Handout 02 Basic straw models. Straw polyhedrons The cube The pyramids

Transcription

1 Handout 02 Basic straw models Straw polyhedrons The cube The pyramids

2 STRAW POLYHEDRON Materials and tools 3 to 6mm diameter straws A ruler 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 Surface s (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) * v + f e = 2 1

3 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

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) 3

5 Straw 4 arm joint template Jan 2011 Nakano (JICA senior volunteer) 4

6 Straw 3 arm and 5 arm joints template Mar 2011 Nakano (JICA senior volunteer) When you make a 3 arm joint, please cut each short arm from end to end. 5

7 STRAW MODEL THE CUBE 1. Parts Cut out the following pieces of straws from 5mm diameter plastic straws. Red lines are representing slits. 1) Three straws to make a reinforcing tetrahedron 2) Six 140mm slit straws to connect reinforcing tetrahedron and edges. 3) Three 130mm edge straws which will be connected to 2) slit straws 4) Nine 170mm edge straws 5) Make 21 pieces of 40mm straws. Then make a transversal slit on the straw like the drawing below. Make a longitudinal slit on the short arm and 23mm slit on the long arm. 6

8 2. How to make reinforcing tetrahedron Connect parts like the drawings below. Insert slit parts into openings of normal straws (A to C). Insert 140mm slit straws into 40mm edges of tetrahedron. Then another three 140mm slit straws are to be inserted into already inserted straws (D and E). 3. Make 7 joints Combine 3 pieces of 45mm straws to make a joint as shown below. Insert the first straws short arm into the second straws long arm (A) Insert the second straw s short arm into the third straw s long arm. Then insert the third straw s short arm into the first straw s long arm (B and C). Squeeze each short arm into its counterpart (D). Adjust the angles of each arm to make a finished joint (E). 4. Final assembly 1) Cover 140mm slit straws with 130mm edge straws. 2) Insert an arm of a joint into open end of each 130mm edge straw. 3) Insert free arms of fixed joints into 170mm edge straws. 4) Keep connecting other joints and 170mm edges to make a cube. 7

9 STRAW MODEL THE SIX-SIDED PYRAMIDS 1. Parts Cut out the following pieces of straws from 5mm diameter plastic straws. Red lines are representing slits. These are parts to make a six-sided pyramid. If you want to make different sided pyramid change the number of edges, oblique lines and joints. 2. How to connect the parts 1) Base 2) Oblique lines to the base 3) Vertex joints 4) Finished pyramid 8