Black Star – Paper Polyhedron

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Introduction: Black Star – Paper Polyhedron

About: We creating models of mathematical polyhedra. Collection of unique in form and coloring geometric shapes, each of which has a name and precise mathematical properties.

Black Star – Paper Polyhedron
To assemble a polyhedron, you need to download a shaped net.

Print the shape net on three A4 sheets.

You can use one of three types of shape nets:

- Or №1 polyhedron shape net (print 3 copies)

- Or №2 polyhedron shape net (print 3 copies)

- Or №3 polyhedron shape net (print 3 copies)

Maybe there is a ready-made kit so that I don't cut out the parts, but just glue it together?

Yes, there is such a set. Called Magic Edges 28.

It can be found on Amazon:

https://www.amazon.com/dp/B07YTZK46V

Step 1: Preparation for Assembling a Polyhedron

For convenience, it is
recommended to draw the fold lines with a

ballpoint pen. This will speed up the bending process of the petals. To draw fold lines, you will need a pen, a ruler, and a few sheets of plain paper to create a soft-surface lining. The ball on the tip of the ballpoint pen, drawing a line, creates pressure on the paper and pushes it slightly. The resulting fold line is quite comfortable. But, if you wish, you can refuse this stage of work and go straight to the next one.

Each detail should be cut along the contour using ordinary scissors.

Step 2: Assembly of a Polyhedron.

1. We glue the parts together through the side triangular surface. An example of two pieces glued together.

2. We glue the third part.

3. We glue three more parts and get a base of six parts.

4. We turn the base over.

5. We glue five more parts.

6. The final stage, we glue the last 12th part.

We get the finished model of the polyhedron.

Step 3: Polyhedron Properties.

The polyhedron has the property of symmetry.
Such a star-shaped form in mathematicians has its own name.

The full name of the polyhedron is the 9th stellated form of the icosahedron.

To obtain such an unusual pattern, it is enough to give one face a certain color.

The combination of 60 of these patterns creates a three-dimensional geometric shape.

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2 People Made This Project!

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10 Comments

0
EnjoyEverything
EnjoyEverything

Question 9 months ago

What kind of paper have you used?

0
Polyhedr
Polyhedr

Answer 9 months ago

This sample is assembled from thick paper - 200 g / m2
It is three times thicker than regular office paper.
The plus is that the construction of such paper is more durable. But there is also a disadvantage: it is more difficult to work with such a paper.
Ordinary office paper can also be glued. And that will be good work too. But the star will be fragile. Falling on the floor may not survive.
The shape net drawing is designed for paper with a density of up to 250 g / m2. If the paper is thicker, but the drawing will have to be corrected.

0
btparrish1
btparrish1

10 months ago on Step 3

My platonic solid game isn't super strong, but isn't this the final stellated form of the dodecahedron which stellates into an icosahedron?

0
Polyhedr
Polyhedr

Reply 10 months ago

Hi. This model is one of the stellated forms of the icosahedron. But not the final form.
The final stellation of icosahedron has 32 beams and looks like this:
https://youtu.be/IPLFWU6wlhs

0
robertmeals
robertmeals

Reply 10 months ago

dodecahedron means 12 sided. icosahedron means 20 sided. btparrish1 is correct. The final stellation you mention actually has 60 points, 32 is possible if you start with a tetrahedron and stellate each side with 4 points, there are only 5 numbers to get a shape from a platonic solid (4,6,8,12,20 sided). I still think you did a wonderful job of design and an ecellent execution of a difficult shape.

0
Polyhedr
Polyhedr

Reply 10 months ago

Robert, thanks!
The shape is really beautiful, but not the most difficult to assemble. For this polyhedron, we managed to create a structure that is very easy to assemble. Even a novice student can handle it.
But we also have more complex forms. Like this one:
https://www.amazon.com/dp/B07FDZQFLT

0
Marcy Kuntz
Marcy Kuntz

Question 10 months ago

Where do you purchase the display spinner?or do you make it...

0
Polyhedr
Polyhedr

Reply 10 months ago

Many thanks!