# Geometric sculpture from 72 pencils

George W. Hart is a sculptor of constructive geometric forms (and writer of the Math Monday columns at Make), and I've long been an admirer of his work. Reproducing his art is far from trivial - I once tried to build his Chronosynclastic Infundibulum, but broke so many CDs I gave up in disgust. However, I recently discovered that Alejandro Erickson, instructable-r and self-confessed mathemagician, lives in the same city as me and runs workshops on geometric construction, so we hired him for an afternoon. He was the great geometry guru we'd hoped he'd be, and he kept 6 kids and 3 adults well entertained and busy making tensegrities. As a special request, he also taught two of us how to make a replica of Hart's 72 pencils sculpture (Hart made a limited edition of 19 unique examples of these). It took a couple of leisurely hours to build and glue, and with supervision was surprisingly easy to make. It can be assembled inexpensively using wooden pencils (conveniently sold in packs of 72!), a few rubber bands and a little superglue, in pretty much exactly the same way as Alejandro makes his Hexastix sculptures (see below for the video). The hexagonal cross-section of the pencils make them a very natural fit for this geometric form, as the holes in the lattice are themselves hexagonal. The erasers are arranged tetrahedrally with respect to one another; the volume enclosed by the pencils is a rhombic dodecahedron. It's a neat piece of art that I'm pleased to own; many thanks to George W. Hart for the inspiration and Alejandro for the instruction!

I made a variant of this sculpture using 76 pencils, in which the pencils form six-pointed stars rather than hexagons.

Video: Follow Alejandro's instructions, but build only as far as a hexagon consisting of a ring of 18 pencils, removing the inner pencils as you go. If you find the erasers aren't arranged tetrahedrally (as I did), just invert one ring one pencil at a time until your sculpture looks like the original. Superglue the joints before removing the rubber bands.

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akarod796 months ago
Saw this and thought what a great project to do with my son (9 yrs old). Of course I left him do 95% of it. He then told me "gluing is going to be tough, so you can do that." So here is our completed project. We had a small accident where we...my son...we broke a pencil and the only other pencil we had was a green one. We decided to keep it as memory.
makendo (author)  akarod796 months ago

Great job!

I didn't have enough pencils so I cut 13 cm lengths out of bamboo BBQ skewers. 72 pieces total.

1 year ago

can you teach me

i am very interstring it

makendo (author)  Jayefuu1 year ago

Cool, thanks for posting. I keep meaning to do it again myself with 4 different colours of pencil, but I never remember to actually buy any...

motions1 year ago
So I had to make one of these. It was a lot easier than it looks. I have absolutely no need for it at ALL but I just had to try it. Luckily, my sister-in-law is a teacher so I gave it to her and she loved it.

Next step, build this using PVC pipe for a huge yard sculpture. ;-)
MOMO1002 years ago
Awesome
hufan2 years ago
I'm gonna try it tomorrow
craftmachine2 years ago
great!
white dragon2 years ago
can i use this as my cantamaths project in school???
makendo (author)  white dragon2 years ago
2 years ago
sorry i didnt catch that...could you please say it differently? THNX
makendo (author)  white dragon2 years ago
"Sure"
2 years ago
thanks you very much!
parmsco2 years ago
I could not find 72 pencils at my house so I made it out of toothpicks and used rubber bands from when I had braces.
makendo (author)  parmsco2 years ago
That's really neat. Thanks for posting it!
playfulplans3 years ago
Wonderful- excellent work.
XP13 years ago
Thank you so much for the Instructable and video. It took a while; however, I finally figured it out. Now I just need to get some Super-Glue.
makendo (author)  XP13 years ago
Nice!
Just like to let you know that I built one of these and that it works as a vary unique pencil holder.
mooner773 years ago
would it be easier or harder to use straws?
makendo (author)  mooner773 years ago
I think pencils are probably easier. Straws would tend to deform too much.
Chimex143 years ago
HEY just btw, this geometric sculpture pencil thing made it to Failblog, and it was categorized as WIN!
It then made it to teh featured section of iFunny.
So kudos
Ppl think that u b epic
I've now made a puzzle based on this sculpture available on ebay:
http://cgi.ebay.ca/ws/eBayISAPI.dll?ViewItem&item=250996113976
Here is an image of it (large version at http://geoburst.ca/ebay/chiastix/chiastixclose.jpg )
I got super enthused and did not see the smaller note above the video saying

"Follow Alejandro's instructions, but build only as far as a hexagon consisting of a ring of 18 pencils, removing the inner pencils as you go. If you find the erasers aren't arranged tetrahedrally (as I did), just invert one ring one pencil at a time until your sculpture looks like the original. "

I had more than enough pencils but realized I used way more than 72... And I also noticed one axis set was not oriented correctly. And on my pencils, the pencil logo is not oriented in any consistent fashion. I figured out the removing the central core of pencils and re-oriented one axis.

Now to super glue...
makendo (author)  innovationcreation3 years ago
Good work... yeah, having one the pencils aligned wrong is annoying but doesn't take too long to fix, fortunately.
AWESOME...no life?
3 years ago
Jealous?
3 years ago
Problem?
footbawl4life3 years ago
bravo.
Xeriel3 years ago
Will it hold precariously together without any glue or elastics, or does the whole thing fall apart?
makendo (author)  Xeriel3 years ago
No, it would just fall apart.
EVM3 years ago
Me and a friend made one and turned it into a pen tray by cutting out the middle and making a floor in it.

Thanks for the great idea

Greetings from the Netherlands
makendo (author)  EVM3 years ago
Wow, it's actually functional now... nice! What did you use to cut out the middle?
3 years ago
We used the blade from a hack saw. The small pegs at both ends of the blade were grinded off with an angle grinder to prevent them damaging other pencils and we wrapped one half with band-aids so we didn't cut ourselves. In total it took 24 cuts
mrpesas3 years ago
I saw this instructable and said "that's cool...wait...I have a box of pencils too" My students were very impressed with my "skillz"
makendo (author)  mrpesas3 years ago
Bet they were, nice!
Win Guy3 years ago
Makers gonna make. I am a maker.