Saturday, November 16, 2019

A STEM Project: A Great Stellated Dodecahedron Model

A Great Stellated Dodecahedron 

A convex regular icosahedron is the foundation for making this great stellated dodecahedron.  Stellated means "star-like".  The icosahedron is transformed into a star-like polyhedron by attaching twenty isosceles triangular pyramids. A great stellated dodecahedron has 12 faces, 20 vertices and 30 edges.  


The convex regular dodecahedron is one of the five regular Platonic solidsThe convex regular dodecahedron has three stellations, all of which are regular star dodecahedra. They are the small stellated dodecahedron, the great dodecahedron. and great stellated dodecahedron. I made the small stellated dodecahedron in a previous post. https://papercraftetc.blogspot.com/2019/11/a-stem-project-small-stellated.html  and the great dodecahedron in a previous post. https://papercraftetc.blogspot.com/2019/11/a-stem-project-great-dodecahedron.html Here I will be making the great stellated dodecahedron.


This video depicts the transformation from a dodecahedron to other stellations. 



Please note, this model requires patience in gluing.  It is not hard to put it together but drying time is crucial. I used Aleene's Fast Grab Tacky glue.

Here is the PDF.  I used 65 lb. cardstock.

https://drive.google.com/file/d/1XFX6jUpF9myYPSNOoZZwakO_jxYyzTPv/view?usp=sharing


Here is the .Studio file.
https://drive.google.com/file/d/1CaRSTpRXyUmiKqFd1aFJ9PhCx_0zOyK7/view?usp=sharing


Fold the perforations on the icosahedron.

Glue the tabs to form the icosahedron.

Fold the perforations of the triangular pyramid. Apply glue on the left side which looks like a triangle. 

Adhere into a pyramid shape.  Repeat to make 18 more triangular pyramids.

I folded the tabs of the base as shown so that they would lay flat for gluing.

Glue the triangular pyramid to the icosahedron. In this photo, I am showing the amount of glue that I applied to the icosahedron and a picture of the glue that I used.

Tape a string in the middle of the last triangular pyramid.  This will allow you to hang up the model. Apply glue on the triangle tab and make sure that the string protrudes from the top at the apex of the pyramid.


7 comments:

  1. Really helpful and clear explanation! Thank you!

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  2. I made one of these thirty odd years ago, using a formula in an old geometry book for the dimensions. I use cardboard for the base, cut crosscuts on each face and put a string of tiny lights inside. I left one face unglued so the string of lights could be changed. This face had two tabs so they could be tucked in to the rest of the base and be flapping about. I then poked one light through each crosscut before gluing on the pyramids, which were cut from vellum. I used a seamstress marking wheel to create tiny perforations along each fold line of the pyramids. I made the pyramid opposite the top one two and a half times as long as the others. The cord for the string of lights came out of the face of the cardboard which was tucked in rather than glued. This served many years as the Star of Bethlehem in many Christmas Pageants! It was truly beautiful as the pyramids glowed, the edges twinkled and the one long pyramid pointed to the manger.

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    1. Glad that my posting allowed you to relive your fond memories! Thanks for sharing! Merry Christmas!

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  3. Do you have a copy of this with just the points?

    Im trying to make a decoration for my preschool class and they were super interested in the small stellated dodecahedron i made from a book the art teacher had lying around.

    Thanks!

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    1. They are simply the points of a regular pentagram. Each little pyramid is three of these around an equilateral triangle base. There are 20 of these pyramids around an icosahedron core. The picture of the the finished model at the beginning of this article is either badly distorted or as I suspect the model is incorrect. There are two length edges for the entire polyhedron they are in Phi proportion to each other.

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    2. Thank you for your input. I have corrected my mistake.

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  4. The PDF which is included in this posting has all of the pieces needed to make the star. You might be interested in my latest blog posting as it is a quick ornament to make (a little too hard for presschoolers) and uses some of the same concepts. https://papercraftetc.blogspot.com/2021/12/25-days-of-christmas-decorations-day-1.html

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