Andrew Smith
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.
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.
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.