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I was looking through old saved urls and when an old Johns Hopkins Applied Physics Laboratory press release link didn't work, it sent me to the PageNotFound page, where I saw the image below.

It seems to relate to a spacecraft or actually a whole project called Transit, (and a design failure, but I'll split that off as a separate question).

Question: What is the spiral pattern on the outside of this satellite that is also repeated on the inside, all the way to the center?

According to the page:

Page Not Found

“You learn more from failures than from successes.”

enter image description here

(non-annotated copy)

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The satellite shown is an early development/test version of the Transit navigation satellites, probably 1 or 3. (Transit 2 had a double helix pattern)

The spiral pattern is a "logarithmic helical antenna". Source: Page 7 at this link

The Space Department needed to develop several novel antennas to radiate the Doppler signal to the ground. The first Transits used an APL-invented spherical projection of a logarithmic spiral.

This document states that the antennas were "silver-painted on". (page 28 of the pdf)

enter image description here

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