Andrew Smith

Statement

THE DIMOTORP For many decades I have been drawing progressions of polygons. Two ways of arranging them are with sides parallel, or points aligned. Lately, I have been intrigued with alternatives by rotating the shapes. The first was the Protomid. Each of its polygons shares a side with the next one. The Dimotorp is the opposite of the Protomid. The Protomid (notice the reverse spelling) starts as a triangle on the top and progresses down to a huge, indeterminable-sided polygon (circle). In contrast, the Dimotorp starts as a triangle at its base and progresses, potentially, up to the thinnest infinitely sided polygon. Unlike the Protomid, which has polygons with equal-length sides, the Dimotorp has polygons of decreasing side-length.

Artworks

Looking down on this Dimotorp, we can see I constructed it with twenty-four polygons. Each shape pivots fifteen degrees from the centre of one of its sides. This illustration is—like the preceding one—truncated after one complete rotation, at the twenty-six-sided cylinder. The height of the structure is finite because I maintained the same-size ratio between the polygons. I achieved an architectural appearance of a building’s storeys by extruding each polygon the same height.

This view is from the ground, looking up at the Dimotorp as it almost disappears into the clouds. Theoretically, it could be an infinitely long needle. But, to achieve this, I would have to make the size ratio between the polygons decrease in progression; that would make the structure’s profile a parabola. I have extruded each polygon in these two illustrations so they are the same height. If I were to have accelerated their height, the structure would become steeper. I depicted its floors alternating between red and white for clarity. The odd-numbered layers are a red colour.