Three Archimedean Solids Which Fill Space Together: The Great Rhombcuboctahedron, the Truncated Tetrahedron, and the Truncated Cube

To start building this space-filling honeycomb of three Archimedean solids, I begin with a great rhombcuboctahedron. This polyhedron is also called the great rhombicuboctahedron, as well as the truncated cuboctahedron.

Trunc Cubocta honeycomb core

Next, I augment the hexagonal faces with truncated tetrahedra.

Trunc Cubocta honeycomb core plus 1.gif

The next polyhedra to be added are truncated cubes.

Trunc Cubocta honeycomb core plus 2

Now it’s time for another layer of great rhombcuboctahedra.

Trunc Cubocta honeycomb core plus 3

Now more truncated tetrahedra are added.

Trunc Cubocta honeycomb core plus 4

Now it’s time for a few more great rhombcuboctahedra.

Trunc Cubocta honeycomb core plus 5

Next come more truncated cubes.

Trunc Cubocta honeycomb core plus 6

More great rhombcuboctahedra come next.

Trunc Cubocta honeycomb core plus 7

More augmentations using these three Archimedean solids can be continued, in this manner, indefinitely. The images above were created with Stella 4d: Polyhedron Navigator, a program you may try for yourself at http://www.software3d.com/Stella.php.

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-moon

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_g1_true-edit1

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. 

Thoughts on Colonizing Space

OSIRIS_Mars_true_color

[Image found here.]

It is no secret than I am not a fan of our current president, Donald Trump. I’ve been watching him carefully, and have found exactly one point of agreement with the man: humans should colonize the planet Mars. The two of us differ, however, on the details. What follows is my set of reasons — not Trump’s — for supporting colonization of Mars.

First, we should not start with Mars. We should start, instead, by establishing a colony on Luna, our own planet’s moon. There are several reasons for this. First, as seen in this iconic 1969 photograph brought to us by NASA, we’ve been to the Moon before; it simply makes sense to start space-colonization efforts there.

apollo-flag2

At its furthest distance, the Moon is ~405,000 km away from Earth’s center, according to NASA. By contrast, at its closest approach to Earth in recent history, Mars was 55,758,006 km away from Earth. With the Moon less than 1% as far away as Mars at closest approach, Luna is the first logical place for an extraterrestrial colony. It need not be a large colony, but should at least be the size of a small town on Earth — say, 100 people or so. There are almost certainly problems we haven’t even discovered — yet — about establishing a sustainable reduced-gravity environment for human habitation; we already know about some of them, such as muscular atrophy and weakening of bones. Creating a lunar colony would demand of us that we solve these problems, before the much more challenging task of establishing a martian colony. (To find out more about such health hazards, this is a good place to start.) Once we have a few dozen people living on the Moon, we could then begin working in earnest on a martian colony, with better chances for success because of what we learned while colonizing the Moon. 

An excellent reason to spend the billions of dollars it would take to colonize Mars (after the Moon) is that it is one of the best investment opportunities of the 21st Century. Space exploration has a fantastic record of sparking the development of new technologies that can help people anywhere. For example, the personal computers we take for granted today would not be nearly as advanced as they are without the enormous amount of computer research which was part of the “space race” of the 1960s. The same thing can be said for your cell phone, and numerous other inventions and discoveries. Even without a major space-colonization effort underway, we already enjoy numerous health benefits as a result of the limited exploration of space we have already undertaken. Space exploration has an excellent track record for paying off, big, in the long run.

Another reason for us to colonize Mars (after the Moon, of course) is geopolitical. The most amazing thing about the 20th Century’s Cold War is that anyone survived it. Had the United States and the Soviet Union simply decided to “nuke it out,” no one would be alive to read this, nor would I be alive to write it. We (on both sides) survived only because the USA and the USSR found alternatives to direct warfare: proxy wars (such as the one in Vietnam), chess tournaments, the Olympics, and the space race. In today’s world, we need safe ways to work out our international disagreements, just as we did then. International competition to colonize space — a new, international “space race” — would be the perfect solution to many of today’s geopolitical problems, particular if it morphs, over the years, into the sort of international cooperation which gave us the International Space Station.

