The two-dimensional sphere can’t be approximated by finite homogeneous spaces. We describe the optimal approximation and its distance from sphere. compare this to achieved all Platonic Archimedean solids.

We consider rotations A, B of finite order in SO(3), about axes separated by an angle of restricted type, and attempt to classify the possible group relations between A and B. We show that the relations responsible for the symmetries of Platonic solids have consequences far beyond that simple geometric setting.

A number of perennial doubts plague genre theory. Are genres really 'out there' in the world, or are they merely the constructions of analysts? Is there a finite taxonomy of genres or are they in principle infinite? Are genres timeless Platonic essences or ephemeral, time-bound entities? Are genres culturebound or transcultural?... Should genre analysis be descriptive or proscriptive? (Stam 200...

Traces the continuity of ideas Neoplatonism in Greek-Byzantine Patristics process developing orthodox doctrine Holy Trinity by Church Fathers. The author emphasizes commonalities and distinctions Christianity. Plotinus’ concept triad, One - Intellect Soul, is considered with a focus on analysis regarding as Deity Origin world. emanation Neo-platonic trinity hypostasis its connection through Wor...

This paper is an artist statement describing a manipulation of the Mandelbrot Set equation as the basis for creating semi-figurative images, using a genetic algorithm. Modernist painting is referenced in terms of the play between representation and abstraction. The Platonic implications of the Mandelbrot Set are considered as a point of departure for manipulation of the complex function.

The notion of a spiral unfolding of a convex polyhedron, resulting by flattening a special type of Hamiltonian cut-path, is explored. The Platonic and Archimedian solids all have nonoverlapping spiral unfoldings, although among generic polyhedra, overlap is more the rule than the exception. The structure of spiral unfoldings is investigated, primarily by analyzing one particular class, the poly...

In this note we will determine the symmetry groups of the Platonic solids. We will use Maple to help us do this. The five Platonic solids are the tetrahedron, the cube, the octahedron, the dodecahedron, and the icosahedron. We will view the symmetry groups of these solids in two ways. By definition, the symmetry group of a solid is the set of isometries of R that stabilize the set. In each of t...