r/GeometryIsNeat

My latest polyhedral build. 60 faces. 3D printed frame, laser cut clear acrylic faces with UV printed pattern.

Advice?

This is just the skeleton grid for an ink drawing. I'm still trying to decide how I'll ink it. But yeah, here's a hand-drafted Voronoi diagram of a 55:89 parastichy spiral phyllotaxis pattern using Vogel's formula. I've done this in a vector art program as well, and honestly I'm not sure which technique was faster: by computer, or by hand. By hand is messier but this will all get inked over. I used Euclid's ruler and compass method for finding a perpendicular midpoint line on each space between nodes.

An animation of the Phobos Deimos ZRVTO (Zero Relative Velocity Transfer Orbit) as described by Paul Penzo on page 45 of the Tethers In Space Handbook: Link

If a payload is released at the right time from the top of 940 tether ascending from Phobos it will arrive at the foot of a 2960 km tether descending from Deimos.

At apoapsis the payload matches the velocity of the Deimos tether foot.

Thus Phobos can send payloads to Deimos with nearly zero propellant. And vice versa.

Penzo notes both Deimos and Phobos are huge momentum banks. So Phobos and Deimos anchored tethers can catch and throw payloads till the cows come home with very little effect on their orbits.

There is a ZRVTO between any two Sarmont tethers in circular orbits of the same inclination.

I believe Penzo's insight can be extremely useful.

Required tether mass goes up exponentially with delta V. Somewhat like propellant in Tsiolkovsky's rocket equation.

With a chain of Sarmont tethers connected by ZRVTOs, the delta V budget is broken into chunks. Thus you can have tethers made from today's materials without ridiculous taper ratios.

https://github.com/PatrickCakes888/Cord-based-topological-projection-app