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**A Plethora of Technical Drawings**

January 9, 2019

Doubling Function for Thrackles with 20-Vertex Thrackle, Pencil on Bristol, 11 x 17 in., 2018

Much of winter break was spent working on a series of geometry problems and this post shows the fruits of that effort. The above drawing illustrates how any thrackle can double its verticies by applying the "Conway Doubling" function. In this example I used it to split a 10-vertix thrackle into a 20-vertix thrackle.

For more on this geometry problem and an explanation of the thrackle, check out this post.

34-Vertex Trhackle, Pencil on Bristol, 11 x 17 in., 2018

The highest vertex count on any thrackle I've ever drawn, above, at 34 vertecies. I did this by constructing a 17-pointed star (heptadecagram) and splitting it using the Conway Double. The diagram to the right of the thrackle explains how to construct a regular 17-sided polygon (heptadecagon), needed to create this thrackle.

Perfect Cube Multiplication in Two Point Perspective, Pencil on Bristol, 11 x 17 in., 2018

This drawing illustrates the construction and multiplication of a perfect cube in two point perspective. This is important in design and engineering because it allows you to assign a unit, one square foot for example, to each cube. From this your perspective drawing can have real-world implications. I've always known how to do this, just wanted to get a nice version for my engineering portfolio. Also a helpful diagram to give to students.

Icosahedron, Pencil on Bristol, 11 x 17 in., 2018

Dodecahedron, Pencil on Bristol, 11 x 17 in., 2018

Top drawing is the icosahedron, a 20 sided regular polyhedron constructed with equalateral triangles. The bottom drawing is the dodecahedron, a 12 sided regular polygon constructed of regular pentagons.

In graduate school I encountered the work of Wenzel Jamnitzer. Jamnitzer was born in Vienna in 1508 and specialized in goldsmithing and etching. He produced a book of geometric etchings illustrating the uniform polyhedra. I was intrigued because I had never learned to draw any of them except for the cube and pyramid. When I searched the internet for instructions on their construction all I got were results explaining how to create them using computer programs. It would be five years before I found the brick and mortar solution when I stumbled upon some drawings by an Italian artist. The solution is to project golden ratios which determine the verticies of the shape. So far I've drawn the two types above and am in pursuit of others.

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