These angles formed between lines of the same faces – referred to as dihedral angle discrepancies – means that, according to Schein and Gayed, the shape is no longer a polyhedron. Instead they claimed ...

Mathematics of Operations Research, Vol. 5, No. 4 (Nov., 1980), pp. 576-594 (19 pages) We introduce the property of k-decomposability for simplicial complexes which, if satisfied by the dual ...

From ancient times, mathematicians have been intrigued by polyhedra, closed surfaces with polygons as sides. They have been especially interested in those in which the polygons are regular – the sides ...

Ancient Greek mathematicians – most notably Plato - classified solid shapes thousands of years ago. Since then, remarkably few geometric ‘solid’ forms have been discovered and the last collection was ...

In the latest verse of a centuries-old mathematical refrain, scientists have figured a way to iron out the wrinkles in a large class of molecular cages. The cages have faces consisting of 12 regular ...

Abstract It is well known that to determine a triangle up to congruence requires 3 measurements: three sides, two sides and an angle, or one side and two angles. We consider various generalizations of ...

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The works of the Greek polymath Plato have kept people busy for millennia. Mathematicians have long pondered Platonic solids, a collection of geometric forms that are highly regular and are frequently ...

The work of the Greek polymath Plato has kept millions of people busy for millennia. A few among them have been mathematicians who have obsessed about Platonic solids, a class of geometric forms that ...