CIF files should be validated before deposition via http://checkcif.iucr.org and the IUCr validation report submitted with the manuscript.
Polyhedron will publish original, fundamental, experimental and theoretical work of the highest quality in all the major areas of inorganic chemistry.
In addition Polyhedron publishes specially commissioned review articles (Polyhedron Reports) and collections of original research papers (Polyhedron Symposia-in-Print) of appropriate timeliness.
The Platonic solids are within the larger grouping known as regularpolyhedrons, in which the polygons of each are regular and congruent (that is, all polygons are identical in size and shape and all edges are identical in length), and are characterized by the same number of polygons meeting at each vertex.
A polyhedron is a three-dimensional analog of a polygon.
Face-uniformity of a polyhedron corresponds to vertex-uniformity of the dual and conversely, and edge-uniformity of a polyhedron corresponds to edge-uniformity of the dual.
Notice that a cone, and a cylinder are not polyhedrons since they have “faces”; that are not polygons.
In the combinatorial definition, a polyhedron is not necessarily a bounded structure: It is defined as the solution set of a finite system of linear inequalities.
Convexpolyhedrons are also known as Euler polyhedrons, and can be defined by the equation E=v+f-e=2, where v is the number of vertices, f is the number of faces, and e is the number of edges.
Polyhedrons are classified and named according to the number and type of faces.
A polyhedron whose faces are all regularpolygons congruent to each other, whose polyhedral angels are all equal, and which has the same number of faces meet at each vertex is called a regularpolyhedron.
Sometimes the term "polyhedron" is used to apply to figures in more than three dimensions; however, analogs of polyhedra in the fourth dimension or higher are also referred to as polytopes.
A polyhedron is said to be Convex if its surface (comprising its faces, edges and vertices) does not intersect itself and the line segment joining any two points of the polyhedron is contained in the interior and surface.
In elementary geometry it is accepted to define a polyhedron as a figure composed of polygons in a special manner [2], after which a convexpolyhedron is defined as a polyhedron lying on one side of the plane passing through any one of its
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