Icosahedron, Youcosahedron, Weallcosahedron

Check out my model of an icosahedron. I’ve been itching to construct one after reading about it in The Power of Limits. I finally found some time during the Christmas Holidays.



The icosahedron is one of the five regular solids discovered by Pythagoras and further explored by Plato, Kepler and many others. (Actually, there is ample evidence that they were well known to non-Greek cultures in times predating Pythagoras, but he is the first, as far as we know, to prove logically and mathematically that there are five and only five regular solids—no others are possible.) The icosahedron has twenty sides, each of which is an equilateral triangle. A glimpse from different angles reveals that it reverberates with both pentagonal and hexagonal harmonies. Most intriguingly, its internal core consists of three golden rectangles which intersect one another at right angles, and whose short sides touch upon opposing edges of the overall form.

For Plato and for the medieval alchemists and astrologists, each of the five regular solids was associated with one of the fundamental “elements” (earth, fire, air, water and ether or quintessence, the “fifth essence”) believed at that time to comprise the universe. The icosahedron was most often associated with water, though some of the lesser authorities assigned it as the representative of ether or quintessence (a role usually filled by the dodecahedron, or twelve-sided solid).

Christmas Card Illustration, 2009

Long about Thanksgiving, I decided it was time to start thinking about some sort of Christmas self promotion. Actually, I had been thinking about it for a while in fits and starts, but it was time (or rather, past time) to begin doing something if it was going to happen at all. So I managed to throw this together in a few days of fairly intense work and wound up using it on both personal and business-related Christmas cards. Anyway, I thought this might serve as a good example to use in explaining my technique, which in this case involves a combination of pen and ink and scratchboard.


The first steps always involve very basic decisions, such as the size and dimensions of the piece as it is to be printed, which in turn helps determine the size and dimensions of the illustration as executed. I had already decided that the final cards would be printed 5" x 7". I typically do the final illustration somewhat larger than the final reproduction size—sometimes up to 200% size, but usually around 130%-150% is more practical. In this case, I decided to execute on a piece of 8" x 10" board, but to keep the relative proportions in conformity with the final 5" x 7" size. When I’m illustrating a scene that has a definite historical context, I really enjoy using Google Earth as a tool to help me accurately visualize the setting, which in this case was the area around Bethlehem. In this case, I chose a vantage point looking SSE, from an area close to Rachel’s Tomb, on the road that leads from Jerusalem to Bethlehem. (The traditional location of the Shepherd’s Field is a bit further SE from this location, but after exploring that as well as some other alternative possibilities, I found this vantage point most to my liking.)


I begin sketching on tracing paper on top of the grid already established above. My initial sketch isn’t much to look at, but it serves the important purpose of fixing the location of all the major elements in the composition. The details of those elements will be worked out in subsequent sketches. Since I’m not the sort of illustrator who can usually render things very convincingly based on memory and imagination alone, I start rounding up some good visual reference for the trees, figures and animals.


Often, the most efficient solution for visual reference involves a quick photo shoot with some help from the family. (My neighbors have gotten acclimated to seeing some very odd scenes played out in our back yard on occasion. My wife always relishes this part of the process.)


Other resources include images found online, in books and magazines, and sometimes in magazines or other works of art. (For instance, I worked out the poses for some of the angels in the heavenly host based on an angelic figure from an illustration by my hero Franklin Booth.) Speaking of the heavenly host, one of my goals in this illustration was to convey the understanding that “host”, in its biblical context, actually denotes a military deployment—a heavenly army arrayed for battle, as opposed to the overly sentimentalized image of angels we are often confronted with. I certainly think that helps to explain the shepherds’ fear. At any rate, I had a couple of recipients comment on this aspect of my rendition, so I take that as a sign that I succeeded in that regard, at least.


Again using tracing paper to further develop the initial sketch, I created a second, more detailed sketch.


Ultimately, I determined that the drama of the composition could be improved by enlarging the figures of the standing shepherd and frightened girl and by moving them further into the foreground. This is a quick pencil sketch (based on some of the other photographs I had taken) which I created in the process of working this out.


Having worked out all the compositional factors to my own satisfaction, I do a third sketch which functions as a value study for the final illustration. This is an important step in the process, since the technique I am using requires some careful planning in regard to where the darkest and lightest areas of the composition will be located, which in turn determines how they will be executed—either “positively”, with pen on a white background, or “negatively”, using a scraper tool on a previously inked-in portion of the illustration. Even at this point, it’s not out of the question that I might change my mind, which is part of the reason for doing the value-study sketch. I had originally planned on inking in only the trees and perhaps the left-hand side of the conjoined foreground figures, but after doing this sketch, I decided that I would ink in most of the sky as well.


Again using tracing paper with an outline sketch of the main compositional elements, I begin transferring the sketch to the board for the final illustration. I use graphite transfer paper for the positive areas and, after inking in the negative areas and allowing them to dry thoroughly, I do the same for them using white transfer paper.


When the transfer is completed and before the actual work of drawing and scratching begins, here is what it looks like.

For the drawing, I used mostly a technical pen for this, but I also often use a dipped pen, usually with a crow quill or very fine nib. For a combo technique such as this, I prefer executing the final on Claybord, which is a very rigid, masonite-like board with an extremely smooth surface. (It’s also relatively expensive.) Esdee scratchboard is also pretty good. If I’m just doing pen and not reversing anything out I will often use bristol board. (I actually find that I get much better line quality, especially with a dipped pen, on bristol board.)


Here is the final in pristine black and white. After scanning this in, the color was added in Photoshop.