Selected Stellations of the Truncated Dodecahedron

This is the truncated dodecahedron. It is one of the Archimedean solids.

Trunc Dodeca

This polyhedron has a long stellation-series, from which I selected several on aesthetic grounds. The figure immediately below is the truncated dodecahedron’s 16th stellation.

16th stellation of Trunc Dodeca

Here is the 21st stellation.

21st stellation of Trunc Dodeca

It’s easy to stellate polyhedra rapidly, and make many other changes to them, with Stella 4d: Polyhedron Navigator. You can try it for free at

25th stellation of Trunc Dodeca.gif

The stellation shown immediately above is the 25th, and the one shown immediately below is the 27th.

27th stellation of Trunc Dodeca

Here is the next stellation: the 28th. Unlike the ones shown above, it is chiral.

28th stellation of Trunc Dodeca.gif

This is the truncated dodecahedron’s 31st stellation.

31st stellation of Trunc Dodeca.gif

This one is the 38th stellation.

38th stellation of Trunc Dodeca.gif

This one is the 44th.

44th stellation of Trunc Dodeca.gif

The last one shown here is called the truncated dodecahedron’s final stellation because, if it is stellated once more, it returns to the original truncated dodecahedron.

Final stellation of Trunc Dodeca

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We should not have to be ashamed of our president.


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Canned Neutrinos

canned neutrinos

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A Proposal: An Ice-Tunneling Lander to Explore Extraterrestrial Sub-Surface Oceans

We have found compelling evidence for the existence of several sub-surface oceans in various places in our solar system. The most well-known of these bodies of liquid water is under the ice crust of Europa, a moon of Jupiter, with others located elsewhere. These oceans are logical places to look for signs of past or present extraterrestrial life. However, we have yet to obtain a sample of any of these oceans for analysis. It is time for that to change, but not without taking precautions to avoid damaging any such life, should it exist.


Europa (source: NASA)

What follows is my idea, freely available for anyone who wishes to use it, to safely obtain and analyze such samples. These ice-tunneling probes could be ejected from a larger lander, or simply dropped directly onto the surface from orbit. This would be far less expensive than any sort of manned interplanetary exploration. Exposure to vacuum and radiation, in space, would thoroughly sterilize the entire apparatus before it even lands, protecting anything which might be alive in the ocean underneath from contamination by organisms from Earth.

Tunneling LASSO Probe (Lander for Analysis of Sub-Surface Oceans)

In this cross-sectional diagram, the light blue area represents the ice crust of Europa, or another solar-system body like that moon. The ice-tunneling lander is shown in red, orange, black, yellow, and green. The dark blue area is the vertical tunnel created by the probe, shown shortly after tunneling begins. As the probe descends, the dome shown in gray caps the tunnel, and stays on the surface, having been previously stored, folded up, in the green section of the egg-shaped probe. The gray section is designed as a geodesic dome, with holes of adjustable size to allow heat to escape into space. An extendable, data-carrying tether connects the egg-shaped tunneling module to the surface dome. Solar-energy panels and radio transmitters and receivers stay at the surface, attached to the gray dome.  

The computers necessary to operate the entire probe are in the yellow section. The black section that extends outward, slightly, from the body of the tunneler would contain mechanisms to obtain samples of water for analysis. The orange section is where actual samples are stored and analyzed.

The red part of the tunneler is weighted, so that gravity forces it to stay at the bottom. It is designed to heat up enough to melt the ice underneath it, allowing the entire “egg” to descend, attached to its tether. Water above the tunneling probe re-freezes, sealing the tunnel so that potentially-damaging holes are not left in the ice crust of Europa. The heating units in the red section can be turned on and off as needed, to slow, hasten, or stop the probe’s descent through the crust.

Oceans in other places in the solar system might require certain adjustments to this design. For example, Ganymede, another moon of Jupiter, is far rockier than Europa. If this design were used on Ganymede, the tunneling probe would likely be stopped by sub-surface rocks. For this type of crust, the probe’s design could be modified to allow lateral movement of the tunneler, in order to go around rocks.


Ganymede (source: NASA)

On Europa, Ganymede, and elsewhere, one limitation of this design is imposed by the maximum length of the tether. We would not want to go all the way down to the subsurface oceans with the earliest of these probes, though. A better strategy would be to only tunnel part-way into the crust at first, capturing liquid samples of water before refreezing of the ice. After all, this ice in the crust could have been part of the lower, liquid ocean at some point in the past, and it should be analyzed thoroughly before heat-tunneling any deeper. The decision to make the tether long enough to go all the way through the crust, into the subsurface ocean itself, is not one to make lightly. It would be best to study what we find in molten crust-samples, first, before tunneling all the way through the protective crusts of these oceans. 

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Nine Zonohedra

Software used to make these gifs: Stella 4d, available here.

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The President of the “United States or America”

I just took this screenshot of a presidential tweet. It might get edited later, but this is what it looks like right now. He literally misspelled the name of our nation. 


Which one is it, Mr. Trump? Are we the United States, or America? 

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Meditating, and Not

I just noticed that I can elect to pay attention to my breathing, or ignore it, but one or the other keeps happening. Changing which one I focus on changes the way I think. This is interesting.

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