Ugo Adriano Graziotti - The Thirteen Duals of the Semi-Regular Archimedean Polyhedra, “Polyhedra:The Realm of Geometric Beauty”, 1962.

In Space, every Figure having Height, Width and Depth, and formed of Planes, Lines and Points, has associated with it another Figure composed of Planes, Lines and Points - its so-called Dual Configuration. In this association lies a far reaching Principle of Mathematics - the Principle of Duality. Each of the Points of the first Body is Transformed into a Plane of the second Body, and a Plane is Transformed into a Point. The new Body thus formed is called the Dual of the first.

PLATE 1: Solid Triakis Tetrahedron
PLATE 2: Solid Triakis Octahedron
PLATE 3: Solid Tetrakis Hexahedron
PLATE 4: Solid Triakis Icosahedron
PLATE 5: Solid Trapezoidal Icositetrahedron
PLATE 6: Solid Rhombic Dodecahedron
PLATE 7: Solid Rhombic Triacontahedron
PLATE 8: Solid Hexakis Octahedron
PLATE 9: Solid Pentakis Dodecahedron
PLATE 10: Solid Trapezoidal Hexecontahedron
PLATE 11: Solid Hexakis Icosahedron
PLATE 12: Solid Pentagonal Icositetrahedron
PLATE 13: Solid Pentagonal Hexecontrahedron

Alto’s Adventure

Alto’s Adventure is very much a casual game, but we were also keen to add a little soul and sensitivity to the mix in a way that’s not normally seen within the genre. This meant establishing a lighthearted tone without resorting to being overly bright or cartoonish. It was important that all aspects of the game’s environment and characters felt grounded, as though they could be just a small part of a much larger world with it’s own history and culture.

The visuals were also informed by a desire to optimise for mobile and play to the strengths of the platform. This involved stripping away unnecessary details and fussy textures, freeing us up to focus instead on the underlying form and composition. We ultimately arrived at a bold, geometric style that combined elements of 2D and 3D with a minimalist / surrealist twist.

The game’s dynamic lighting and weather also allowed us to explore a range of contrasting colour palettes to add some variety and intrigue to the game, as well as enhancing the overall level of ambience and immersion.

- Harry Nesbitt

Maxwell’s Formulation – Differential Forms on Euclidean Space

Maxwell’s Formulation – Differential Forms on Euclidean Space
Author: Jing Wang
Institute: School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore

One of the greatest advances in theoretical physics of the nineteenth century was Maxwell’s formulation of the the equations of electromagnetism. This article uses differential forms to solve a problem related to Maxwell’s formulation. The notion of differential form encompasses such ideas as elements of surface area and volume elements, the work exerted by a force, the flow of a fluid, and the curvature of a surface, space or hyperspace. An important operation on differential forms is exterior differentiation, which generalizes the operators div, grad, curl of vector calculus. the study of differential forms, which was initiated by E.Cartan in the years around 1900, is often termed the exterior differential calculus.However, Maxwell’s equations have many very important implications in the life of a modern person, so much so that people use devices that function off the principles in Maxwell’s equations every day without even knowing it.