Results tagged “Origami” from Kazza the Blank One

So the dodecahedron and the icosahedron are dual solids.   The icosahedron has 20 faces and 12 vertices, while the dodecahedron has 12 faces and 20 vertices.  It means that if you truncate either one of them to the same point, you send up with the same shape - the icosidodecahedron.

I made the paper solid from a net from

Paper icosidodecahedron

And I made the paper geodesic version from Vince Matsko..  (If using his nets, you will need three pages of the pentagons, and one page of the triangles.  The tabs for the five triangles making up each pentagon will go in the middle.  The triangle is equilateral so doesn't matter where you put the tab).

Paper geodesic icosidodecahedron

Here's the two of them together..


Four frequency paper geodesic icosahedron

Over the past few weeks I've been making the paper geodesic icosahedron pictured above.

As with all my other balls in the past few months, I got the nets from Vince Matsko's website.  The problem with this model is his instructions aren't very useful if you don't have Magnus Wenninger's Spherical Models book:  

Not so challenging as its 8-frequency companion, this model requires just 320 individual spherical triangles of 5 distinct types. Bands are labelled numerically as in Figure 48 (p. 95) of Wenninger's Spherical Models. Although not individually labelled, the bands adhere to the following scheme: in Table 4, the arc in the third column of the list of bands is always next to the tab. You can easily check this by noting that in a circle, larger angles subtend larger chords, so you can measure chords to find out which angle is which.

The finished model will be approximately 14 inches (36 cm) in diameter.

Vince's net pdf document contains bands for the five different triangles.  But without Wenninger's book, you've got no way to know which band is which.  So here's one I prepared earlier:

Four frequency icosahedron instructions from Wenninger

You can see from the diagram there are five different shaped triangles, numbered 1 to 5.  This matches the pdf document on Vince Matsko's site.  Also take note of the lettering - letters a to d indicate the length of each side (remember these aren't equilateral triangles!  see Wenninger's book for more details on the mathematics of it).

The next line of instructions:

Although not individually labelled, the bands adhere to the following scheme: in Table 4, the arc in the third column of the list of bands is always next to the tab.

Again, without the book you've got no hope.  And even if you do have the book, it can take a while to figure out what he actually means.  Eventually I figured it out.  Here's the table he's talking about:

Four frequency icosahedron instructions from Wenninger

Highlighted on the right is the "third column" he's talking about.  If you look at the first picture from the book further up, you can see that triangle number 1 has "a", "a", and "b" as the lengths of its bands.  And triangle 2 has "b", "d" and "d".  And so on.  The table above shows this as well.  Now, in the table above, what he's saying is that the "tab" in the printouts is always next to the letter in the third column.  So for triangle 1, in his pdf it will be a-b-a-tab.  Triangle 2 will be d-b-d-tab, and so on.  Here's what it will look like:

Four frequency icosahedron bands

You'll note above that triangle 3 is asymmetric (look at the big triangle at the top to confirm this).  Half the triangles are "left-handed" and half are "right-handed".  If you were to print out all the copies of triangle 3 and fold them the same way it wouldn't work.  

Here's the diagram from the book, but also showing the locations of the tabs once it's all put together, and showing left and right handed triangle 3.

Four frequency icosahedron instructions from Wenninger

Now the triangle above is just one "face" of an icosahedron.  Remember an icosahedron has twenty sides.  So you will need 60 bands for triangle 1, 60 for triangle 2, 120 for triangle 3 (60 left-handed and 60 right handed), 60 for triangle 4 and 20 for triangle 5.  Using Vince Matsko's nets that's 10 pages for 1, 2 and 4, 20 pages of 3, and 3.3 pages of 5 (4 pages with a couple of leftovers).

But.  If you were to print out the nets on A4 paper, the ball would be *huge* - double the size he says in his instructions.  So I resized the images and pasted them into a word document.  While I was at it, I flipped a copy of triangle 3 so the black lines would always be on the outside.  Attached is my word doc with the nets that I used.  It includes instructions on how many of each triangle you will need.

Right.  So now we've got the design sorted, let's get started.

I printed each triangle on a different coloured piece of paper.  And for triangle 3, I did the left and right handed triangles on different coloured paper (blue and green).

Four frequency icosahedron paper

Next, cut them up.  Each one took about thirty five seconds to cut.

Once they're cut, fold them up.  I folded them so that the black line from the printout would always been on the outside.  Each one took about twenty five seconds to fold.  I did most of this in front of the tv.

Four frequency icosahedron bands folded

Once they're glued into triangles (each one took about fifteen seconds), you can lay them out to see what they will look like before gluing.

Four frequency icosahedron triangles

I started a production line - got all sixteen little triangles for each face and put them together.

Four frequency icosahedron production line

Four frequency icosahedron production line

Then I put them together in the correct configuration, with all the tabs in the correct locations.

