Making a Snub Dodecahedron

A polyhedron (many sided) is a three dimensional object that has four or more flat faces that are polygons (many edges). It is one of 13 different polyhedrons that can be built only with a combination of triangles, squares, pentagons, hexagons, and octagons. What makes at special is that of all 13, it has the most faces. The are 12 face pentagons, 60 edge triangles, and 20 corner triangles, for a total of 92 faces.

This Instructable includes a pdf for you to print the required pieces. The rest of the Instructable will show how to assemble it.

Also included is a SVG file if you care to laser cut your pieces.

Step 1: Prep Your Pieces

You are going to need 80 tabbed triangles and 12 tabbed pentagons. The pattern has 20 and 3 respectfully so you will need to print four pages and cut them out. Then fold the tabs of all the pieces. (It is easier to fold in you score the fold lines.)

Step 2: Assemble 12 Stars

Each star uses one tabbed pentagon and five triangles. Assemble them with you glue of choice. I used.

glue.

Step 3: Assemble the First Three Stars

When assembling the stars you must always glue the left side of a point on a star to the left side of a point of the other star. If it isn't left on left you are doing something wrong. You may find it easier to mark the left side tabs, on the glue surface, with a pencil or marker.

Glue the 2nd star to the 1st star and the 3rd star to the 2nd star has shown in the 1st photo. This photo also points to how the 3rd star is glued to the 1st star. The 2nd photo shows what it looks like completed.

Step 4: Add on the Next Three Stars

Take the assembly from step 3 and place the next three stars as shown in the 1st photo. The 2nd photo shows them glued on, each by one tab. (remember left/left) Also there are arrows to show where they are next glued. Turn this assembly over. It should look like the 3rd photo.

You now have an assembly with six tabbed pentagons and ten tabbed triangles.

Step 5: Three More Stars Make Nine

With the assembly turned upside down, glue on the next three stars. Their position is fairly apparent but it is shown in the 1st photo. Again the left dots help a lot. The 2nd photo shows how it should look.

Step 6: Make the Top and Attach

Follow the directions in Step 3 to make the top. Now the top is ready to be attached. This would be a god time to place anything you what trapped inside. The 2nd photo shows it all closed up.

Step 7: You Can Stop Here If You Want

Presently you have a polyhedron with 12 pentagons face pieces, 60 triangles used for edge pieces, and 20 empty triangular spaces in the corners. However. it is stable and you can leave it this way if you wish. You have 20 tabbed triangle left. I used them to make an icosahedrons as shown in the photo.

The next one you make you could place the icosahedron inside the snub dodecahedron to make an interesting table piece. You can put anything in you want in it except soup. You could also wire the a snub dodecahedron with a small corded light and you have an interesting hanging architectural lighting fixture.

The diameter of the snub dodecahedron is roughly four time the length of the sides that make up the pentagons and triangles. So it would be very easy to size you patterns to what ever diameter you want.

Step 8: Fill in the Corners

I built the polyhedron this way to show the leaving the corners is an option. For the next and all another ones it is best to glue in the corners while assembling it. Anyway glue all 20 corners into place.

Before placing the last corner you may want to put something in it. Fill it with candy and you have a pinata. Again the diameter is roughly four times the edge length.

Make one the size you want and attach a cord to it and of have hanging decoration. Spray with glitter, glue on some small mirrors, and you a disco ball. In fact I saw some shiny silver colored poster board at the art store. I might just have to make one just as soon as I can find my old polyester bell bottom slacks.

Comments

[blissjodie]

Hi! I am going to make this out of metal and need to know the angles for attaching the pieces since they will not be as flexible as the paper, can you help me with that?

Gratefully,

Jodie

[dave.vaness.79]

There are websites that will show all the dimensions of a snub dodecahedron. If you set have problems make a model from poster board and measure the angles yourself.
Did this help?

[blissjodie]

I’m actually currently printing one to make a model- paper will obviously be easier to adjust that steel- I’ve been googling trying to find the angles so I can make the metal model with a jig, but I’m not finding the angles and Don’t mathematically know how to calculate them. Hopefully the 3-d poet model will help

[rycoryco]

Hi, sir. Your istructables, collectively, are intelligent, thorough, easy to follow, and quite humorously written. I've followed, so please keep it up. (But please also go back in and do some proofreading for spelling and incorrect words chosen by autocorrect! Your content is much too good to have so many distractions!)

[dave.vaness.79]

Thank you for the kind words and the suggestion. However I have dyslexia and I just don't see a lot of the mistakes. The spell checker finds many of the mistakes but it doesn't get wrong words spelled correctly. I am an author for engineering and woodworking magazines but for those I get an editor. (also get paid) I have no such luxury here. It would be helpful is if you would sent to me the edits you find and I can fix them. Something like manskybook did. (Although I wish both of you had sent them as a private message to me instead of a public discussion.) The mistakes I find in peoples work is usually math related and I contact them privately. to inform them.

As to my dyslexia, I don't suffer from it, I enjoy it. I get a chance to see the world differently than most others. The word "rose" and "horse" look the same to me and I see the difference from contex in the sentence. Roy Rodgers is most likely riot riding a rose. but if I was to write the sentence I would not find the error.). I guess my filters that allow me to read also keep me from finding the errors in my writing.

I like to share what I see, even though it comes with distractions.
So stop and smell the horses!

ps When I edit my work I read it out loud, It slows me down and I am more likely to find errors. It also has the benefit of having me rephrase things to make then sound nice being spoken. I often wonder how many playwrights have dyslexia?

[manskybook]

A pleasing shape, and a fine educational tool. I was wondering about a few things -- first, what materials work best with this design (light paper, heavy paper, cardboard, thin metal...)? Also, while educational in defining the shapes, wouldn't the template and process work as well if the pentagons were drawn as stars with folds on the pentagon edges, rather than cuts and tabs? And, finally, while the result is quite attractive, couldn't an equally pleasing form without tabs be created by facing the tabs inward?

I have an IKEA lamp that's a polyhedron made of a stiff paper where the tabs are rounded at their ends so that the polyhedron can be assembled with rubber bands. It seems an interesting variation on your process.

[Errata: the editor in me can help point out a couple of ambiguities or errors; in the second sentence "It is" might be more clear as "This is" or, better, "The dodecahedron is"; the caption in Step 2 should say, "five triangles" (not pentagons); in Step 8, "but" should be "put, and "shinny" should be "shiny".]

[dave.vaness.79]

I kije to use card stock 65 lb or higher. Your comment about using stars leads right into my next instructable on Pythagorean dodecahedrons. A interesting observation. I place the tabs on the outside because I like the look. Also when they are on the outside, misalignment is less apparent. What I would like to do is cut the stars for tin or copper and solder them together without tabs.