Three Stellations of the Truncated Cube

12TH STELLATION OF Trunc Cube.gif

The polyhedron above is the 12th stellation of the truncated cube. The one below is the 14th.

14th-stellation-of-trunc-cube

The next one shown is the 18th and final stellation. If stellated again, the result is an ordinary truncated cube.

18th-and-final-stellation-of-trunc-cube

These virtual models were made using Stella 4d, software you may try for yourself at http://www.software3d.com/Stella.php.

 

Calvin and Hobbes, and the Peanuts Gang: Describing Christmas in America

The cartoonists Charles Schultz knew, and Bill Watterson knows, an immense amount about the uniquely American way to celebrate Christmas.

wake-up.

Their work speaks for itself. no-money

I hope you enjoy these cartoons, and have both a Happy Christmas and Merry New Year.

calvin_xmas

Please buy the books with these comic strips. They’re easy to find on Amazon, and many other places. 

linus-assembly

Books make excellent gifts, not just for holidays, but at any time. Christmas is also a time associated with eating good food, too, of course. Calvin’s table manners are atrocious, of course, but his parents do try.

calvin

 

calvin-and-hobbes-family-dinner

Christmas Break, Winter vacation, or whatever you choose to call it gives us all time to be with our families and friends.

camping-with-friends

Santa Claus is also a big part of Christmas in America. Whether we like it or not, the same is true of capitalism.

financed-santa

flamethrower1

capitalism-interrupts

Reality often clashes with our ideals. That’s part of being human, in any season.

money

flamethrower0

charlie-brown-acting-like-calvin

flamethrower

An emotionally-charged phrase, “true meaning of Christmas,” is repeatedly explained, forgotten, rediscovered, celebrated, etc. — and, of course, we argue about it. We’re Americans, after all.

Sometimes, we also listen to each other. Other times, we don’t, even when we need to, and the opportunity presents itself. 

competition

grenade-launcher

christmas-tree

The holiday season is often rough on those of us who struggle with depression. These cartoonists tackled such issues head-on. However, they never claimed to have all the answers.

get-some-friends

if-i-get-a-present

santa-flambe

Happy Christmas, and Merry New Year, to you and yours.

charlie-brown-acting-like-calvin

show-and-tell

show-and-tell

Peace be with you.

lifestyle

mom-dad-santa-hobbes

cute-snoopy

lukewarm-tapioca

smack-susie

who-needs-santa-claus

loot

nap-time

marx-and-tv

One thing both comic strips have in common is a focus on children and childhood. Reading them can help one keep from losing the essence of youth, no matter what age one reaches.

mcdonalds-and-walmart

national-dog-week

xmas

Bill Watterson, Charles Schultz: thank you for sharing your ideas about Christmas, and life itself, with us, over the decades. I’ll let Schultz have the last word.

laugh-at-oneself

 

The Minute of the Winter Solstice

winter-solstice

Shortly before Winter began at 4:44 CST (USA), I wondered if it were Winter yet, and googled it. Here’s what I found. I was astonished when I looked at the current time and the time of the Winter solstice, using a Google-search, and they matched. This was a bizarre coincidence, and I thought it worth a screen-shot and a blog-post, all while in a bewildered state.

2016: a year that could never have been predicted. There’s little time before 2017 is here. May it be a better year for us all.

Reading: It’s What You Do

read

I have observed many families where reading is simply what people do. In one, a favorite family story is of a little girl (a toddler) whose parents and older brother were sitting in the living room, reading. No one told anyone else to read; this was simply something people did. The little girl was so young that she was holding her book upside-down, but she was doing her best.

This family does not consent to be identified by name, but I do have permission to describe the scene above. There are thousands of families like this — in the USA alone. May they increase in number.

When reading is simply what you do, it has a huge impact on who you are.

President-elect Donald Trump, and President Vladimir Putin

putin-and-trump

Source of quote: The Washington Post, online edition, December 14, 2016: https://www.washingtonpost.com/world/europe/the-kremlin-likes-the-hacking-attention-but-not-the-blame/2016/12/14/65279738-c177-11e6-92e8-c07f4f671da4_story.html?utm_term=.fc453119c6fd.

Fiona Hill co-authored the 2015 book Mr. Putin: Operative at the Kremlin, available here, on Amazon. She is also (according to the Washington Post story linked above, written by David Filipov) a scholar at the Brookings Institution. Here’s the headline, taken from a screenshot.

moscow

For those who do not know, The Washington Post is the newspaper which blew open the Watergate scandal, and that, in turn, brought down the Nixon administration.

These are facts.

A Space-Filling Lattice of Truncated Octahedra

augmented-trunc-octa

Truncated octahedra are among the special polyhedra which can fill space without leaving any gaps. There are others, as well. This image was created using Stella 4d, software you may try, for yourself, right here. There is a free “try it before you buy it” download available.