Four frequency icosahedron production line

And then glued them all together.  Here's all twenty faces glued:

Four frequency icosahedron production line

Now for the really fun part - gluing all twenty faces together into a ball!

Four frequency icosahedron with five faces glued

Four frequency icosahedron half way

Four frequency icosahedron half way

With six faces to go, it will fit quite nicely over your head.. ;)

Four frequency icosahedron helmet

And finally, we're finished!

Four frequency paper geodesic icosahedron

A very time consuming, but quite impressive effort :)

Another model I started making nearly three years ago was a paper geodesic octahedron.

Geodesic Octahedron

Or, if you please, a geodesic hexahedron (cube).

Geodesic Hexahedron

It's a dual model because the model is made up of forty-eight triangles and you can look at it as eight faces of six triangles (octahedron), or six faces of eight triangles (hexahedron/cube).

This was another pretty simple model to make, with the net taken from Vince Matsko.  You'll need to print eight pages of that net, but there's a catch: you need to make half of the triangles "left-handed" and half of the triangles "right-handed" - folding the strips "inwards" for half, and "outwards" for the other half.  If you want to make a two-colour model, as I have above, you'll need to make all the triangles of one colour left-handed, and all the triangles of the other colour right-handed.  Again, I stuffed this up when I was making it, and so I've had to make two models - oops!

Geodesic Dodecahedron

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A little while ago (crap it was nearly three years ago!) I started building one of Vince Matsko's geodesic dodecahdrons out of paper, based on Magnus Wenninger's Spherical Models.  I finished it a weekend ago (after realising I'd stuffed up when I started and was trying to do it with three colours, but it looks a lot better with four colours, so had to make the white pentagons as you see below).

Geodesic Dodecahedron

It's a pretty straightforward model to build.  Each pentagon face of the twelve faces of the dodecahdron is divided into five triangles, so you'll need sixty triangles.  Vince Matsko's net has twenty per page, so you'll need three pages.  Although if you want to make different colours like I have you may need more and have some leftover.  When you fold each strip, the little tab will always be right in the middle of the group of five triangles.  I stuck each group of five triangles together, giving me the twelve faces, then glued the twelve faces together into the ball.

A simple and fun little model to make.

Rainy Club Weekend

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After the Lego movie I went home to get my car and *stuff* then headed out to the club to meet up with the sweetie who went out earlier in the day.

We had the place to ourselves for most of it which was nice.  Saturday afternoon I went for a wander around the perimeter.

Club corner

Club bug

It rained most of the weekend too, so the planned hazard reduction bonfire never went ahead.  I cut and folded and glued little bits of paper.

Geodesic octahedron

Geodesic dodecahedron

Geodesic dodecahedron

I left Sunday morning to get a quick visit in to the Airport Open Day.

Other Fun Stuff

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Just a stack more photos that still haven't made it online..

A truncated dodecahedron I made for a guy at work

Truncated Dodecahedron

George, who jumped onto my seat straight after I got up because it was warm

George takes my seat

Some daffodils out the front


Lego R2-D2 and C-3PO in Myer in Sydney

Lego in Myer

Lego mosaic in Myer in Sydney

Lego in Myer

Sometimes the algae in the pool gets away from me.


Add flocculent and wait a day for it to settle


Vaccum to waste - shiny!


A lovely dragonfly at work that obligingly sat still for us to photograph it


A ginormous caterpillar - a White-Stemmed Gum Moth


The Birds!  A huge flock of galahs out the back (this wasn't even all of them)

The Birds

Neil with his brand new car that he got himself for Christmas.  His last car was a Datsun 120Y that he bought new - in 1978!

Neil and his new car

Last week (or over the weekend?) I made an icosahedron to take to work to demonstrate how my buckyballs are made.  Of course I also needed a truncated icosahedron.  Took a couple of nights to make it, and finished it tonight.  Made from one sheet of A4 paper, cut, folded and glued.

Truncated icosahedron
And here it is with the larger one I made years and years ago.  It's very delicate so wouldn't survive going to work.

Truncated icosahedra
I think our printer needs more toner.  Time to buy a new printer? hrmmm

You're a Star!!

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Ok that's what I said to the sweetie when I handed him this...

Stellated Dodecahedron

Isn't it cute!! :)  I suppose the picture doesn't really give you an idea of scale, but it's pretty little, because I made it out of a single piece of paper cut from one A4 sheet of paper.  I haven't had a stellated dodecahedron in years.  I used to have one hanging in my window at Como.  And one painted silver that was totally spectacular.  Those ones I had to draw the nets for myself! Gah! Give me the cheat's method of the internet any day ;)  If it didn't take like an hour to make them and be so delicate I'd make them as Christmas decorations :)  I made it from the net on the first page of this PDF, but you could make a little bigger using the split page version.

