Understanding the Vegreville Pysanka

This egg was designed by Ron Resch while he was Professor of Computer Science at the University of Utah. In the concept and planning of the Egg, 9 "firsts" were achieved in mathematics, engineering and architecture. The design involved cutting edge computer graphics and students like Jim Blinn and Robert McDermott. I found 4 books that describe this project: (1)Paul Hoffman's book "Archimede's Revenge", chapter 5 "Adventures of an Egg Man". (2)Jim Blinn's book "Dirty Pixels" , chapter 1 "The World's Largest Easter Egg". (3) Jay Kappraff "Connections", page 336 Figure 9.13, Chapter 9 "Transformations of the Platonic Solids", (4)Theoni Pappas "The Magic of Mathematics", page 73 "Laying an Egg Mathematically".

Because the egg shape is axisymmetrical, the analogy with the earth is convenient. The pointed end on top is the North Pole (the POINT) and the fat end on the bottom is the South Pole (the END). The axis of symmetry is tilted 60 degrees from vertical. The area near the equator is a barrel shape. The poles are made of computer simulated caps. At the poles are 6-point stars, which is a common motif in Canada. At the equator the stars are made out of 2 colors (gold and silver) in the Mitsubishi arrangement. The stars are placed at the middle of a rhombus shape. The barrel of rhombi is bound by the silver bands. Outside of the silver bands, there are rows of 3-point stars.

To simplify the fabrication, Prof. Ron Resch chose to use the maximum number of 12-inch equilateral triangles. There are 2208 pieces of equilateral triangles and cover nearly half of the surface. To make this surface follow the egg smoothly, the equilateral triangles are interlaced with isosceles triangles or 3-point stars. Symmetry helps to minimize the number of different tiles. The two caps each have a 6-point star. The sector(half-slice of a point) is repeated 12 times. The barrel has 9 rhombi. Each rhombus is symmetrical about the y axis. Only 1/18 of the barrel surface needs to be modeled. If color is ignored, the number of different shapes is again reduced in half. The barrel has 36 identical staves that cover 10 degrees of longitude. The staves are made of alternating columns of triangles and stars.

Within the barrel, the circumference is largest at the equator. The circumference shrinks as we move towards the silver band. This shrinkage is minimal around the equator and all the tiles are nearly triangular. Outside of the silver bands, the gaps between the equilateral triangles turn into 3-point stars. The stars are hexagons with sides of 12 inches. The stars get progressively thinner as we move towards the poles. The top row (near the North Pole) of stars are more narrow than the bottom row (near the South Pole) because the shrinkage is more severe near the North Pole. The barrel extends from the 5 bands of stars at the top to the 4 bands of stars at the bottom. All the stars point down. The columns of stars are separated by columns of fix-size triangles pointing up. Between the barrel and the caps are the dark area (bronze-brown) which hides the irregular shapes. The tiling in dark color merges the 6-fold rotation symmetry of pole design with the 9-fold symmetry of the barrel. This is also the area where the curvatures of the barrel are matched closely to the curvatures of the two ends.

To state the problem in another way, the egg surface is covered by 3 piece of continuous triangulation: the BARREL, the END and the POINT. The triangulation consists of a fix-size 12-inch equilateral triangle and a shrinkable 3-point star. The area of this star is 4X the fix-size triangle at the equator (24 inch equilateral triangle). The star area can be compressed down to zero. In practice, the barrel is truncated before the 3-point stars get too small. The 3-point stars are colored silver and gold in 9 bands at the top and the bottom of the barrel. The bronze-brown triangles in these bands between the stars are the 12-inch equilateral triangles. The triangles are flat aluminum plates (0.125 inch thick) and structurally connected to the axis of symmetry with spokes. The 3-point stars are aluminum plates (0.062 inch thick) bend into 4 planes. The stars are bolted to 6 equilateral triangles on its boundary and not connected to the core.

The size of the egg can be measured by the number of triangles. The diamond shape(rhombus) on the barrel has 6 triangles across the equator. So the shorter diagonal of the diamond is 6 feet long (roughly). The longer diagonal of the diamond is 10.63 feet long. About 10 adults holding hands can surround the equator of this giant egg.

If you compare the photos of the egg and the background, it is amazing how everything seems to change. The background is always different. The pysanka is kinetic and turns in the wind like a weathervane. This is a good way to minimize the loading from the 100-mile-per hour wind that sweeps across Vegreville. The coloring of the tiles has symbolic meaning. The color arrangement was a joint effort by Prof. Ron Resch and Paul Sembaliuk. Sembaliuk is an Albertan artist and authority on Ukrainian culture. Prof. Ron Resch has training in sculpture and industrial design. To make the egg a reality, he has also taken the task of fabrication of the tiles and designing the ingenious way the tiles are bolted together. The on-site installation is truly awesome.

The SYMBOLOGY is described by Annette Zoppo in a booklet: "By beginning at either end of the Egg in sequence, 5 distinct symbols are inherent in the design. The radiating gold star on the end section, symbolizes Life and Good Fortune. This leads to the series of 3-pointed stars in alternating gold and silver, which symbolizes the Trinity, representative of the strong devotion to the faith of our ancestors. A band of silver, circumscribing the Egg, has no end and no beginning, symbolizes Eternity. On the central barrel section are located windmills, of 6 vanes and points in gold and silver, which symbolize the rich harvest. The silver wolves' teeth pointing to the center from the silver band, which is the most prominent motif of the design, symbolize the main message, of protection and security afforded our pioneers by the R.C.M.P. The 3 colors, bronze, silver and gold are rich color symbolizing Prosperity. Bronze (charcoal brown) is the basic color of the design and suggests the Good Earth, the land on which our forefathers struggled for existence."

Vegreville is a farming community with the largest Ukrainian settlement in Canada. The idea of an egg monument came from Town Council member Mrs. Kay McKenzie. The timing and funding of the project were related to the 100th Anniversary of the Royal Canadian Mounted Police. The Egg was dedicated in the summer of 1976.

This may be a crazy idea for a science fair project. Start the form with a balloon. Add paper mÓche or plaster gauze on the surface to get a rigid form. The aspect ratio and the profile of the egg are important parameters. After the form is done, mark with a pencil the necessary lines for the tessellation. Finish the surface with color patches of origami paper. It is not as easy as it sounds, but you will learn a lot from doing this. First paint the background color (the 3-point stars or the dark-brown irregular shapes), then glue on the 2208 equilateral triangles made from color paper. Send me a photo when you are done !

Tessellation with JAVA programs

Examples of Math/Art

M.C. Escher interlocking shapes

Vegreville, Canada World's largest Easter Egg

Vegreville Pysanka photo album

Penrose tile in Architecture

Screenshots from the Tessellations CD

William's Home Page

I like to thank all the people who have posted the pysanka on the WEB. I have spent a few hours thinking about the wonder of this egg. Please send me more photos. If you see any analysis or description of the egg construction, please send me a copy or a reference!