonal Polyhedron
An orthogonal polyhedron is a polyhedron in which all edges are parallel to the axes of a Cartesian coordinate system, resulting in the orthogonal faces and implying the dihedral angle between faces are right angles. The angle between Jessen's icosahedron's faces is right, but the edges are not axis-parallel, which is not an orthogonal polyhedron. Polycubes are a special case of orthogonal polyhedra that can be decomposed into identical cubes and are three-dimensional analogs of planar polyominoes. Orthogonal polyhedra can be either convex (such as rectangular cuboids) or non-convex. Orthogonal polyhedra were used in in which he showed that any polyhedron is equivalent to a cube: it can be decomposed into pieces which later can be used to construct a cube. This showed the requirements for the polyhedral equivalence conditions by Dehn invariant. Orthogonal polyhedra may also be used in computational geometry, where their constrained structure has enabled advances in problems un ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Orthogonal Polyhedron With No Vertex Visible From Center
In mathematics, orthogonality is the generalization of the geometric notion of ''perpendicularity''. Although many authors use the two terms ''perpendicular'' and ''orthogonal'' interchangeably, the term ''perpendicular'' is more specifically used for lines and planes that intersect to form a right angle, whereas ''orthogonal'' is used in generalizations, such as ''orthogonal vectors'' or ''orthogonal curves''. ''Orthogonality'' is also used with various meanings that are often weakly related or not related at all with the mathematical meanings. Etymology The word comes from the Ancient Greek ('), meaning "upright", and ('), meaning "angle". The Ancient Greek (') and Classical Latin ' originally denoted a rectangle. Later, they came to mean a right triangle. In the 12th century, the post-classical Latin word ''orthogonalis'' came to mean a right angle or something related to a right angle. Mathematics Physics Optics In optics, polarization states are said to be orthog ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