The other thing I made on the weekend was my first sonobe model - a simple sonobe cube.  I followed this pattern for putting the cube together, although this pattern to fold the sonobe units.  There seems to be a couple of different ways to fold them.. hrmm.

Sonobe Cube

Day today was ok.  Sorted tax nonsense.  Really need to get an accountant methinks.  Anyone recommend any good ones in Canberra? 

Oh, and nearly forgot .. AMAZING RACE AUSTRALIA!!!!!! SQUEEE :)
I used a double episode of Lie to Me last week to fold 90 green phizz units.  I used the entire drive back from the coast on Sunday to fold 90 pink phizz units.  I folded 90 blue phizz units on Sunday night while watching Border Security, The Force and Bones.

The result:  270 phizz units.

Bag of phizz units
I started construction on Sunday night.

Three phizz units joined
The top pentagon
Top of phizz ball
Then I spent just about all of last night building it, and finished it this morning.

270-edge phizz buckyball
So there we have a 270-edge buckyball.  I actually don't know what this solid is called.  It has twelve pentagons for the apexes and seven hexagons on each of the twenty "faces" (the two edge ones are common to the adjoining faces).  

Rather than using blue paper for the pentagons and pink paper for the intervening hexagons (as seen in my previous balls), I decided to use three colours and make a Hamiltonian Path ball.  This effectively means that a colour never touches the same colour - always at the points there are the three different colours.  I'd tried this with a dodecahedron (which is pretty simple) and there are patterns floating around for doing it with truncated icosahedrons (here and here, although I think there's a mistake on that second link. Edit: looks like it's been fixed).  But I can't find anything for a ball this size.  So I had to wing it.  I expected it to be a nice double helix all the way around from top to bottom, starting with the top pentagon and finishing with the bottom pentagon.  But this wasn't the case.  Two-thirds of the way through, the loop doubled back on itself around a couple of the lower half pentagons and went the other way.  I'm still trying to figure out how to show this, as it really doesn't all fit in one photo and drawing a 3D shape like this is pretty complicated.  If I can figure out a way to do it I will.

So here's all my phizz balls.  I don't think I'll be making any more any time soon.
I still want have a techie post about them.. one day .. ;)

Phizz Balls

So after much searching, I finally found some more info on my geodesic buckyball.

Geodesic paper sphere

It turns out the book I probably originally got it from was Spherical Models by Magnus J. Wenninger.  (I found a reference on this site, and there's also his other book - "Polyhedron Models" - which I even have some old photocopies of some of the other shapes! A full list is on Wikipedia).

So with that reference I did some more hunting and found this site which has all the nets for the spherical models!!  Or at least a bunch of them.  I was most interested in the truncated icosahedron, but will have a look at making some more of them as well.  

Excitement!! :)


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Went to Fyshwick this arvo so the sweetie could get a new mini stereo for the bedroom (the last one died - won't power on - probably something simple, but not for us.  Besides, he wanted one with an iPod dock).  Stopped in at Officeworks so I could buy some paper (so I don't have to keep stealing paper from work to make my origami). 

Apparently the water signs had another farewell message on them yesterday, but when we went past the one on Barry Drive today it was turned off :(

Came home and made another dodecahedron, this time a three-coloured one.  Looks pretty good.  It's a pity it takes so long to fold PHiZZ units, or I'd have made a bigger one.  Learnt about the Hamiltonian Path.  Photos soon - will be doing some more dedicated stuff for all the origami I've been doing.  This site totally made my night!  Will be naffing some of the patterns off that to make :)

Also made excellent progress on the jigsaw.  Did more on it today than in the three weeks or so that I worked on the flowers.

And just so this blog entry isn't completely colourless..

An eastern rosella in the neighbour's tree the other morning.

Eastern Rosella



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Finished the larger buckyball tonight.  And made a dodecahedron as well.  But I want dedicate a bigger post to the creation of them.  

I will provide a quick picture of the three of them (so far) together, and the phizz units needed to make the 120-unit ball.

Many phizz units
Phizz Balls

Hump Day

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Slightly less crazy day at work, and Windy figured out something that I never could last year, so that was pretty nifty.

The sweetie cooked dinner tonight, so got my news feeds read early, and scanned another eighty photos mostly from 1993.

That album had another St Clements bushwalk to the National Park, Rock by Megalite concert, a trip to Barrington Tops Guest House, a Sydney Harbour cruise, Easter Camp 93, and a trip to the zoo with my mum.  

The Barrington Tops trip was really cool.  I wouldn't mind going back there again one day.

