let alpha = arcsin(1/sqrt(3)) = 35.264 degrees, be the semi-apex angle of an equilateral square-based prism.

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Let alpha = arcsin(1/sqrt(3)) = 35.264 degrees, be the semi-apex angle of an equilateral square-based prism.

(A mnemonic for this is that the inclination of a face is 54.7 degrees, which is the complement, and is half the well-known "bond angle of methane" at 109 degrees 28 minutes, which I've always remembered for some reason).

(A mnemonic for this is that the inclination of a face is 54.7 degrees, which is the complement, and is half the well-known "bond angle of methane" at 109 degrees 28 minutes, which I've always remembered for some reason).

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Then each segment of the curve moves through 2*alpha - 60 degrees = 10.528 degrees

Then each segment of the curve moves through 2*alpha - 60 degrees = 10.528 degrees

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So, 34 segments move trough 357 degrees, which is close enough to absorb.

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So, 34 segments move through 357 degrees, which is just 3 degrees short of a complete circle, and easily close enough for the structure to absornb the error.

A fully suspended closed circle on two support legs. The loop is composed of 34 segments, alternating trianges with pyramids.

Building Instructions

Create the bottom arc of 9 segments.

Add the support legs downward from the ends of the arc.

Continue adding segments upwards to complete the entire circle.

Keep the two sides balanced as you are building upwards.

Calculations

Let alpha = arcsin(1/sqrt(3)) = 35.264 degrees, be the semi-apex angle of an equilateral square-based prism.

(A mnemonic for this is that the inclination of a face is 54.7 degrees, which is the complement, and is half the well-known "bond angle of methane" at 109 degrees 28 minutes, which I've always remembered for some reason).

Then each segment of the curve moves through 2*alpha - 60 degrees = 10.528 degrees

So, 34 segments move through 357 degrees, which is just 3 degrees short of a complete circle, and easily close enough for the structure to absornb the error.