Finally, there is the best reason to establish space colonies, and that is to increase the longevity of our species, as well as other forms of life on Earth. Right now, all our “eggs” are in one “basket,” at the bottom of Earth’s gravity well, which is the deepest one in the solar system, of all bodies with a visible solid surface to stand on. A 10-kilometer-wide asteroid ended the age of the dinosaurs 65 million years ago, and there will be more asteroid impacts in the future — we just don’t know when. We do know, however, that past and present human activity is causing significant environmental damage here, so we may not even need the “help” of an asteroid to wipe ourselves out. The point is, the Earth has problems. The Moon also has problems, as does the planet Mars — the two places are far from being paradises — but if people, along with our crops and animals, are located on Earth, the Moon, and Mars, we have “insurance” against a global disaster, in the form of interplanetary diversification. This would allow us to potentially repopulate the Earth, after the smoke clears, if Earth did suffer something like a major asteroid impact.

Since Moon landings ended in the 1970s, we’ve made many significant discoveries with space probes and telescopes. It’s time to start following them with manned missions, once again, that go far beyond low-Earth orbit. There’s a whole universe out there; the Moon and Mars could be our first “baby steps” to becoming a true spacefaring species.

[Later edit: Please see the first comment, below, for more material of interest added by one of my readers.]

Initial Transmission After Arrival, from the First Automated Spacecraft from the Pluto/Charon System, “Wizonn Shore,” to Visit the Mysterious Planet Earth, Surrounded by Its Atmosphere of High-Pressure Nitrogen (and Toxic Oxygen) High-Temperature Vapors

[Source: This is the lead story in the most recent issue of The Charon Space Central Daily, published electronically every 6th or 7th Earth day, since Pluto’s day lasts almost as long as our week. I simply translated it into English, after I intercepted the transmission, so that at least some other humans can read it.]

Earth is the most massive of the inner rocky planets, with the mass of 459 plutos, according to the most accurate measurements relayed so far by Wizonn Shore, in recent days, on the robotic spacecraft’s approach to the giant rocky world. Earth’s radius, 5.5 times that of Pluto, gives it a volume of about 160 plutos, so it is almost three times as dense as either of our homeworlds. Its surface area, as the largest rocky body in the solar system, is almost 23 times greater than that of Pluto and Charon combined. However, as this chart shows, much of Earth’s surface is covered with deadly oceans, utterly useless for any form of life as it evolved in the Pluto / Charon system. These enormous accumulations of liquid dihydrogen monoxide are the largest yet discovered anywhere, so incredibly hot (averaging ~300 kelvins) that, at Earth’s high atmospheric pressure, that compound exists as a freely-flowing, highly-reactive liquid covering over 70% of earth’s surface, except for rare areas where it is frozen, mostly near the poles and/or at the top of Earth’s taller mountains. Unfortunately, 300 kelvins is about seven times what natives of Pluto, Charon, or our colonies are used to, in terms of temperatures above absolute zero, so Earth is believed by most scientists to hold no potential for colonization.

It was this high temperature that prevented exploration of the inner solar system’s rocky planets — until recent developments in high-temperature adaptive technology made it possible for us to begin our exploration of the inner solar system, breaking the previously-inviolable heat-barrier at the asteroid belt, and sending our now more heat-resistant spacecraft into the previously “forbidden” region — first, Mars, which has been studied already with two separate mission; and now, finally, Earth. The exploration of Venus and Mercury by robot craft, however, at least for now, awaits further improvements in heat-resistant materials science.

 

The first surface-reconnaissance rover, similar to those used on Mars, was sent to a place with relatively low large-alien population density, as estimated by artificial light-output from different parts of the land surface, during Earth’s night. However, of course, its landing position had to be somewhere in the 29.2% of Earth’s surface not covered with oceans — for a rover landing in liquid dihydrogen monoxide would instantly be destroyed, as it sank to ever-more-crushing pressures in a hot liquid often called, on decoded Earth voice-transmissions, “water.” On both Pluto and Charon, in all laboratory experiments, this dangerous “water” has quickly rendered inert any electronic components — of anything — to which it is exposed. (Indeed, this, as well as the numerous deaths which resulted, was the reason that such “water” experiments have largely been abandoned, except by Earth-colonization advocates who have, a few admit, no good answers to the questions about Earth already being inhabited, nor how to deal with the toxic oxygen gas making up nearly one-fifth of Earth’s atmosphere.)

Despite the care given to choosing a landing-spot, this was still the first and only image sent before our spacecraft’s first rover was unexpectedly deactivated, for unknown reasons. These reasons are suspected to be related to the strange, pink alien creature dominating the image, although that is, at this point, speculation.

