Maths Starters, Omnigraph, Nubble!, Mental Arithmetic, Fractions, Numeracy Starters, Algebra

Virtual Image Publishing Ltd  184 Reddish Road, South Reddish, Stockport SK5 7HS, UK Tel: (+44) 0161 480 1915  Fax: (+44) 0161 612 2965


 Adding a new dimension to mathematics

POLYTOPIA I: Tessellations and Polyhedra


From Tessellations to Polyhedra
Geometrical Alchemy
The Archimedean Polyhedra
A Polyhedral Universe

trochon balviv

Kepler's Rhombic Polyhedra
Polyhedra and the Natural World
Stellated Polyhedra
The Euler Characteristic



“The modern child may still have to write that awful rubric QED at the end of the core curriculum theorem but has at least the further option of stepping through the construction of Plato's five regular polyhedra and animating them through their axes. If, that is, he or she has access to such learning tools as Virtual Images Polytopia I, which makes sense of the structures in a way no text book ever did for me. It's organised into 10 modules dealing with two and three-dimensional structures. The accompanying text starts from first principles, is clearly written, and should present few problems for anyone older than about 12. It's accompanied by diagrams, tables, pictures, and animated sequences. Most of it is straightforward enough and even entertaining.”
                                                                       The Guardian

POLYTOPIA II: Honeycombs and Polytopes

tiles2 compviv

3D Tessellations
Crystal Lattices
Crystals of Compounds
The Fourth Dimension
Sections of 4D Polytopes

The nD Generalization
Duality in 4D
Stellated Polytopes
Vertex Figures
4D Honeycombs



“Polytopia I uses, text, tables, movies and interactive graphics to explore ways polygons can spread out in sheets or curl up into balls. The sequel Polytopia II pursues these themes into higher dimensions. The prettiest parts of Polytopia I are the movies: imaginatively conceived and nicely ray-traced, with objects rendered in subtle colours and pleasingly textured materials including transparents. There is nice scenery, too: fractals, Leonardo sketches, the Pleiades, rippling water and reflective spheres in which you almost expect to catch the eye of Maurits Escher. Polytopia II largely abandons the photorealistic world of bright, hard surfaces in favour of jaggy wire-frame graphics against a dark background... But they come into their own on the second disc as we meet objects whose structure is more than skin deep. What is lost in ray-traced eye appeal is gained in interactivity and potential for learning. If you cannot have a physical model of a polyhedron or honeycomb in your hand, it does help to be able to turn it around and view it from all angles on the computer... The mathematical content is leavened with history and philosophy... Computer graphics like those of Polytopia II (or the pioneering work of Thomas Banchoff during the 1980's) are probably the closest we can get to mentally grasping the worlds of 4D, 5D and beyond.”
                                                   Times Higher Educational Supplement

“Stunningly visual it is. POLYTOPIA is about as addictive as many a prohibited substance.”
                                                           The Glasgow Herald

      Each volume of POLYTOPIA is priced:
      extended site licence - 100 + VAT
      unlimited user site licence - 80 + VAT
      30-59 user licence - 60 + VAT
      2-29 user licence - 40 + VAT
      single user licence - 20 + VAT

      (The extended licence includes home use by teachers and pupils.)

      Buy POLYTOPIA I & II bundle with single home user licences NOW for just 30 + VAT
      (Click the orange ‘Buy Now’ button.)




16 November 2016