The Cover Image
Making the Escher-style hyperbolic dodecahedron symbolizing Mathematica 5
Copyright Michael Trott 2003
Outline of the Procedure
We construct a regular dodecahedron centered at the origin.
The faces of the dodecahedron are then subdivided into right triangles (similar to M. C. Escher's Quadratlimit work), each of which is then scaled down so that gaps are introduced between them.
Each triangle is further subdivided so that, when the surfaces are transformed in the next step, the resulting surfaces are relatively smooth.
Outlines of all triangles are constructed.
A radial transformation is applied to each triangle. Then each triangle is given depth by connecting it to a slightly smaller copy moved closer to the origin.
Step 1: The Regular Dodecahedron
Step 2: Dividing into Triangles
Step 3: Subdividing the Triangles
Steps 4: Triangle Edge Construction
Steps 5: Radial Transformation and Thickening