in suhrawardi philosophy – like any philosophy which seeks to explain the general facts of being – the issuance of plurality is an important element in the cosmology and defers with mashsha basis in this regard. the issuance of plurality contains several stages in suhrawardi's main works: agreement with mashsha’ on the emanation of the first caused, criticizing them for the issuance of und...

The tetrahedron, the cube, the octahedron, the dodecahedron, and the icosahedron. From a first glance, one immediately notices that the Platonic Solids exhibit remarkable symmetry. They are the only convex polyhedra for which the same same regular polygon is used for each face, and the same number of faces meet at each vertex. Their symmetries are aesthetically pleasing, like those of stones cu...

Research supported by NSA and NSF. 1980 Mathematics Subject Classi cation (1985 Revision): 20E99.

In our work on robotic manipulation, we required a method for determining the orientation of a marked sphere from a single visual image. Our solution utilizes features of different colors painted on the sphere at the vertices of the Platonic solids. The main result of this paper is the minimization of the number of feature colors needed to solve the correspondence problem. The minimization of c...

Understanding the nature of dense particle packings is a subject of intense research in the physical, mathematical, and biological sciences. The preponderance of previous work has focused on spherical particles and very little is known about dense polyhedral packings. We formulate the problem of generating dense packings of nonoverlapping, nontiling polyhedra within an adaptive fundamental cell...

We describe a new class of spherically symmetric, high degree of freedom robots called “platonic beasts.” A robot in this family is kinematically equivalent to a symmetric polyhedron, such as one of the Platonic solids, with identical multi-purpose limbs attached to its vertices. The symmetry and regularity of the design have several advantages including robustness to toppling, novel gaits such...