During some 10 months of pre-planning, Prof. Resch with two University of Utah Ph.D. students, Robert McDermott and James Blinn, solved these problems and others involved in accomplishing Vegreville's dream for an Egg; and in doing so achieved some nine mathematical, architectural and engineering firsts.

Resch's systems utilize repetitious geometric modules. He designed the Egg structure to use only two types of modules: equilateral triangular pieces, whose size and shape remain constant; and three-point star-shape pieces, whose width varies ever so slightly through-out the Egg's surface. Once a precise analytical definition was determined and computation of the geometry complete, the symmetrical modular design (placement of the facets) was fixed. Resch worked with Albertan artist Paul Sembaliuk, an authority on Ukrainian culture, in determining coloring of the geometric facets to symbolize and interpret traditional Ukrainian designs where possible.

Prof. Resch had initially spent several weeks considering the feasibility of the project, conferring with Robert McDermott and others, before accepting Vegreville's challenge and making a proposal. During the subsequent six months of work, there were many delays and setbacks while Resch and his associates developed _ new mathematics, geometries and programming. They tried three different of his modular designs but could not resolve the geometry problems.

It was during this time that local chamber members Kay McKenzie, Ralph Gorrie, P.M. Shavchook, Mayor Moshansky and Provincial officials Paul Sembaliuk and Tom Tinkler, who had been monitoring progress of the work and saw promise in it, persuaded the R.C.M.P. Committee to extend the grant period.  An additional grant of $10,000 was given, and with the extension of time a new geometric system for the Egg was begun which resolved all prior difficulties.

With the new approach, Resch created an algorithm for distributing the equilateral triangles on the Egg surface. Robert McDermott and Jim Blinn are jointly responsible for the precise mathematics and computer programming which implemented the geometric concept Accomplishment of the highly sophisticated and complex mathematics brought to a close the long-sought-after geometric definition of the faceted Egg.