With data transmissions from the first landing probe ceased, Pluto/Charon’s automated spacecraft Wizonn Shore, launched from Charon eight years ago, continues to take pictures, from Earth-orbit, as fast as it can, while waiting on instructions from Charon Space Central regarding when to risk launching a second landing rover. Transmission of the images taken from orbit is a secondary priority to actually taking the pictures, as is happening now, so our news services do not yet have images of Earth of any higher resolutions than those already sent as Wizonn Shore approached Earth over the last few weeks.

While there has been some speculation in the press that the alien pictured in the one image sent from Earth might be the dominant species on Earth, that is not supported by visual transmissions decoded in the radio part of the electromagnetic spectrum, most of which depict the activity of a relatively hairless biped which compensates for its nudity, for reasons unknown, by covering itself with “clothes,” the buying and selling of which is, judging from the transmissions we have decoded so far, a major activity for Earth’s bipedal inhabitants.

It is these mysterious bipeds, and their activity as observed by our own devices, which all of Pluto, Charon, and our colonies on the outer moons are waiting to see images of, as taken by Wizonn Shore. Will it match what they beam out in all directions, using radio waves, with what seems to be careless abandon — or will the “as seen on TV” version of Earth prove to be an elaborate deception, on the part of Earth’s inhabitants?

Of course, the computers processing these images do not care about our collective frustration, and so we continue to wait. Might “clothes” be adopted only at a certain age by Earth’s dominant bipeds? Might that single, naked, pink-skinned alien, photographed by our short-lived landing-rover, simply be an immature form of the same species? At this time, those questions, and more, remain open.

The Misadventures of Jynx the Kitten, Chapter Two: Jynx vs. My Computer

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Jynx: 1, Computer: 0.

Tonight’s feline insanity started while we were watching Star Trek — the episode where Captain Kirk and Mr. Spock go up against a planet full of nuclear-armed Space Nazis.

Apparently, cats — or, at least, this cat — find Nazis disturbing, which, of course, they were — and will be again, if they appear in the 23rd Century . . . because some half-crazed future historian went and violated the Prime Directive, becoming, a few years later, a fully-crazed future historian. Jynx was so incredibly disturbed by the Space Nazis, in fact, that he bounced over pillows and blankets, in a series of nicely Newtonian . . .


&^ (Stop that, Jynx!)

. . . parabolic arcs, to land on my computer. He then proceeded to pause the episode — then close my browser (the picture-moment, with my wife laughing hysterically as she took it), and finally tried to bite the heads off several Space Nazis as the screen slowly darkened. After due consideration, Jynx decided this was not enough, and so, next, he reached out a paw, and quickly turned my computer completely off. A smug look followed. You haven’t seen a look this smug, unless, maybe, you’ve also seen one on the face of a kitten.

Getting it (my computer, not Jynx) turned back on was not easy. For a little while, in fact, I thought Jynx had destroyed the Internet. In reality, the Internet had been fine all along, for this picture, taken a little earlier, with a tablet, got to my e-mail account almost instantly. It took much longer, however, for me to actually get to my e-mail account.

My computer now has tiny bite marks all over it, and plays Radiohead’s song “2 + 2 = 5” so slowly that it’s turned the song into “1.5 + 1.5 = π” – and that song sounds terrible.

I hope my computer lives long enough for this post to make it to my blog. In the meantime, Jynx reigns — OW! — triumphant.

[2016 update: that computer is now officially dead. Jynx the Cat lives on.]

Craters and Slopes Near the South Pole of the Moon Adorn the Faces of a Rhombic Enneacontahedron

Zonohedrified Dodeca

The images on the faces of this polyhedron are based on information sent from NASA’s Lunar Reconnaisance Orbiter, as seen at http://lunar.gsfc.nasa.gov/lola/feature-20110705.html and tweeted by @LRO_NASA, which has been happily tweeting about its fifth anniversary in a polar lunar orbit recently. I have no idea whether this is actually an A.I. onboard the LRO, or simply someone at NASA getting paid to have fun on Twitter.

To get these images from near the Lunar South Pole onto the faces of a rhombic enneacontahedron, and then create this rotating image, I used Stella 4d:  Polyhedron Navigator. There is no better tool available for polyhedral research. To check this program out for yourself, simply visit www.software3d.com/Stella.php.