Barrington Tops Guest House
Me with crimson rosellas
Horse riding
February 1993 saw me rearrange my room again.  The previous arrangement had the biggest open area in front of my desk and bed, but in plain view of the door.  This became problematic because whenever I had any mess on the floor, it was clearly visible to anyone walking past.  So I swapped the desk and bed, leaving the biggest area nicely hidden behind the bed.  It stayed in basically this configuration until I moved out of home in 2000, although a big bookshelf was added, I got a new desk for my first computer(s), and I had a budgie on the drawers on the right for five years..  It's weird because it felt like I didn't have it that way for very long, yet it was probably that way for the longest of any room configuration.  I guess that's what happens when you get old and time speeds up heh.

My room

I was also determined tonight to get the Jackstone right.  So watched this video again and figured out which step I'd missed.  So it turned out relatively well.  Although I did manage to get grease on my fingers from somewhere, maybe the scissors, and ended up with a couple of grease spots on it :/

Blue Jackstone


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So after last night's very productive night .. today was crazy (as always, must remember to breathe, lower blood pressure .. *sigh*) then accidently got trodden on so just felt *blah* tonight..  so all I got done tonight was to put out the bins and backup my hard drive.  Yay.

Had another go at making a Jackstone.  Got frustrated *again* by the crazy thing.  Even watched a video of the tricky bit and couldn't see how it was done.  Persisted but still had the same problem I have every time at the end, where when I go to pull it apart, there's no folds to mark the definition of the horizontal spikes.  So it doesn't snap into place properly.  Obviously I'm doing something wrong when you have to work with the underside bit.  I even pulled it all apart so I could try and get them right.  But no luck.  So again, a pretty pitiful attempt (photo is of the best side, the other sides are pretty terrible).

Pink jackstone

Paper and Cyclones

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Spent the better part of tonight researching geometric origami.

I started off looking for a template/net for this sphere - 

Geodesic paper sphere
I made that sphere in second year uni (1993) when I was off sick for two weeks with pneumonia.  I was too tired to concentrate on uni work, and this was technical but mindless, so provided a nice distraction from feeling pretty blah.  It's made from curved strips of paper folded into little triangles (5x12 for the pentagons and 6x12 for the hexagons).  The little triangles are all stuck together into the pentagons and hexagons, and then those building blocks are stuck together to make a nifty little geodesic sphere.  Quite simple really.  But of course I can't find the templates to make the strips of paper anywhere on the internet.  I could always create my own, but it's so much easier if someone's already created templates!  The closest I came to even finding anything like this on the web was this site but no templates there.

So meandered on from there and went looking for instructions for Jack Skillman's Jackstone.  This has been discussed previously on this blog here, here and here.  Still no closer to finding any decent instructions on the net though :(

So a pretty unsuccessful night all up.  But did look at *lots* of geometric origami pages so will probably do something from one of them soon.

Here's what I have decorating my desk at work now..

Desk origami

And now for something completely different..

Former Tropical Cyclone Yasi is still going.  It's made its way all the way across Queensland and is now raining all over the Northern Territory.

Cyclone Yasi
This picture, taken from Channel 9, stood out for me.  Even though the roof has been blown off this house in Tully, everything in the kitchen, from water bottles to eggs, is all just sitting there as if nothing had happened!  Freaky!!

Yasi aftermath

PHiZZ Ball

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So yesterday my boss' boss' boss' boss was on the floor and said that the person she'd passed my five intersecting tetrahedra link to had also gone and done a PHiZZ ball.

So of course I had to do one too :)

Took home five pieces of blue paper (to make 60x7cm squares) and three pieces of pink paper (to make 30x7cm squares) - twelve 7cm squares to an A4 page.

And spent all of last night folding.

PHiZZ units
PHiZZ units

Tonight we got home late (after having dinner at The Dumpling Inn and doing our shopping), so then spent the night putting the thing together.

PhiZZ Ball construction
PhiZZ Ball construction
Ta da!

PhiZZ Bucky Ball
PhiZZ Bucky Ball
Fun fun fun.  And surprisingly frustrating to do without a right-hand thumbnail (mine shattered the other night trying to lock one of our windows).

For some reason last night I had the urge to build five intersecting tetrahedrons.  I'd built one before, but wanted to do a smaller, coloured one for work.

So did some research, and stole a piece of four different coloured papers and a white and brought them home tonight.

Here's the old one and all the paper cut up.  The ones on the right were the offcuts.

Five intersecting tetrahedrons - the beginning

One tetrahedron..

One tetrahedron

Two tetrahedrons..

Two tetrahedrons

Three tetrahedrons..

Three tetrahedrons

Four tetrahedrons..

Four tetrahedrons

And finally, five intersecting tetrahedrons!

Five intersecting tetrahedrons

Kazza's "Boring Life Of a Geek" aka BLOG

IT geek, originally from Sydney, moved to Canberra in 2007. Married to "the sweetie", aka Stu. Prolific photographer, Lego junkie and tropical fish keeper.

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