Straw Polyhedron

 

 

Materials and tools

Ø         3 to 6mm diameter straws

Ø         A ruler

Ø         A (good) pair of scissors

 

Introduction

    This explanation sheet shows how to make three dimensional-shapes with plastic straws without any glue.  Each edge is connected by two apex joints.  The joints are also made with plastic straws.  We need different numbers of straws in order to make different polyhedron.  For example, to make tetrahedron a joint needs 3 pieces of short straw and to make octahedron we use four pieces.  The following table shows required numbers of short straw.

 

Table 1.

Polyhedron

Surfaces

(f)*

Number of

Edges (e)*

Number of

Apexes (v)*

Required number of short straws for 1 apex joint (c)

Total number of short straws to make all joints (c*v)

4

6

4

3

12

6

12

8

3

24

8

12

6

4

24

12

30

20

3

60

20

30

12

5

60

* v + f – e = 2

 

Sample: How to make a 4 arm joint for octahedron

    Follow the drawing and explanation below to make good joints.  When you insert the short arm into next straw’s long arm, it is very easy to slide the short arm up to the end of the slit on it, but from the end of the slit it becomes difficult then squeeze short arm slowly and firmly into the long arm.

    After you cut out a small straw, make a transverse slits apart about 2.5cm from one edge of the straw. Do not cut the straw thoroughly. Cut about 70% of straw’s diameter. Then make a longitudinal slit on both arms of the straw.  The depth of longitudinal slit on joints’ arms depends on the hardness of the straw.  Adjust the depth flexibly to the quality of your straw.

 

 

    In order to make a regular octahedron, prepare 12 same length long straws, then push each joint arm into long straw and connect 8 triangles. It becomes a regular octahedron.

    Pictures below show alternative method for how to connect four short straws.

 

1

2

3

4

 

How to make a 3 arm joint

    When you make a tetrahedron, a hexahedron (cube) and a dodecahedron model, use 3 arm joints shown below.  Pictures below show how to connect four short straws.

 

1. Insert the 1st short straw’s short arm into the 2nd straw’s long arm.

 

2. Insert the 2nd short straw’s short arm into the 3rd straw’s long arm only 5mm deep.

3. Bend the 3rd straw like this picture and insert the 3rd straw’s short arm into 1st straw’s long arm.

4. Connect 3 straws firmly

 

 

Other samples of Math model

Regular polyhedron

Regular octahedron

Regular dodecahedron

Regular icosahedron

Apex joint

close-up

 

    You can apply this technique to make various different mathematical shapes and models. Check the following pictures.

    Three dimensional-shapes composed of triangular shape are strong enough to keep the shape while squares and pentagons are not strong enough.  In order to make a strong straw model, add some triangular structure in the model like reinforced cube model below.

 

Approximate model of circle

Reinforced cube model

Body frame of vehicle model

Anemometer model

Tower

 

“Straw polyhedron” copyright JICA Senior Volunteer Hideo Nakano (Dec 2005, revised September 2007)

 

 

inserted by FC2 system